case study analysis journal

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• Published: 27 June 2011

The case study approach

• Sarah Crowe 1 ,
• Kathrin Cresswell 2 ,
• Ann Robertson 2 ,
• Guro Huby 3 ,
• Anthony Avery 1 &
• Aziz Sheikh 2  

BMC Medical Research Methodology volume  11 , Article number:  100 ( 2011 ) Cite this article

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The case study approach allows in-depth, multi-faceted explorations of complex issues in their real-life settings. The value of the case study approach is well recognised in the fields of business, law and policy, but somewhat less so in health services research. Based on our experiences of conducting several health-related case studies, we reflect on the different types of case study design, the specific research questions this approach can help answer, the data sources that tend to be used, and the particular advantages and disadvantages of employing this methodological approach. The paper concludes with key pointers to aid those designing and appraising proposals for conducting case study research, and a checklist to help readers assess the quality of case study reports.

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Introduction

The case study approach is particularly useful to employ when there is a need to obtain an in-depth appreciation of an issue, event or phenomenon of interest, in its natural real-life context. Our aim in writing this piece is to provide insights into when to consider employing this approach and an overview of key methodological considerations in relation to the design, planning, analysis, interpretation and reporting of case studies.

The illustrative 'grand round', 'case report' and 'case series' have a long tradition in clinical practice and research. Presenting detailed critiques, typically of one or more patients, aims to provide insights into aspects of the clinical case and, in doing so, illustrate broader lessons that may be learnt. In research, the conceptually-related case study approach can be used, for example, to describe in detail a patient's episode of care, explore professional attitudes to and experiences of a new policy initiative or service development or more generally to 'investigate contemporary phenomena within its real-life context' [ 1 ]. Based on our experiences of conducting a range of case studies, we reflect on when to consider using this approach, discuss the key steps involved and illustrate, with examples, some of the practical challenges of attaining an in-depth understanding of a 'case' as an integrated whole. In keeping with previously published work, we acknowledge the importance of theory to underpin the design, selection, conduct and interpretation of case studies[ 2 ]. In so doing, we make passing reference to the different epistemological approaches used in case study research by key theoreticians and methodologists in this field of enquiry.

This paper is structured around the following main questions: What is a case study? What are case studies used for? How are case studies conducted? What are the potential pitfalls and how can these be avoided? We draw in particular on four of our own recently published examples of case studies (see Tables 1 , 2 , 3 and 4 ) and those of others to illustrate our discussion[ 3 – 7 ].

What is a case study?

A case study is a research approach that is used to generate an in-depth, multi-faceted understanding of a complex issue in its real-life context. It is an established research design that is used extensively in a wide variety of disciplines, particularly in the social sciences. A case study can be defined in a variety of ways (Table 5 ), the central tenet being the need to explore an event or phenomenon in depth and in its natural context. It is for this reason sometimes referred to as a "naturalistic" design; this is in contrast to an "experimental" design (such as a randomised controlled trial) in which the investigator seeks to exert control over and manipulate the variable(s) of interest.

Stake's work has been particularly influential in defining the case study approach to scientific enquiry. He has helpfully characterised three main types of case study: intrinsic , instrumental and collective [ 8 ]. An intrinsic case study is typically undertaken to learn about a unique phenomenon. The researcher should define the uniqueness of the phenomenon, which distinguishes it from all others. In contrast, the instrumental case study uses a particular case (some of which may be better than others) to gain a broader appreciation of an issue or phenomenon. The collective case study involves studying multiple cases simultaneously or sequentially in an attempt to generate a still broader appreciation of a particular issue.

These are however not necessarily mutually exclusive categories. In the first of our examples (Table 1 ), we undertook an intrinsic case study to investigate the issue of recruitment of minority ethnic people into the specific context of asthma research studies, but it developed into a instrumental case study through seeking to understand the issue of recruitment of these marginalised populations more generally, generating a number of the findings that are potentially transferable to other disease contexts[ 3 ]. In contrast, the other three examples (see Tables 2 , 3 and 4 ) employed collective case study designs to study the introduction of workforce reconfiguration in primary care, the implementation of electronic health records into hospitals, and to understand the ways in which healthcare students learn about patient safety considerations[ 4 – 6 ]. Although our study focusing on the introduction of General Practitioners with Specialist Interests (Table 2 ) was explicitly collective in design (four contrasting primary care organisations were studied), is was also instrumental in that this particular professional group was studied as an exemplar of the more general phenomenon of workforce redesign[ 4 ].

What are case studies used for?

According to Yin, case studies can be used to explain, describe or explore events or phenomena in the everyday contexts in which they occur[ 1 ]. These can, for example, help to understand and explain causal links and pathways resulting from a new policy initiative or service development (see Tables 2 and 3 , for example)[ 1 ]. In contrast to experimental designs, which seek to test a specific hypothesis through deliberately manipulating the environment (like, for example, in a randomised controlled trial giving a new drug to randomly selected individuals and then comparing outcomes with controls),[ 9 ] the case study approach lends itself well to capturing information on more explanatory ' how ', 'what' and ' why ' questions, such as ' how is the intervention being implemented and received on the ground?'. The case study approach can offer additional insights into what gaps exist in its delivery or why one implementation strategy might be chosen over another. This in turn can help develop or refine theory, as shown in our study of the teaching of patient safety in undergraduate curricula (Table 4 )[ 6 , 10 ]. Key questions to consider when selecting the most appropriate study design are whether it is desirable or indeed possible to undertake a formal experimental investigation in which individuals and/or organisations are allocated to an intervention or control arm? Or whether the wish is to obtain a more naturalistic understanding of an issue? The former is ideally studied using a controlled experimental design, whereas the latter is more appropriately studied using a case study design.

Case studies may be approached in different ways depending on the epistemological standpoint of the researcher, that is, whether they take a critical (questioning one's own and others' assumptions), interpretivist (trying to understand individual and shared social meanings) or positivist approach (orientating towards the criteria of natural sciences, such as focusing on generalisability considerations) (Table 6 ). Whilst such a schema can be conceptually helpful, it may be appropriate to draw on more than one approach in any case study, particularly in the context of conducting health services research. Doolin has, for example, noted that in the context of undertaking interpretative case studies, researchers can usefully draw on a critical, reflective perspective which seeks to take into account the wider social and political environment that has shaped the case[ 11 ].

How are case studies conducted?

Here, we focus on the main stages of research activity when planning and undertaking a case study; the crucial stages are: defining the case; selecting the case(s); collecting and analysing the data; interpreting data; and reporting the findings.

Defining the case

Carefully formulated research question(s), informed by the existing literature and a prior appreciation of the theoretical issues and setting(s), are all important in appropriately and succinctly defining the case[ 8 , 12 ]. Crucially, each case should have a pre-defined boundary which clarifies the nature and time period covered by the case study (i.e. its scope, beginning and end), the relevant social group, organisation or geographical area of interest to the investigator, the types of evidence to be collected, and the priorities for data collection and analysis (see Table 7 )[ 1 ]. A theory driven approach to defining the case may help generate knowledge that is potentially transferable to a range of clinical contexts and behaviours; using theory is also likely to result in a more informed appreciation of, for example, how and why interventions have succeeded or failed[ 13 ].

For example, in our evaluation of the introduction of electronic health records in English hospitals (Table 3 ), we defined our cases as the NHS Trusts that were receiving the new technology[ 5 ]. Our focus was on how the technology was being implemented. However, if the primary research interest had been on the social and organisational dimensions of implementation, we might have defined our case differently as a grouping of healthcare professionals (e.g. doctors and/or nurses). The precise beginning and end of the case may however prove difficult to define. Pursuing this same example, when does the process of implementation and adoption of an electronic health record system really begin or end? Such judgements will inevitably be influenced by a range of factors, including the research question, theory of interest, the scope and richness of the gathered data and the resources available to the research team.

Selecting the case(s)

The decision on how to select the case(s) to study is a very important one that merits some reflection. In an intrinsic case study, the case is selected on its own merits[ 8 ]. The case is selected not because it is representative of other cases, but because of its uniqueness, which is of genuine interest to the researchers. This was, for example, the case in our study of the recruitment of minority ethnic participants into asthma research (Table 1 ) as our earlier work had demonstrated the marginalisation of minority ethnic people with asthma, despite evidence of disproportionate asthma morbidity[ 14 , 15 ]. In another example of an intrinsic case study, Hellstrom et al.[ 16 ] studied an elderly married couple living with dementia to explore how dementia had impacted on their understanding of home, their everyday life and their relationships.

For an instrumental case study, selecting a "typical" case can work well[ 8 ]. In contrast to the intrinsic case study, the particular case which is chosen is of less importance than selecting a case that allows the researcher to investigate an issue or phenomenon. For example, in order to gain an understanding of doctors' responses to health policy initiatives, Som undertook an instrumental case study interviewing clinicians who had a range of responsibilities for clinical governance in one NHS acute hospital trust[ 17 ]. Sampling a "deviant" or "atypical" case may however prove even more informative, potentially enabling the researcher to identify causal processes, generate hypotheses and develop theory.

In collective or multiple case studies, a number of cases are carefully selected. This offers the advantage of allowing comparisons to be made across several cases and/or replication. Choosing a "typical" case may enable the findings to be generalised to theory (i.e. analytical generalisation) or to test theory by replicating the findings in a second or even a third case (i.e. replication logic)[ 1 ]. Yin suggests two or three literal replications (i.e. predicting similar results) if the theory is straightforward and five or more if the theory is more subtle. However, critics might argue that selecting 'cases' in this way is insufficiently reflexive and ill-suited to the complexities of contemporary healthcare organisations.

The selected case study site(s) should allow the research team access to the group of individuals, the organisation, the processes or whatever else constitutes the chosen unit of analysis for the study. Access is therefore a central consideration; the researcher needs to come to know the case study site(s) well and to work cooperatively with them. Selected cases need to be not only interesting but also hospitable to the inquiry [ 8 ] if they are to be informative and answer the research question(s). Case study sites may also be pre-selected for the researcher, with decisions being influenced by key stakeholders. For example, our selection of case study sites in the evaluation of the implementation and adoption of electronic health record systems (see Table 3 ) was heavily influenced by NHS Connecting for Health, the government agency that was responsible for overseeing the National Programme for Information Technology (NPfIT)[ 5 ]. This prominent stakeholder had already selected the NHS sites (through a competitive bidding process) to be early adopters of the electronic health record systems and had negotiated contracts that detailed the deployment timelines.

It is also important to consider in advance the likely burden and risks associated with participation for those who (or the site(s) which) comprise the case study. Of particular importance is the obligation for the researcher to think through the ethical implications of the study (e.g. the risk of inadvertently breaching anonymity or confidentiality) and to ensure that potential participants/participating sites are provided with sufficient information to make an informed choice about joining the study. The outcome of providing this information might be that the emotive burden associated with participation, or the organisational disruption associated with supporting the fieldwork, is considered so high that the individuals or sites decide against participation.

In our example of evaluating implementations of electronic health record systems, given the restricted number of early adopter sites available to us, we sought purposively to select a diverse range of implementation cases among those that were available[ 5 ]. We chose a mixture of teaching, non-teaching and Foundation Trust hospitals, and examples of each of the three electronic health record systems procured centrally by the NPfIT. At one recruited site, it quickly became apparent that access was problematic because of competing demands on that organisation. Recognising the importance of full access and co-operative working for generating rich data, the research team decided not to pursue work at that site and instead to focus on other recruited sites.

Collecting the data

In order to develop a thorough understanding of the case, the case study approach usually involves the collection of multiple sources of evidence, using a range of quantitative (e.g. questionnaires, audits and analysis of routinely collected healthcare data) and more commonly qualitative techniques (e.g. interviews, focus groups and observations). The use of multiple sources of data (data triangulation) has been advocated as a way of increasing the internal validity of a study (i.e. the extent to which the method is appropriate to answer the research question)[ 8 , 18 – 21 ]. An underlying assumption is that data collected in different ways should lead to similar conclusions, and approaching the same issue from different angles can help develop a holistic picture of the phenomenon (Table 2 )[ 4 ].

Brazier and colleagues used a mixed-methods case study approach to investigate the impact of a cancer care programme[ 22 ]. Here, quantitative measures were collected with questionnaires before, and five months after, the start of the intervention which did not yield any statistically significant results. Qualitative interviews with patients however helped provide an insight into potentially beneficial process-related aspects of the programme, such as greater, perceived patient involvement in care. The authors reported how this case study approach provided a number of contextual factors likely to influence the effectiveness of the intervention and which were not likely to have been obtained from quantitative methods alone.

In collective or multiple case studies, data collection needs to be flexible enough to allow a detailed description of each individual case to be developed (e.g. the nature of different cancer care programmes), before considering the emerging similarities and differences in cross-case comparisons (e.g. to explore why one programme is more effective than another). It is important that data sources from different cases are, where possible, broadly comparable for this purpose even though they may vary in nature and depth.

Analysing, interpreting and reporting case studies

Making sense and offering a coherent interpretation of the typically disparate sources of data (whether qualitative alone or together with quantitative) is far from straightforward. Repeated reviewing and sorting of the voluminous and detail-rich data are integral to the process of analysis. In collective case studies, it is helpful to analyse data relating to the individual component cases first, before making comparisons across cases. Attention needs to be paid to variations within each case and, where relevant, the relationship between different causes, effects and outcomes[ 23 ]. Data will need to be organised and coded to allow the key issues, both derived from the literature and emerging from the dataset, to be easily retrieved at a later stage. An initial coding frame can help capture these issues and can be applied systematically to the whole dataset with the aid of a qualitative data analysis software package.

The Framework approach is a practical approach, comprising of five stages (familiarisation; identifying a thematic framework; indexing; charting; mapping and interpretation) , to managing and analysing large datasets particularly if time is limited, as was the case in our study of recruitment of South Asians into asthma research (Table 1 )[ 3 , 24 ]. Theoretical frameworks may also play an important role in integrating different sources of data and examining emerging themes. For example, we drew on a socio-technical framework to help explain the connections between different elements - technology; people; and the organisational settings within which they worked - in our study of the introduction of electronic health record systems (Table 3 )[ 5 ]. Our study of patient safety in undergraduate curricula drew on an evaluation-based approach to design and analysis, which emphasised the importance of the academic, organisational and practice contexts through which students learn (Table 4 )[ 6 ].

Case study findings can have implications both for theory development and theory testing. They may establish, strengthen or weaken historical explanations of a case and, in certain circumstances, allow theoretical (as opposed to statistical) generalisation beyond the particular cases studied[ 12 ]. These theoretical lenses should not, however, constitute a strait-jacket and the cases should not be "forced to fit" the particular theoretical framework that is being employed.

When reporting findings, it is important to provide the reader with enough contextual information to understand the processes that were followed and how the conclusions were reached. In a collective case study, researchers may choose to present the findings from individual cases separately before amalgamating across cases. Care must be taken to ensure the anonymity of both case sites and individual participants (if agreed in advance) by allocating appropriate codes or withholding descriptors. In the example given in Table 3 , we decided against providing detailed information on the NHS sites and individual participants in order to avoid the risk of inadvertent disclosure of identities[ 5 , 25 ].

What are the potential pitfalls and how can these be avoided?

The case study approach is, as with all research, not without its limitations. When investigating the formal and informal ways undergraduate students learn about patient safety (Table 4 ), for example, we rapidly accumulated a large quantity of data. The volume of data, together with the time restrictions in place, impacted on the depth of analysis that was possible within the available resources. This highlights a more general point of the importance of avoiding the temptation to collect as much data as possible; adequate time also needs to be set aside for data analysis and interpretation of what are often highly complex datasets.

Case study research has sometimes been criticised for lacking scientific rigour and providing little basis for generalisation (i.e. producing findings that may be transferable to other settings)[ 1 ]. There are several ways to address these concerns, including: the use of theoretical sampling (i.e. drawing on a particular conceptual framework); respondent validation (i.e. participants checking emerging findings and the researcher's interpretation, and providing an opinion as to whether they feel these are accurate); and transparency throughout the research process (see Table 8 )[ 8 , 18 – 21 , 23 , 26 ]. Transparency can be achieved by describing in detail the steps involved in case selection, data collection, the reasons for the particular methods chosen, and the researcher's background and level of involvement (i.e. being explicit about how the researcher has influenced data collection and interpretation). Seeking potential, alternative explanations, and being explicit about how interpretations and conclusions were reached, help readers to judge the trustworthiness of the case study report. Stake provides a critique checklist for a case study report (Table 9 )[ 8 ].

Conclusions

The case study approach allows, amongst other things, critical events, interventions, policy developments and programme-based service reforms to be studied in detail in a real-life context. It should therefore be considered when an experimental design is either inappropriate to answer the research questions posed or impossible to undertake. Considering the frequency with which implementations of innovations are now taking place in healthcare settings and how well the case study approach lends itself to in-depth, complex health service research, we believe this approach should be more widely considered by researchers. Though inherently challenging, the research case study can, if carefully conceptualised and thoughtfully undertaken and reported, yield powerful insights into many important aspects of health and healthcare delivery.

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Acknowledgements

We are grateful to the participants and colleagues who contributed to the individual case studies that we have drawn on. This work received no direct funding, but it has been informed by projects funded by Asthma UK, the NHS Service Delivery Organisation, NHS Connecting for Health Evaluation Programme, and Patient Safety Research Portfolio. We would also like to thank the expert reviewers for their insightful and constructive feedback. Our thanks are also due to Dr. Allison Worth who commented on an earlier draft of this manuscript.

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Sarah Crowe & Anthony Avery

Centre for Population Health Sciences, The University of Edinburgh, Edinburgh, UK

Kathrin Cresswell, Ann Robertson & Aziz Sheikh

School of Health in Social Science, The University of Edinburgh, Edinburgh, UK

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AS conceived this article. SC, KC and AR wrote this paper with GH, AA and AS all commenting on various drafts. SC and AS are guarantors.

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Crowe, S., Cresswell, K., Robertson, A. et al. The case study approach. BMC Med Res Methodol 11 , 100 (2011). https://doi.org/10.1186/1471-2288-11-100

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28 Case Selection for Case‐Study Analysis: Qualitative and Quantitative Techniques

John Gerring is Professor of Political Science, Boston University.

• Published: 02 September 2009
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This article presents some guidance by cataloging nine different techniques for case selection: typical, diverse, extreme, deviant, influential, crucial, pathway, most similar, and most different. It also indicates that if the researcher is starting from a quantitative database, then methods for finding influential outliers can be used. In particular, the article clarifies the general principles that might guide the process of case selection in case-study research. Cases are more or less representative of some broader phenomenon and, on that score, may be considered better or worse subjects for intensive analysis. The article then draws attention to two ambiguities in case-selection strategies in case-study research. The first concerns the admixture of several case-selection strategies. The second concerns the changing status of a case as a study proceeds. Some case studies follow only one strategy of case selection.

Case ‐study analysis focuses on one or several cases that are expected to provide insight into a larger population. This presents the researcher with a formidable problem of case selection: Which cases should she or he choose?

In large‐sample research, the task of case selection is usually handled by some version of randomization. However, in case‐study research the sample is small (by definition) and this makes random sampling problematic, for any given sample may be wildly unrepresentative. Moreover, there is no guarantee that a few cases, chosen randomly, will provide leverage into the research question of interest.

In order to isolate a sample of cases that both reproduces the relevant causal features of a larger universe (representativeness) and provides variation along the dimensions of theoretical interest (causal leverage), case selection for very small samples must employ purposive (nonrandom) selection procedures. Nine such methods are discussed in this chapter, each of which may be identified with a distinct case‐study “type:” typical, diverse, extreme, deviant, influential, crucial, pathway, most‐similar , and most‐different . Table 28.1 summarizes each type, including its general definition, a technique for locating it within a population of potential cases, its uses, and its probable representativeness.

While each of these techniques is normally practiced on one or several cases (the diverse, most‐similar, and most‐different methods require at least two), all may employ additional cases—with the proviso that, at some point, they will no longer offer an opportunity for in‐depth analysis and will thus no longer be “case studies” in the usual sense ( Gerring 2007 , ch. 2 ). It will also be seen that small‐ N case‐selection procedures rest, at least implicitly, upon an analysis of a larger population of potential cases (as does randomization). The case(s) identified for intensive study is chosen from a population and the reasons for this choice hinge upon the way in which it is situated within that population. This is the origin of the terminology—typical, diverse, extreme, et al. It follows that case‐selection procedures in case‐study research may build upon prior cross‐case analysis and that they depend, at the very least, upon certain assumptions about the broader population.

In certain circumstances, the case‐selection procedure may be structured by a quantitative analysis of the larger population. Here, several caveats must be satisfied. First, the inference must pertain to more than a few dozen cases; otherwise, statistical analysis is problematic. Second, relevant data must be available for that population, or a significant sample of that population, on key variables, and the researcher must feel reasonably confident in the accuracy and conceptual validity of these variables. Third, all the standard assumptions of statistical research (e.g. identification, specification, robustness) must be carefully considered, and wherever possible, tested. I shall not dilate further on these familiar issues except to warn the researcher against the unreflective use of statistical techniques. 1 When these requirements are not met, the researcher must employ a qualitative approach to case selection.

The point of this chapter is to elucidate general principles that might guide the process of case selection in case‐study research, building upon earlier work by Harry Eckstein, Arend Lijphart, and others. Sometimes, these principles can be applied in a quantitative framework and sometimes they are limited to a qualitative framework. In either case, the logic of case selection remains quite similar, whether practiced in small‐ N or large‐ N contexts.

Before we begin, a bit of notation is necessary. In this chapter “ N ” refers to cases, not observations. Here, I am concerned primarily with causal inference, rather than inferences that are descriptive or predictive in nature. Thus, all hypotheses involve at least one independent variable ( X ) and one dependent variable ( Y ). For convenience, I shall label the causal factor of special theoretical interest X   1 , and the control variable, or vector of controls (if there are any), X   2 . If the writer is concerned to explain a puzzling outcome, but has no preconceptions about its causes, then the research will be described as Y‐centered . If a researcher is concerned to investigate the effects of a particular cause, with no preconceptions about what these effects might be, the research will be described as X‐centered . If a researcher is concerned to investigate a particular causal relationship, the research will be described as X   1 / Y‐centered , for it connects a particular cause with a particular outcome. 2   X ‐ or Y ‐centered research is exploratory; its purpose is to generate new hypotheses. X   1 / Y‐centered research, by contrast, is confirmatory/disconfirmatory; its purpose is to test an existing hypothesis.

1 Typical Case

In order for a focused case study to provide insight into a broader phenomenon it must be representative of a broader set of cases. It is in this context that one may speak of a typical‐case approach to case selection. The typical case exemplifies what is considered to be a typical set of values, given some general understanding of a phenomenon. By construction, the typical case is also a representative case.

Some typical cases serve an exploratory role. Here, the author chooses a case based upon a set of descriptive characteristics and then probes for causal relationships. Robert and Helen Lynd (1929/1956) selected a single city “to be as representative as possible of contemporary American life.” Specifically, they were looking for a city with

1) a temperate climate; 2) a sufficiently rapid rate of growth to ensure the presence of a plentiful assortment of the growing pains accompanying contemporary social change; 3) an industrial culture with modern, high‐speed machine production; 4) the absence of dominance of the city's industry by a single plant (i.e., not a one‐industry town); 5) a substantial local artistic life to balance its industrial activity …; and 6) the absence of any outstanding peculiarities or acute local problems which would mark the city off from the midchannel sort of American community. ( Lynd and Lynd 1929/1956 , quoted in Yin 2004 , 29–30)

After examining a number of options the Lynds decided that Muncie, Indiana, was more representative than, or at least as representative as, other midsized cities in America, thus qualifying as a typical case.

This is an inductive approach to case selection. Note that typicality may be understood according to the mean, median, or mode on a particular dimension; there may be multiple dimensions (as in the foregoing example); and each may be differently weighted (some dimensions may be more important than others). Where the selection criteria are multidimensional and a large sample of potential cases is in play, some form of factor analysis may be useful in identifying the most‐typical case(s).

However, the more common employment of the typical‐case method involves a causal model of some phenomenon of theoretical interest. Here, the researcher has identified a particular outcome ( Y ), and perhaps a specific X   1 / Y hypothesis, which she wishes to investigate. In order to do so, she looks for a typical example of that causal relationship. Intuitively, one imagines that a case selected according to the mean values of all parameters must be a typical case relative to some causal relationship. However, this is by no means assured.

Suppose that the Lynds were primarily interested in explaining feelings of trust/distrust among members of different social classes (one of the implicit research goals of the Middletown study). This outcome is likely to be affected by many factors, only some of which are included in their six selection criteria. So choosing cases with respect to a causal hypothesis involves, first of all, identifying the relevant parameters. It involves, secondly, the selection of a case that has a “typical” value relative to the overall causal model; it is well explained. Cases with untypical scores on a particular dimension (e.g. very high or very low) may still be typical examples of a causal relationship. Indeed, they may be more typical than cases whose values lie close to the mean. Thus, a descriptive understanding of typicality is quite different from a causal understanding of typicality. Since it is the latter version that is more common, I shall adopt this understanding of typicality in the remainder of the discussion.

From a qualitative perspective, causal typicality involves the selection of a case that conforms to expectations about some general causal relationship. It performs as expected. In a quantitative setting, this notion is measured by the size of a case's residual in a large‐ N cross‐case model. Typical cases lie on or near the regression line; their residuals are small. Insofar as the model is correctly specified, the size of a case's residual (i.e. the number of standard deviations that separate the actual value from the fitted value) provides a helpful clue to how representative that case is likely to be. “Outliers” are unlikely to be representative of the target population.

Of course, just because a case has a low residual does not necessarily mean that it is a representative case (with respect to the causal relationship of interest). Indeed, the issue of case representativeness is an issue that can never be definitively settled. When one refers to a “typical case” one is saying, in effect, that the probability of a case's representativeness is high, relative to other cases. This test of typicality is misleading if the statistical model is mis‐specified. And it provides little insurance against errors that are purely stochastic. A case may lie directly on the regression line but still be, in some important respect, atypical. For example, it might have an odd combination of values; the interaction of variables might be different from other cases; or additional causal mechanisms might be at work. For this reason, it is important to supplement a statistical analysis of cases with evidence drawn from the case in question (the case study itself) and with our deductive knowledge of the world. One should never judge a case solely by its residual. Yet, all other things being equal, a case with a low residual is less likely to be unusual than a case with a high residual, and to this extent the method of case selection outlined here may be a helpful guide to case‐study researchers faced with a large number of potential cases.

By way of conclusion, it should be noted that because the typical case embodies a typical value on some set of causally relevant dimensions, the variance of interest to the researcher must lie within that case. Specifically, the typical case of some phenomenon may be helpful in exploring causal mechanisms and in solving identification problems (e.g. endogeneity between X   1 and Y , an omitted variable that may account for X   1   and Y , or some other spurious causal association). Depending upon the results of the case study, the author may confirm an existing hypothesis, disconfirm that hypothesis, or reframe it in a way that is consistent with the findings of the case study. These are the uses of the typical‐case study.

2 Diverse Cases

A second case‐selection strategy has as its primary objective the achievement of maximum variance along relevant dimensions. I refer to this as a diverse‐case method. For obvious reasons, this method requires the selection of a set of cases—at minimum, two—which are intended to represent the full range of values characterizing X   1 , Y , or some particular X   1 / Y relationship. 3

Where the individual variable of interest is categorical (on/off, red/black/blue, Jewish/Protestant/Catholic), the identification of diversity is readily apparent. The investigator simply chooses one case from each category. For a continuous variable, the choices are not so obvious. However, the researcher usually chooses both extreme values (high and low), and perhaps the mean or median as well. The researcher may also look for break‐points in the distribution that seem to correspond to categorical differences among cases. Or she may follow a theoretical hunch about which threshold values count, i.e. which are likely to produce different values on Y .

Another sort of diverse case takes account of the values of multiple variables (i.e. a vector), rather than a single variable. If these variables are categorical, the identification of causal types rests upon the intersection of each category. Two dichotomous variables produce a matrix with four cells. Three trichotomous variables produce a matrix of eight cells. And so forth. If all variables are deemed relevant to the analysis, the selection of diverse cases mandates the selection of one case drawn from within each cell. Let us say that an outcome is thought to be affected by sex, race (black/white), and marital status. Here, a diverse‐case strategy of case selection would identify one case within each of these intersecting cells—a total of eight cases. Things become slightly more complicated when one or more of the factors is continuous, rather than categorical. Here, the diversity of case values do not fall neatly into cells. Rather, these cells must be created by fiat—e.g. high, medium, low.

It will be seen that where multiple variables are under consideration, the logic of diverse‐case analysis rests upon the logic of typological theorizing—where different combinations of variables are assumed to have effects on an outcome that vary across types ( Elman 2005 ; George and Bennett 2005 , 235; Lazarsfeld and Barton 1951 ). George and Smoke, for example, wish to explore different types of deterrence failure—by “fait accompli,” by “limited probe,” and by “controlled pressure.” Consequently, they wish to find cases that exemplify each type of causal mechanism. 4

Diversity may thus refer to a range of variation on X or Y , or to a particular combination of causal factors (with or without a consideration of the outcome). In each instance, the goal of case selection is to capture the full range of variation along the dimension(s) of interest.

Since diversity can mean many things, its employment in a large‐ N setting is necessarily dependent upon how this key term is defined. If it is understood to pertain only to a single variable ( X   1 or Y ), then the task is fairly simple. A categorical variable mandates the choice of at least one case from each category—two if dichotomous, three if trichotomous, and so forth. A continuous variable suggests the choice of at least one “high” and “low” value, and perhaps one drawn from the mean or median. But other choices might also be justified, according to one's hunch about the underlying causal relationship or according to natural thresholds found in the data, which may be grouped into discrete categories. Single‐variable traits are usually easy to discover in a large‐ N setting through descriptive statistics or through visual inspection of the data.

Where diversity refers to particular combinations of variables, the relevant cross‐ case technique is some version of stratified random sampling (in a probabilistic setting) or Qualitative Comparative Analysis (in a deterministic setting) ( Ragin 2000 ). If the researcher suspects that a causal relationship is affected not only by combinations of factors but also by their sequencing , then the technique of analysis must incorporate temporal elements ( Abbott 2001 ; Abbott and Forrest 1986 ; Abbott and Tsay 2000 ). Thus, the method of identifying causal types rests upon whatever method of identifying causal relationships is employed in the large‐ N sample.

Note that the identification of distinct case types is intended to identify groups of cases that are internally homogeneous (in all respects that might affect the causal relationship of interest). Thus, the choice of cases within each group should not be problematic, and may be accomplished through random sampling or purposive case selection. However, if there is suspected diversity within each category, then measures should be taken to assure that the chosen cases are typical of each category. A case study should not focus on an atypical member of a subgroup.

Indeed, considerations of diversity and typicality often go together. Thus, in a study of globalization and social welfare systems, Duane Swank (2002) first identifies three distinctive groups of welfare states: “universalistic” (social democratic), “corporatist conservative,” and “liberal.” Next, he looks within each group to find the most‐typical cases. He decides that the Nordic countries are more typical of the universalistic model than the Netherlands since the latter has “some characteristics of the occupationally based program structure and a political context of Christian Democratic‐led governments typical of the corporatist conservative nations” ( Swank 2002 , 11; see also Esping‐Andersen 1990 ). Thus, the Nordic countries are chosen as representative cases within the universalistic case type, and are accompanied in the case‐study portion of his analysis by other cases chosen to represent the other welfare state types (corporatist conservative and liberal).

Evidently, when a sample encompasses a full range of variation on relevant parameters one is likely to enhance the representativeness of that sample (relative to some population). This is a distinct advantage. Of course, the inclusion of a full range of variation may distort the actual distribution of cases across this spectrum. If there are more “high” cases than “low” cases in a population and the researcher chooses only one high case and one low case, the resulting sample of two is not perfectly representative. Even so, the diverse‐case method probably has stronger claims to representativeness than any other small‐ N sample (including the standalone typical case). The selection of diverse cases has the additional advantage of introducing variation on the key variables of interest. A set of diverse cases is, by definition, a set of cases that encompasses a range of high and low values on relevant dimensions. There is, therefore, much to recommend this method of case selection. I suspect that these advantages are commonly understood and are applied on an intuitive level by case‐study researchers. However, the lack of a recognizable name—and an explicit methodological defense—has made it difficult for case‐study researchers to utilize this method of case selection, and to do so in an explicit and self‐conscious fashion. Neologism has its uses.

3 Extreme Case

The extreme‐case method selects a case because of its extreme value on an independent ( X   1 ) or dependent ( Y ) variable of interest. Thus, studies of domestic violence may choose to focus on extreme instances of abuse ( Browne 1987 ). Studies of altruism may focus on those rare individuals who risked their lives to help others (e.g. Holocaust resisters) ( Monroe 1996 ). Studies of ethnic politics may focus on the most heterogeneous societies (e.g. Papua New Guinea) in order to better understand the role of ethnicity in a democratic setting ( Reilly 2000–1 ). Studies of industrial policy often focus on the most successful countries (i.e. the NICS) ( Deyo 1987 ). And so forth. 5

Often an extreme case corresponds to a case that is considered to be prototypical or paradigmatic of some phenomena of interest. This is because concepts are often defined by their extremes, i.e. their ideal types. Italian Fascism defines the concept of Fascism, in part, because it offered the most extreme example of that phenomenon. However, the methodological value of this case, and others like it, derives from its extremity (along some dimension of interest), not its theoretical status or its status in the literature on a subject.

The notion of “extreme” may now be defined more precisely. An extreme value is an observation that lies far away from the mean of a given distribution. This may be measured (if there are sufficient observations) by a case's “Z score”—the number of standard deviations between a case and the mean value for that sample. Extreme cases have high Z scores, and for this reason may serve as useful subjects for intensive analysis.

For a continuous variable, the distance from the mean may be in either direction (positive or negative). For a dichotomous variable (present/absent), extremeness may be interpreted as unusual . If most cases are positive along a given dimension, then a negative case constitutes an extreme case. If most cases are negative, then a positive case constitutes an extreme case. It should be clear that researchers are not simply concerned with cases where something “happened,” but also with cases where something did not. It is the rareness of the value that makes a case valuable, in this context, not its positive or negative value. 6 Thus, if one is studying state capacity, a case of state failure is probably more informative than a case of state endurance simply because the former is more unusual. Similarly, if one is interested in incest taboos a culture where the incest taboo is absent or weak is probably more useful than a culture where it is present or strong. Fascism is more important than nonfascism. And so forth. There is a good reason, therefore, why case studies of revolution tend to focus on “revolutionary” cases. Theda Skocpol (1979) had much more to learn from France than from Austro‐Hungary since France was more unusual than Austro‐Hungary within the population of nation states that Skocpol was concerned to explain. The reason is quite simple: There are fewer revolutionary cases than nonrevolutionary cases; thus, the variation that we explore as a clue to causal relationships is encapsulated in these cases, against a background of nonrevolutionary cases.

Note that the extreme‐case method of case selection appears to violate the social science folk wisdom warning us not to “select on the dependent variable.” 7 Selecting cases on the dependent variable is indeed problematic if a number of cases are chosen, all of which lie on one end of a variable's spectrum (they are all positive or negative), and if the researcher then subjects this sample to cross‐case analysis as if it were representative of a population. 8 Results for this sort of analysis would almost assuredly be biased. Moreover, there will be little variation to explain since the values of each case are explicitly constrained.

However, this is not the proper employment of the extreme‐case method. (It is more appropriately labeled an extreme‐ sample method.) The extreme‐case method actually refers back to a larger sample of cases that lie in the background of the analysis and provide a full range of variation as well as a more representative picture of the population. It is a self‐conscious attempt to maximize variance on the dimension of interest, not to minimize it. If this population of cases is well understood— either through the author's own cross‐case analysis, through the work of others, or through common sense—then a researcher may justify the selection of a single case exemplifying an extreme value for within‐case analysis. If not, the researcher may be well advised to follow a diverse‐case method, as discussed above.

By way of conclusion, let us return to the problem of representativeness. It will be seen that an extreme case may be typical or deviant. There is simply no way to tell because the researcher has not yet specified an X   1 / Y causal proposition. Once such a causal proposition has been specified one may then ask whether the case in question is similar to some population of cases in all respects that might affect the X   1 / Y relationship of interest (i.e. unit homogeneous). It is at this point that it becomes possible to say, within the context of a cross‐case statistical model, whether a case lies near to, or far from, the regression line. However, this sort of analysis means that the researcher is no longer pursuing an extreme‐case method. The extreme‐case method is purely exploratory—a way of probing possible causes of Y , or possible effects of X , in an open‐ended fashion. If the researcher has some notion of what additional factors might affect the outcome of interest, or of what relationship the causal factor of interest might have with Y , then she ought to pursue one of the other methods explored in this chapter. This also implies that an extreme‐case method may transform into a different kind of approach as a study evolves; that is, as a more specific hypothesis comes to light. Useful extreme cases at the outset of a study may prove less useful at a later stage of analysis.

4 Deviant Case

The deviant‐case method selects that case(s) which, by reference to some general understanding of a topic (either a specific theory or common sense), demonstrates a surprising value. It is thus the contrary of the typical case. Barbara Geddes (2003) notes the importance of deviant cases in medical science, where researchers are habitually focused on that which is “pathological” (according to standard theory and practice). The New England Journal of Medicine , one of the premier journals of the field, carries a regular feature entitled Case Records of the Massachusetts General Hospital. These articles bear titles like the following: “An 80‐Year‐Old Woman with Sudden Unilateral Blindness” or “A 76‐Year‐Old Man with Fever, Dyspnea, Pulmonary Infiltrates, Pleural Effusions, and Confusion.” 9 Another interesting example drawn from the field of medicine concerns the extensive study now devoted to a small number of persons who seem resistant to the AIDS virus ( Buchbinder and Vittinghoff 1999 ; Haynes, Pantaleo, and Fauci 1996 ). Why are they resistant? What is different about these people? What can we learn about AIDS in other patients by observing people who have built‐in resistance to this disease?

Likewise, in psychology and sociology case studies may be comprised of deviant (in the social sense) persons or groups. In economics, case studies may consist of countries or businesses that overperform (e.g. Botswana; Microsoft) or underperform (e.g. Britain through most of the twentieth century; Sears in recent decades) relative to some set of expectations. In political science, case studies may focus on countries where the welfare state is more developed (e.g. Sweden) or less developed (e.g. the United States) than one would expect, given a set of general expectations about welfare state development. The deviant case is closely linked to the investigation of theoretical anomalies. Indeed, to say deviant is to imply “anomalous.” 10

Note that while extreme cases are judged relative to the mean of a single distribution (the distribution of values along a single variable), deviant cases are judged relative to some general model of causal relations. The deviant‐case method selects cases which, by reference to some (presumably) general relationship, demonstrate a surprising value. They are “deviant” in that they are poorly explained by the multivariate model. The important point is that deviant‐ness can only be assessed relative to the general (quantitative or qualitative) model. This means that the relative deviant‐ness of a case is likely to change whenever the general model is altered. For example, the United States is a deviant welfare state when this outcome is gauged relative to societal wealth. But it is less deviant—and perhaps not deviant at all—when certain additional (political and societal) factors are included in the model, as discussed in the epilogue. Deviance is model dependent. Thus, when discussing the concept of the deviant case it is helpful to ask the following question: Relative to what general model (or set of background factors) is Case A deviant?

Conceptually, we have said that the deviant case is the logical contrary of the typical case. This translates into a directly contrasting statistical measurement. While the typical case is one with a low residual (in some general model of causal relations), a deviant case is one with a high residual. This means, following our previous discussion, that the deviant case is likely to be an un representative case, and in this respect appears to violate the supposition that case‐study samples should seek to reproduce features of a larger population.

However, it must be borne in mind that the primary purpose of a deviant‐case analysis is to probe for new—but as yet unspecified—explanations. (If the purpose is to disprove an extant theory I shall refer to the study as crucial‐case, as discussed below.) The researcher hopes that causal processes identified within the deviant case will illustrate some causal factor that is applicable to other (more or less deviant) cases. This means that a deviant‐case study usually culminates in a general proposition, one that may be applied to other cases in the population. Once this general proposition has been introduced into the overall model, the expectation is that the chosen case will no longer be an outlier. Indeed, the hope is that it will now be typical , as judged by its small residual in the adjusted model. (The exception would be a circumstance in which a case's outcome is deemed to be “accidental,” and therefore inexplicable by any general model.)

This feature of the deviant‐case study should help to resolve questions about its representativeness. Even if it is not possible to measure the new causal factor (and thus to introduce it into a large‐ N cross‐case model), it may still be plausible to assert (based on general knowledge of the phenomenon) that the chosen case is representative of a broader population.

5 Influential Case

Sometimes, the choice of a case is motivated solely by the need to verify the assumptions behind a general model of causal relations. Here, the analyst attempts to provide a rationale for disregarding a problematic case or a set of problematic cases. That is to say, she attempts to show why apparent deviations from the norm are not really deviant, or do not challenge the core of the theory, once the circumstances of the special case or cases are fully understood. A cross‐case analysis may, after all, be marred by several classes of problems including measurement error, specification error, errors in establishing proper boundaries for the inference (the scope of the argument), and stochastic error (fluctuations in the phenomenon under study that are treated as random, given available theoretical resources). If poorly fitting cases can be explained away by reference to these kinds of problems, then the theory of interest is that much stronger. This sort of deviant‐case analysis answers the question, “What about Case A (or cases of type A)? How does that, seemingly disconfirming, case fit the model?”

Because its underlying purpose is different from the usual deviant‐case study, I offer a new term for this method. The influential case is a case that casts doubt upon a theory, and for that reason warrants close inspection. This investigation may reveal, after all, that the theory is validated—perhaps in some slightly altered form. In this guise, the influential case is the “case that proves the rule.” In other instances, the influential‐case analysis may contribute to disconfirming, or reconceptualizing, a theory. The key point is that the value of the case is judged relative to some extant cross‐case model.

A simple version of influential‐case analysis involves the confirmation of a key case's score on some critical dimension. This is essentially a question of measurement. Sometimes cases are poorly explained simply because they are poorly understood. A close examination of a particular context may reveal that an apparently falsifying case has been miscoded. If so, the initial challenge presented by that case to some general theory has been obviated.

However, the more usual employment of the influential‐case method culminates in a substantive reinterpretation of the case—perhaps even of the general model. It is not just a question of measurement. Consider Thomas Ertman's (1997) study of state building in Western Europe, as summarized by Gerardo Munck. This study argues

that the interaction of a) the type of local government during the first period of statebuilding, with b) the timing of increases in geopolitical competition, strongly influences the kind of regime and state that emerge. [Ertman] tests this hypothesis against the historical experience of Europe and finds that most countries fit his predictions. Denmark, however, is a major exception. In Denmark, sustained geopolitical competition began relatively late and local government at the beginning of the statebuilding period was generally participatory, which should have led the country to develop “patrimonial constitutionalism.” But in fact, it developed “bureaucratic absolutism.” Ertman carefully explores the process through which Denmark came to have a bureaucratic absolutist state and finds that Denmark had the early marks of a patrimonial constitutionalist state. However, the country was pushed off this developmental path by the influence of German knights, who entered Denmark and brought with them German institutions of local government. Ertman then traces the causal process through which these imported institutions pushed Denmark to develop bureaucratic absolutism, concluding that this development was caused by a factor well outside his explanatory framework. ( Munck 2004 , 118)

Ertman's overall framework is confirmed insofar as he has been able to show, by an in‐depth discussion of Denmark, that the causal processes stipulated by the general theory hold even in this apparently disconfirming case. Denmark is still deviant, but it is so because of “contingent historical circumstances” that are exogenous to the theory ( Ertman 1997 , 316).

Evidently, the influential‐case analysis is similar to the deviant‐case analysis. Both focus on outliers. However, as we shall see, they focus on different kinds of outliers. Moreover, the animating goals of these two research designs are quite different. The influential‐case study begins with the aim of confirming a general model, while the deviant‐case study has the aim of generating a new hypothesis that modifies an existing general model. The confusion stems from the fact that the same case study may fulfill both objectives—qualifying a general model and, at the same time, confirming its core hypothesis.

Thus, in their study of Roberto Michels's “iron law of oligarchy,” Lipset, Trow, and Coleman (1956) choose to focus on an organization—the International Typographical Union—that appears to violate the central presupposition. The ITU, as noted by one of the authors, has “a long‐term two‐party system with free elections and frequent turnover in office” and is thus anything but oligarchic ( Lipset 1959 , 70). As such, it calls into question Michels's grand generalization about organizational behavior. The authors explain this curious result by the extraordinarily high level of education among the members of this union. Michels's law is shown to be true for most organizations, but not all. It is true, with qualifications. Note that the respecification of the original model (in effect, Lipset, Trow, and Coleman introduce a new control variable or boundary condition) involves the exploration of a new hypothesis. In this instance, therefore, the use of an influential case to confirm an existing theory is quite similar to the use of a deviant case to explore a new theory.

In a quantitative idiom, influential cases are those that, if counterfactually assigned a different value on the dependent variable, would most substantially change the resulting estimates. They may or may not be outliers (high‐residual cases). Two quantitative measures of influence are commonly applied in regression diagnostics ( Belsey, Kuh, and Welsch 2004 ). The first, often referred to as the leverage of a case, derives from what is called the hat matrix . Based solely on each case's scores on the independent variables, the hat matrix tells us how much a change in (or a measurement error on) the dependent variable for that case would affect the overall regression line. The second is Cook's distance , a measure of the extent to which the estimates of all the parameters would change if a given case were omitted from the analysis. Cases with a large leverage or Cook's distance contribute quite a lot to the inferences drawn from a cross‐case analysis. In this sense, such cases are vital for maintaining analytic conclusions. Discovering a significant measurement error on the dependent variable or an important omitted variable for such a case may dramatically revise estimates of the overall relationships. Hence, it may be quite sensible to select influential cases for in‐depth study.

Note that the use of an influential‐case strategy of case selection is limited to instances in which a researcher has reason to be concerned that her results are being driven by one or a few cases. This is most likely to be true in small to moderate‐sized samples. Where N is very large—greater than 1,000, let us say—it is extremely unlikely that a small set of cases (much less an individual case) will play an “influential” role. Of course, there may be influential sets of cases, e.g. countries within a particular continent or cultural region, or persons of Irish extraction. Sets of influential observations are often problematic in a time‐series cross‐section data‐set where each unit (e.g. country) contains multiple observations (through time), and hence may have a strong influence on aggregate results. Still, the general rule is: the larger the sample, the less important individual cases are likely to be and, hence, the less likely a researcher is to use an influential‐case approach to case selection.

6 Crucial Case

Of all the extant methods of case selection perhaps the most storied—and certainly the most controversial—is the crucial‐case method, introduced to the social science world several decades ago by Harry Eckstein. In his seminal essay, Eckstein (1975 , 118) describes the crucial case as one “that must closely fit a theory if one is to have confidence in the theory's validity, or, conversely, must not fit equally well any rule contrary to that proposed.” A case is crucial in a somewhat weaker—but much more common—sense when it is most, or least, likely to fulfill a theoretical prediction. A “most‐likely” case is one that, on all dimensions except the dimension of theoretical interest, is predicted to achieve a certain outcome, and yet does not. It is therefore used to disconfirm a theory. A “least‐likely” case is one that, on all dimensions except the dimension of theoretical interest, is predicted not to achieve a certain outcome, and yet does so. It is therefore used to confirm a theory. In all formulations, the crucial‐case offers a most‐difficult test for an argument, and hence provides what is perhaps the strongest sort of evidence possible in a nonexperimental, single‐case setting.

Since the publication of Eckstein's influential essay, the crucial‐case approach has been claimed in a multitude of studies across several social science disciplines and has come to be recognized as a staple of the case‐study method. 11 Yet the idea of any single case playing a crucial (or “critical”) role is not widely accepted among most methodologists (e.g. Sekhon 2004 ). (Even its progenitor seems to have had doubts.)

Let us begin with the confirmatory (a.k.a. least‐likely) crucial case. The implicit logic of this research design may be summarized as follows. Given a set of facts, we are asked to contemplate the probability that a given theory is true. While the facts matter, to be sure, the effectiveness of this sort of research also rests upon the formal properties of the theory in question. Specifically, the degree to which a theory is amenable to confirmation is contingent upon how many predictions can be derived from the theory and on how “risky” each individual prediction is. In Popper's (1963 , 36) words, “Confirmations should count only if they are the result of risky predictions ; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory—and event which would have refuted the theory. Every ‘good’ scientific theory is a prohibition; it forbids certain things to happen. The more a theory forbids, the better it is” (see also Popper 1934/1968 ). A risky prediction is therefore one that is highly precise and determinate, and therefore unlikely to be achieved by the product of other causal factors (external to the theory of interest) or through stochastic processes. A theory produces many such predictions if it is fully elaborated, issuing predictions not only on the central outcome of interest but also on specific causal mechanisms, and if it is broad in purview. (The notion of riskiness may also be conceptualized within the Popperian lexicon as degrees of falsifiability .)

These points can also be articulated in Bayesian terms. Colin Howson and Peter Urbach explain: “The degree to which h [a hypothesis] is confirmed by e [a set of evidence] depends … on the extent to which P(eČh) exceeds P (e) , that is, on how much more probable e is relative to the hypothesis and background assumptions than it is relative just to background assumptions.” Again, “confirmation is correlated with how much more probable the evidence is if the hypothesis is true than if it is false” ( Howson and Urlbach 1989 , 86). Thus, the stranger the prediction offered by a theory—relative to what we would normally expect—the greater the degree of confirmation that will be afforded by the evidence. As an intuitive example, Howson and Urbach (1989 , 86) offer the following:

If a soothsayer predicts that you will meet a dark stranger sometime and you do in fact, your faith in his powers of precognition would not be much enhanced: you would probably continue to think his predictions were just the result of guesswork. However, if the prediction also gave the correct number of hairs on the head of that stranger, your previous scepticism would no doubt be severely shaken.

While these Popperian/Bayesian notions 12 are relevant to all empirical research designs, they are especially relevant to case‐study research designs, for in these settings a single case (or, at most, a small number of cases) is required to bear a heavy burden of proof. It should be no surprise, therefore, that Popper's idea of “riskiness” was to be appropriated by case‐study researchers like Harry Eckstein to validate the enterprise of single‐case analysis. (Although Eckstein does not cite Popper the intellectual lineage is clear.) Riskiness, here, is analogous to what is usually referred to as a “most‐ difficult” research design, which in a case‐study research design would be understood as a “least‐likely” case. Note also that the distinction between a “must‐fit” case and a least‐likely case—that, in the event, actually does fit the terms of a theory—is a matter of degree. Cases are more or less crucial for confirming theories. The point is that, in some circumstances, a paucity of empirical evidence may be compensated by the riskiness of the theory.

The crucial‐case research design is, perforce, a highly deductive enterprise; much depends on the quality of the theory under investigation. It follows that the theories most amenable to crucial‐case analysis are those which are lawlike in their precision, degree of elaboration, consistency, and scope. The more a theory attains the status of a causal law, the easier it will be to confirm, or to disconfirm, with a single case. Indeed, risky predictions are common in natural science fields such as physics, which in turn served as the template for the deductive‐nomological (“covering‐law”) model of science that influenced Eckstein and others in the postwar decades (e.g. Hempel 1942 ).

A frequently cited example is the first important empirical demonstration of the theory of relativity, which took the form of a single‐event prediction on the occasion of the May 29, 1919, solar eclipse ( Eckstein 1975 ; Popper 1963 ). Stephen Van Evera (1997 , 66–7) describes the impact of this prediction on the validation of Einstein's theory.

Einstein's theory predicted that gravity would bend the path of light toward a gravity source by a specific amount. Hence it predicted that during a solar eclipse stars near the sun would appear displaced—stars actually behind the sun would appear next to it, and stars lying next to the sun would appear farther from it—and it predicted the amount of apparent displacement. No other theory made these predictions. The passage of this one single‐case‐study test brought the theory wide acceptance because the tested predictions were unique—there was no plausible competing explanation for the predicted result—hence the passed test was very strong.

The strength of this test is the extraordinary fit between the theory and a set of facts found in a single case, and the corresponding lack of fit between all other theories and this set of facts. Einstein offered an explanation of a particular set of anomalous findings that no other existing theory could make sense of. Of course, one must assume that there was no—or limited—measurement error. And one must assume that the phenomenon of interest is largely invariant; light does not bend differently at different times and places (except in ways that can be understood through the theory of relativity). And one must assume, finally, that the theory itself makes sense on other grounds (other than the case of special interest); it is a plausible general theory. If one is willing to accept these a priori assumptions, then the 1919 “case study” provides a very strong confirmation of the theory. It is difficult to imagine a stronger proof of the theory from within an observational (nonexperimental) setting.

In social science settings, by contrast, one does not commonly find single‐case studies offering knockout evidence for a theory. This is, in my view, largely a product of the looseness (the underspecification) of most social science theories. George and Bennett point out that while the thesis of the democratic peace is as close to a “law” as social science has yet seen, it cannot be confirmed (or refuted) by looking at specific causal mechanisms because the causal pathways mandated by the theory are multiple and diverse. Under the circumstances, no single‐case test can offer strong confirmation of the theory ( George and Bennett 2005 , 209).

However, if one adopts a softer version of the crucial‐case method—the least‐likely (most difficult) case—then possibilities abound. Indeed, I suspect that, implicitly , most case‐study work that makes a positive argument focusing on a single case (without a corresponding cross‐case analysis) relies largely on the logic of the least‐ likely case. Rarely is this logic made explicit, except perhaps in a passing phrase or two. Yet the deductive logic of the “risky” prediction is central to the case‐study enterprise. Whether a case study is convincing or not often rests on the reader's evaluation of how strong the evidence for an argument might be, and this in turn—wherever cross‐ case evidence is limited and no manipulated treatment can be devised—rests upon an estimation of the degree of “fit” between a theory and the evidence at hand, as discussed.

Lily Tsai's (2007) investigation of governance at the village level in China employs several in‐depth case studies of villages which are chosen (in part) because of their least‐likely status relative to the theory of interest. Tsai's hypothesis is that villages with greater social solidarity (based on preexisting religious or familial networks) will develop a higher level of social trust and mutual obligation and, as a result, will experience better governance. Crucial cases, therefore, are villages that evidence a high level of social solidarity but which, along other dimensions, would be judged least likely to develop good governance, e.g. they are poor, isolated, and lack democratic institutions or accountability mechanisms from above. “Li Settlement,” in Fujian province, is such a case. The fact that this impoverished village nonetheless boasts an impressive set of infrastructural accomplishments such as paved roads with drainage ditches (a rarity in rural China) suggests that something rather unusual is going on here. Because her case is carefully chosen to eliminate rival explanations, Tsai's conclusions about the special role of social solidarity are difficult to gainsay. How else is one to explain this otherwise anomalous result? This is the strength of the least‐likely case, where all other plausible causal factors for an outcome have been minimized. 13

Jack Levy (2002 , 144) refers to this, evocatively, as a “Sinatra inference:” if it can make it here, it can make it anywhere (see also Khong 1992 , 49; Sagan 1995 , 49; Shafer 1988 , 14–6). Thus, if social solidarity has the hypothesized effect in Li Settlement it should have the same effect in more propitious settings (e.g. where there is greater economic surplus). The same implicit logic informs many case‐study analyses where the intent of the study is to confirm a hypothesis on the basis of a single case.

Another sort of crucial case is employed for the purpose of dis confirming a causal hypothesis. A central Popperian insight is that it is easier to disconfirm an inference than to confirm that same inference. (Indeed, Popper doubted that any inference could be fully confirmed, and for this reason preferred the term “corroborate.”) This is particularly true of case‐study research designs, where evidence is limited to one or several cases. The key proviso is that the theory under investigation must take a consistent (a.k.a. invariant, deterministic) form, even if its predictions are not terrifically precise, well elaborated, or broad.

As it happens, there are a fair number of invariant propositions floating around the social science disciplines (Goertz and Levy forthcoming; Goertz and Starr 2003 ). It used to be argued, for example, that political stability would occur only in countries that are relatively homogeneous, or where existing heterogeneities are mitigated by cross‐cutting cleavages ( Almond 1956 ; Bentley 1908/1967 ; Lipset 1960/1963 ; Truman 1951 ). Arend Lijphart's (1968) study of the Netherlands, a peaceful country with reinforcing social cleavages, is commonly viewed as refuting this theory on the basis of a single in‐depth case analysis. 14

Granted, it may be questioned whether presumed invariant theories are really invariant; perhaps they are better understood as probabilistic. Perhaps, that is, the theory of cross‐cutting cleavages is still true, probabilistically, despite the apparent Dutch exception. Or perhaps the theory is still true, deterministically, within a subset of cases that does not include the Netherlands. (This sort of claim seems unlikely in this particular instance, but it is quite plausible in many others.) Or perhaps the theory is in need of reframing; it is true, deterministically, but applies only to cross‐ cutting ethnic/racial cleavages, not to cleavages that are primarily religious. One can quibble over what it means to “disconfirm” a theory. The point is that the crucial case has, in all these circumstances, provided important updating of a theoretical prior.

Heretofore, I have treated causal factors as dichotomous. Countries have either reinforcing or cross‐cutting cleavages and they have regimes that are either peaceful or conflictual. Evidently, these sorts of parameters are often matters of degree. In this reading of the theory, cases are more or less crucial. Accordingly, the most useful—i.e. most crucial—case for Lijphart's purpose is one that has the most segregated social groups and the most peaceful and democratic track record. In these respects, the Netherlands was a very good choice. Indeed, the degree of disconfirmation offered by this case study is probably greater than the degree of disconfirmation that might have been provided by other cases such as India or Papua New Guinea—countries where social peace has not always been secure. The point is that where variables are continuous rather than dichotomous it is possible to evaluate potential cases in terms of their degree of crucialness .

Note that the crucial‐case method of case‐selection, whether employed in a confirmatory or disconfirmatory mode, cannot be employed in a large‐ N context. This is because an explicit cross‐case model would render the crucial‐case study redundant. Once one identifies the relevant parameters and the scores of all cases on those parameters, one has in effect constructed a cross‐case model that confirms or disconfirms the theory in question. The case study is thenceforth irrelevant, at least as a means of decisive confirmation or disconfirmation. 15 It remains highly relevant as a means of exploring causal mechanisms, of course. Yet, because this objective is quite different from that which is usually associated with the term, I enlist a new term for this technique.

7 Pathway Case

One of the most important functions of case‐study research is the elucidation of causal mechanisms. But which sort of case is most useful for this purpose? Although all case studies presumably shed light on causal mechanisms, not all cases are equally transparent. In situations where a causal hypothesis is clear and has already been confirmed by cross‐case analysis, researchers are well advised to focus on a case where the causal effect of X   1 on Y can be isolated from other potentially confounding factors ( X   2 ). I shall call this a pathway case to indicate its uniquely penetrating insight into causal mechanisms. In contrast to the crucial case, this sort of method is practicable only in circumstances where cross‐case covariational patterns are well studied and where the mechanism linking X   1 and Y remains dim. Because the pathway case builds on prior cross‐case analysis, the problem of case selection must be situated within that sample. There is no standalone pathway case.

The logic of the pathway case is clearest in situations of causal sufficiency—where a causal factor of interest, X   1 , is sufficient by itself (though perhaps not necessary) to account for Y 's value (0 or 1). The other causes of Y , about which we need make no assumptions, are designated as a vector, X   2 .

Note that wherever various causal factors are substitutable for one another, each factor is conceptualized (individually) as sufficient ( Braumoeller 2003 ). Thus, situations of causal equifinality presume causal sufficiency on the part of each factor or set of conjoint factors. An example is provided by the literature on democratization, which stipulates three main avenues of regime change: leadership‐initiated reform, a controlled opening to opposition, or the collapse of an authoritarian regime ( Colomer 1991 ). The case‐study format constrains us to analyze one at a time, so let us limit our scope to the first one—leadership‐initiated reform. So considered, a causal‐pathway case would be one with the following features: (a) democratization, (b) leadership‐initiated reform, (c) no controlled opening to the opposition, (d) no collapse of the previous authoritarian regime, and (e) no other extraneous factors that might affect the process of democratization. In a case of this type, the causal mechanisms by which leadership‐initiated reform may lead to democratization will be easiest to study. Note that it is not necessary to assume that leadership‐initiated reform always leads to democratization; it may or may not be a deterministic cause. But it is necessary to assume that leadership‐initiated reform can sometimes lead to democratization on its own (given certain background features).

Now let us move from these examples to a general‐purpose model. For heuristic purposes, let us presume that all variables in that model are dichotomous (coded as 0 or 1) and that the model is complete (all causes of Y are included). All causal relationships will be coded so as to be positive: X   1 and Y covary as do X   2 and Y . This allows us to visualize a range of possible combinations at a glance.

Recall that the pathway case is always focused, by definition, on a single causal factor, denoted X   1 . (The researcher's focus may shift to other causal factors, but may only focus on one causal factor at a time.) In this scenario, and regardless of how many additional causes of Y there might be (denoted X   2 , a vector of controls), there are only eight relevant case types, as illustrated in Table 28.2 . Identifying these case types is a relatively simple matter, and can be accomplished in a small‐ N sample by the construction of a truth‐table (modeled after Table 28.2 ) or in a large‐ N sample by the use of cross‐tabs.

Notes : X   1 = the variable of theoretical interest. X   2 = a vector of controls (a score of 0 indicates that all control variables have a score of 0, while a score of 1 indicates that all control variables have a score of 1). Y = the outcome of interest. A–H = case types (the N for each case type is indeterminate). G, H = possible pathway cases. Sample size = indeterminate.

Assumptions : (a) all variables can be coded dichotomously (a binary coding of the concept is valid); (b) all independent variables are positively correlated with Y in the general case; ( c ) X   1 is (at least sometimes) a sufficient cause of Y .

Note that the total number of combinations of values depends on the number of control variables, which we have represented with a single vector, X   2 . If this vector consists of a single variable then there are only eight case types. If this vector consists of two variables ( X   2a , X   2b ) then the total number of possible combinations increases from eight (2 3 ) to sixteen (2 4 ). And so forth. However, none of these combinations is relevant for present purposes except those where X   2a and X   2b have the same value (0 or 1). “Mixed” cases are not causal pathway cases, for reasons that should become clear.

The pathway case, following the logic of the crucial case, is one where the causal factor of interest, X   1 , correctly predicts Y while all other possible causes of Y (represented by the vector, X   2 ) make “wrong” predictions. If X   1 is—at least in some circumstances—a sufficient cause of Y , then it is these sorts of cases that should be most useful for tracing causal mechanisms. There are only two such cases in Ta b l e 28.2—G and H. In all other cases, the mechanism running from X   1 to Y would be difficult to discern either because X   1 and Y are not correlated in the usual way (constituting an unusual case, in the terms of our hypothesis) or because other confounding factors ( X   2 ) intrude. In case A, for example, the positive value on Y could be a product of X   1 or X   2 . An in‐depth examination of this case is not likely to be very revealing.

Keep in mind that because the researcher already knows from her cross‐case examination what the general causal relationships are, she knows (prior to the case‐ study investigation) what constitutes a correct or incorrect prediction. In the crucial‐ case method, by contrast, these expectations are deductive rather than empirical. This is what differentiates the two methods. And this is why the causal pathway case is useful principally for elucidating causal mechanisms rather than verifying or falsifying general propositions (which are already more or less apparent from the cross‐case evidence). Of course, we must leave open the possibility that the investigation of causal mechanisms would invalidate a general claim, if that claim is utterly contingent upon a specific set of causal mechanisms and the case study shows that no such mechanisms are present. However, this is rather unlikely in most social science settings. Usually, the result of such a finding will be a reformulation of the causal processes by which X   1 causes Y —or, alternatively, a realization that the case under investigation is aberrant (atypical of the general population of cases).

Sometimes, the research question is framed as a unidirectional cause: one is interested in why 0 becomes 1 (or vice versa) but not in why 1 becomes 0. In our previous example, we asked why democracies fail, not why countries become democratic or authoritarian. So framed, there can be only one type of causal‐pathway case. (Whether regime failure is coded as 0 or 1 is a matter of taste.) Where researchers are interested in bidirectional causality—a movement from 0 to 1 as well as from 1 to 0—there are two possible causal‐pathway cases, G and H. In practice, however, one of these case types is almost always more useful than the other. Thus, it seems reasonable to employ the term “pathway case” in the singular. In order to determine which of these two case types will be more useful for intensive analysis the researcher should look to see whether each case type exhibits desirable features such as: (a) a rare (unusual) value on X   1 or Y (designated “extreme” in our previous discussion), (b) observable temporal variation in X   1 , ( c ) an X   1 / Y relationship that is easier to study (it has more visible features; it is more transparent), or (d) a lower residual (thus indicating a more typical case, within the terms of the general model). Usually, the choice between G and H is intuitively obvious.

Now, let us consider a scenario in which all (or most) variables of concern to the model are continuous, rather than dichotomous. Here, the job of case selection is considerably more complex, for causal “sufficiency” (in the usual sense) cannot be invoked. It is no longer plausible to assume that a given cause can be entirely partitioned, i.e. rival factors eliminated. However, the search for a pathway case may still be viable. What we are looking for in this scenario is a case that satisfies two criteria: (1) it is not an outlier (or at least not an extreme outlier) in the general model and (2) its score on the outcome ( Y ) is strongly influenced by the theoretical variable of interest ( X   1 ), taking all other factors into account ( X   2 ). In this sort of case it should be easiest to “see” the causal mechanisms that lie between X   1 and Y .

Achieving the second desiderata requires a bit of manipulation. In order to determine which (nonoutlier) cases are most strongly affected by X   1 , given all the other parameters in the model, one must compare the size of the residuals for each case in a reduced form model, Y = Constant + X   2 + Res reduced , with the size of the residuals for each case in a full model, Y = Constant + X   2 + X   1 + Res full . The pathway case is that case, or set of cases, which shows the greatest difference between the residual for the reduced‐form model and the full model (ΔResidual). Thus,

Note that the residual for a case must be smaller in the full model than in the reduced‐ form model; otherwise, the addition of the variable of interest ( X   1 ) pulls the case away from the regression line. We want to find a case where the addition of X   1 pushes the case towards the regression line, i.e. it helps to “explain” that case.

As an example, let us suppose that we are interested in exploring the effect of mineral wealth on the prospects for democracy in a society. According to a good deal of work on this subject, countries with a bounty of natural resources—particularly oil—are less likely to democratize (or once having undergone a democratic transition, are more likely to revert to authoritarian rule) ( Barro 1999 ; Humphreys 2005 ; Ross 2001 ). The cross‐country evidence is robust. Yet as is often the case, the causal mechanisms remain rather obscure. In order to better understand this phenomenon it may be worthwhile to exploit the findings of cross‐country regression models in order to identify a country whose regime type (i.e. its democracy “score” on some general index) is strongly affected by its natural‐research wealth, all other things held constant. An analysis of this sort identifies two countries— the United Arab Emirates and Kuwait—with high Δ Residual values and modest residuals in the full model (signifying that these cases are not outliers). Researchers seeking to explore the effect of oil wealth on regime type might do well to focus on these two cases since their patterns of democracy cannot be well explained by other factors—e.g. economic development, religion, European influence, or ethnic fractionalization. The presence of oil wealth in these countries would appear to have a strong independent effect on the prospects for democratization in these cases, an effect that is well modeled by general theory and by the available cross‐case evidence.

To reiterate, the logic of causal “elimination” is much more compelling where variables are dichotomous and where causal sufficiency can be assumed ( X   1 is sufficient by itself, at least in some circumstances, to cause Y ). Where variables are continuous, the strategy of the pathway case is more dubious, for potentially confounding causal factors ( X   2 ) cannot be neatly partitioned. Even so, we have indicated why the selection of a pathway case may be a logical approach to case‐study analysis in many circumstances.

The exceptions may be briefly noted. Sometimes, where all variables in a model are dichotomous, there are no pathway cases, i.e. no cases of type G or H (in Table 28.2 ). This is known as the “empty cell” problem, or a problem of severe causal multicollinearity. The universe of observational data does not always oblige us with cases that allow us to independently test a given hypothesis. Where variables are continuous, the analogous problem is that of a causal variable of interest ( X   1 ) that has only minimal effects on the outcome of interest. That is, its role in the general model is quite minor. In these situations, the only cases that are strongly affected by X   1 —if there are any at all—may be extreme outliers, and these sorts of cases are not properly regarded as providing confirmatory evidence for a proposition, for reasons that are abundantly clear by now.

Finally, it should be clarified that the identification of a causal pathway case does not obviate the utility of exploring other cases. One might, for example, want to compare both sorts of potential pathway cases—G and H—with each other. Many other combinations suggest themselves. However, this sort of multi‐case investigation moves beyond the logic of the causal‐pathway case.

8 Most‐similar Cases

The most‐similar method employs a minimum of two cases. 16 In its purest form, the chosen pair of cases is similar in all respects except the variable(s) of interest. If the study is exploratory (i.e. hypothesis generating), the researcher looks for cases that differ on the outcome of theoretical interest but are similar on various factors that might have contributed to that outcome, as illustrated in Table 28.3 (A) . This is a common form of case selection at the initial stage of research. Often, fruitful analysis begins with an apparent anomaly: two cases are apparently quite similar, and yet demonstrate surprisingly different outcomes. The hope is that intensive study of these cases will reveal one—or at most several—factors that differ across these cases. These differing factors ( X   1 ) are looked upon as putative causes. At this stage, the research may be described by the second diagram in Table 28.3 (B) . Sometimes, a researcher begins with a strong hypothesis, in which case her research design is confirmatory (hypothesis testing) from the get‐go. That is, she strives to identify cases that exhibit different outcomes, different scores on the factor of interest, and similar scores on all other possible causal factors, as illustrated in the second (hypothesis‐testing) diagram in Table 28.3 (B) .

The point is that the purpose of a most‐similar research design, and hence its basic setup, often changes as a researcher moves from an exploratory to a confirmatory mode of analysis. However, regardless of where one begins, the results, when published, look like a hypothesis‐testing research design. Question marks have been removed: (A) becomes (B) in Table 28.3 .

As an example, let us consider Leon Epstein's classic study of party cohesion, which focuses on two “most‐similar” countries, the United States and Canada. Canada has highly disciplined parties whose members vote together on the floor of the House of Commons while the United States has weak, undisciplined parties, whose members often defect on floor votes in Congress. In explaining these divergent outcomes, persistent over many years, Epstein first discusses possible causal factors that are held more or less constant across the two cases. Both the United States and Canada inherited English political cultures, both have large territories and heterogeneous populations, both are federal, and both have fairly loose party structures with strong regional bases and a weak center. These are the “control” variables. Where they differ is in one constitutional feature: Canada is parliamentary while the United States is presidential. And it is this institutional difference that Epstein identifies as the crucial (differentiating) cause. (For further examples of the most‐similar method see Brenner 1976 ; Hamilton 1977 ; Lipset 1968 ; Miguel 2004 ; Moulder 1977 ; Posner 2004 .)

X   1 = the variable of theoretical interest. X   2 = a vector of controls. Y = the outcome of interest.

Several caveats apply to any most‐similar analysis (in addition to the usual set of assumptions applying to all case‐study analysis). First, each causal factor is understood as having an independent and additive effect on the outcome; there are no “interaction” effects. Second, one must code cases dichotomously (high/low, present/absent). This is straightforward if the underlying variables are also dichotomous (e.g. federal/unitary). However, it is often the case that variables of concern in the model are continuous (e.g. party cohesion). In this setting, the researcher must “dichotomize” the scoring of cases so as to simplify the two‐case analysis. (Some flexibility is admissible on the vector of controls ( X   2 ) that are “held constant” across the cases. Nonidentity is tolerable if the deviation runs counter to the predicted hypothesis. For example, Epstein describes both the United States and Canada as having strong regional bases of power, a factor that is probably more significant in recent Canadian history than in recent American history. However, because regional bases of power should lead to weaker parties, rather than stronger parties, this element of nonidentity does not challenge Epstein's conclusions. Indeed, it sets up a most‐difficult research scenario, as discussed above.)

In one respect the requirements for case control are not so stringent. Specifically, it is not usually necessary to measure control variables (at least not with a high degree of precision) in order to control for them. If two countries can be assumed to have similar cultural heritages one needn't worry about constructing variables to measure that heritage. One can simply assert that, whatever they are, they are more or less constant across the two cases. This is similar to the technique employed in a randomized experiment, where the researcher typically does not attempt to measure all the factors that might affect the causal relationship of interest. She assumes, rather, that these unknown factors have been neutralized across the treatment and control groups by randomization or by the choice of a sample that is internally homogeneous.

The most useful statistical tool for identifying cases for in‐depth analysis in a most‐ similar setting is probably some variety of matching strategy—e.g. exact matching, approximate matching, or propensity‐score matching. 17 The product of this procedure is a set of matched cases that can be compared in whatever way the researcher deems appropriate. These are the “most‐similar” cases. Rosenbaum and Silber (2001 , 223) summarize:

Unlike model‐based adjustments, where [individuals] vanish and are replaced by the coefficients of a model, in matching, ostensibly comparable patterns are compared directly, one by one. Modern matching methods involve statistical modeling and combinatorial algorithms, but the end result is a collection of pairs or sets of people who look comparable, at least on average. In matching, people retain their integrity as people, so they can be examined and their stories can be told individually.

Matching, conclude the authors, “facilitates, rather than inhibits, thick description” ( Rosenbaum and Silber 2001 , 223).

In principle, the same matching techniques that have been used successfully in observational studies of medical treatments might also be adapted to the study of nation states, political parties, cities, or indeed any traditional paired cases in the social sciences. Indeed, the current popularity of matching among statisticians—relative, that is, to garden‐variety regression models—rests upon what qualitative researchers would recognize as a “case‐based” approach to causal analysis. If Rosenbaum and Silber are correct, it may be perfectly reasonable to appropriate this large‐ N method of analysis for case‐study purposes.

As with other methods of case selection, the most‐similar method is prone to problems of nonrepresentativeness. If employed in a qualitative fashion (without a systematic cross‐case selection strategy), potential biases in the chosen case must be addressed in a speculative way. If the researcher employs a matching technique of case selection within a large‐ N sample, the problem of potential bias can be addressed by assuring the choice of cases that are not extreme outliers, as judged by their residuals in the full model. Most‐similar cases should also be “typical” cases, though some scope for deviance around the regression line may be acceptable for purposes of finding a good fit among cases.

X   1 = the variable of theoretical interest. X   2a–d = a vector of controls. Y = the outcome of interest.

9 Most‐different Cases

A final case‐selection method is the reverse image of the previous method. Here, variation on independent variables is prized, while variation on the outcome is eschewed. Rather than looking for cases that are most‐similar, one looks for cases that are most‐ different . Specifically, the researcher tries to identify cases where just one independent variable ( X   1 ), as well as the dependent variable ( Y ), covary, while all other plausible factors ( X   2a–d ) show different values. 18

The simplest form of this two‐case comparison is illustrated in Table 28.4 . Cases A and B are deemed “most different,” though they are similar in two essential respects— the causal variable of interest and the outcome.

As an example, I follow Marc Howard's (2003) recent work, which explores the enduring impact of Communism on civil society. 19 Cross‐national surveys show a strong correlation between former Communist regimes and low social capital, controlling for a variety of possible confounders. It is a strong result. Howard wonders why this relationship is so strong and why it persists, and perhaps even strengthens, in countries that are no longer socialist or authoritarian. In order to answer this question, he focuses on two most‐different cases, Russia and East Germany. These two countries were quite different—in all ways other than their Communist experience— prior to the Soviet era, during the Soviet era (since East Germany received substantial subsidies from West Germany), and in the post‐Soviet era, as East Germany was absorbed into West Germany. Yet, they both score near the bottom of various cross‐ national indices intended to measure the prevalence of civic engagement in the current era. Thus, Howard's (2003 , 6–9) case selection procedure meets the requirements of the most‐different research design: Variance is found on all (or most) dimensions aside from the key factor of interest (Communism) and the outcome (civic engagement).

What leverage is brought to the analysis from this approach? Howard's case studies combine evidence drawn from mass surveys and from in‐depth interviews of small, stratified samples of Russians and East Germans. (This is a good illustration, incidentally, of how quantitative and qualitative evidence can be fruitfully combined in the intensive study of several cases.) The product of this analysis is the identification of three causal pathways that, Howard (2003 , 122) claims, help to explain the laggard status of civil society in post‐Communist polities: “the mistrust of communist organizations, the persistence of friendship networks, and the disappointment with post‐communism.” Simply put, Howard (2003 , 145) concludes, “a great number of citizens in Russia and Eastern Germany feel a strong and lingering sense of distrust of any kind of public organization, a general satisfaction with their own personal networks (accompanied by a sense of deteriorating relations within society overall), and disappointment in the developments of post‐communism.”

The strength of this most‐different case analysis is that the results obtained in East Germany and Russia should also apply in other post‐Communist polities (e.g. Lithuania, Poland, Bulgaria, Albania). By choosing a heterogeneous sample, Howard solves the problem of representativeness in his restricted sample. However, this sample is demonstrably not representative across the population of the inference, which is intended to cover all countries of the world.

More problematic is the lack of variation on key causal factors of interest— Communism and its putative causal pathways. For this reason, it is difficult to reach conclusions about the causal status of these factors on the basis of the most‐different analysis alone. It is possible, that is, that the three causal pathways identified by Howard also operate within polities that never experienced Communist rule.

Nor does it seem possible to conclusively eliminate rival hypotheses on the basis of this most‐different analysis. Indeed, this is not Howard's intention. He wishes merely to show that whatever influence on civil society might be attributed to economic, cultural, and other factors does not exhaust this subject.

My considered judgment is that the most‐different research design provides minimal leverage into the problem of why Communist systems appear to suppress civic engagement, years after their disappearance. Fortunately, this is not the only research design employed by Howard in his admirable study. Indeed, the author employs two other small‐ N cross‐case methods, as well as a large‐ N cross‐country statistical analysis. These methods do most of the analytic work. East Germany may be regarded as a causal pathway case (see above). It has all the attributes normally assumed to foster civic engagement (e.g. a growing economy, multiparty competition, civil liberties, a free press, close association with Western European culture and politics), but nonetheless shows little or no improvement on this dimension during the post‐ transition era ( Howard 2003 , 8). It is plausible to attribute this lack of change to its Communist past, as Howard does, in which case East Germany should be a fruitful case for the investigation of causal mechanisms. The contrast between East and West Germany provides a most‐similar analysis since the two polities share virtually everything except a Communist past. This variation is also deftly exploited by Howard.

I do not wish to dismiss the most‐different research method entirely. Surely, Howard's findings are stronger with the intensive analysis of Russia than they would be without. Yet his book would not stand securely on the empirical foundation provided by most‐different analysis alone. If one strips away the pathway‐case (East Germany) and the most‐similar analysis (East/West Germany) there is little left upon which to base an analysis of causal relations (aside from the large‐ N cross‐national analysis). Indeed, most scholars who employ the most‐different method do so in conjunction with other methods. 20 It is rarely, if ever, a standalone method. 21

Generalizing from this discussion of Marc Howard's work, I offer the following summary remarks on the most‐different method of case analysis. (I leave aside issues faced by all case‐study analyses, issues that are explored in Gerring 2007 .)

Let us begin with a methodological obstacle that is faced by both Millean styles of analysis—the necessity of dichotomizing every variable in the analysis. Recall that, as with most‐similar analysis, differences across cases must generally be sizeable enough to be interpretable in an essentially dichotomous fashion (e.g. high/low, present/absent) and similarities must be close enough to be understood as essentially identical (e.g. high/high, present/present). Otherwise the results of a Millean style analysis are not interpretable. The problem of “degrees” is deadly if the variables under consideration are, by nature, continuous (e.g. GDP). This is a particular concern in Howard's analysis, where East Germany scores somewhat higher than Russia in civic engagement; they are both low, but Russia is quite a bit lower. Howard assumes that this divergence is minimal enough to be understood as a difference of degrees rather than of kinds, a judgment that might be questioned. In these respects, most‐different analysis is no more secure—but also no less—than most‐similar analysis.

In one respect, most‐different analysis is superior to most‐similar analysis. If the coding assumptions are sound, the most‐different research design may be quite useful for eliminating necessary causes . Causal factors that do not appear across the chosen cases—e.g. X   2a–d in Table 28.4 —are evidently unnecessary for the production of Y . However, it does not follow that the most‐different method is the best method for eliminating necessary causes. Note that the defining feature of this method is the shared element across cases— X   1 in Table 28.4 . This feature does not help one to eliminate necessary causes. Indeed, if one were focused solely on eliminating necessary causes one would presumably seek out cases that register the same outcomes and have maximum diversity on other attributes. In Table 28.4 , this would be a set of cases that satisfy conditions X   2a–d , but not X   1 . Thus, even the presumed strength of the most‐different analysis is not so strong.

Usually, case‐study analysis is focused on the identification (or clarification) of causal relations, not the elimination of possible causes. In this setting, the most‐ different technique is useful, but only if assumptions of causal uniqueness hold. By “causal uniqueness,” I mean a situation in which a given outcome is the product of only one cause: Y cannot occur except in the presence of X . X is necessary, and in some situations (given certain background conditions) sufficient, to cause Y . 22

Consider the following hypothetical example. Suppose that a new disease, about which little is known, has appeared in Country A. There are hundreds of infected persons across dozens of affected communities in that country. In Country B, located at the other end of the world, several new cases of the disease surface in a single community. In this setting, we can imagine two sorts of Millean analyses. The first examines two similar communities within Country A, one of which has developed the disease and the other of which has not. This is the most‐similar style of case comparison, and focuses accordingly on the identification of a difference between the two cases that might account for variation across the sample. A second approach focuses on communities where the disease has appeared across the two countries and searches for any similarities that might account for these similar outcomes. This is the most‐different research design.

Both are plausible approaches to this particular problem, and we can imagine epidemiologists employing them simultaneously. However, the most‐different design demands stronger assumptions about the underlying factors at work. It supposes that the disease arises from the same cause in any setting. This is often a reasonable operating assumption when one is dealing with natural phenomena, though there are certainly many exceptions. Death, for example, has many causes. For this reason, it would not occur to us to look for most‐different cases of high mortality around the world. In order for the most‐different research design to effectively identify a causal factor at work in a given outcome, the researcher must assume that X   1 —the factor held constant across the diverse cases—is the only possible cause of Y (see Table 28.4 ). This assumption rarely holds in social‐scientific settings. Most outcomes of interest to anthropologists, economists, political scientists, and sociologists have multiple causes. There are many ways to win an election, to build a welfare state, to get into a war, to overthrow a government, or—returning to Marc Howard's work—to build a strong civil society. And it is for this reason that most‐different analysis is rarely applied in social science work and, where applied, is rarely convincing.

If this seems a tad severe, there is a more charitable way of approaching the most‐different method. Arguably, this is not a pure “method” at all but merely a supplement, a way of incorporating diversity in the sub‐sample of cases that provide the unusual outcome of interest. If the unusual outcome is revolutions, one might wish to encompass a wide variety of revolutions in one's analysis. If the unusual outcome is post‐Communist civil society, it seems appropriate to include a diverse set of post‐Communist polities in one's sample of case studies, as Marc Howard does. From this perspective, the most‐different method (so‐called) might be better labeled a diverse‐case method, as explored above.

10 Conclusions

In order to be a case of something broader than itself, the chosen case must be representative (in some respects) of a larger population. Otherwise—if it is purely idiosyncratic (“unique”)—it is uninformative about anything lying outside the borders of the case itself. A study based on a nonrepresentative sample has no (or very little) external validity. To be sure, no phenomenon is purely idiosyncratic; the notion of a unique case is a matter that would be difficult to define. One is concerned, as always, with matters of degree. Cases are more or less representative of some broader phenomenon and, on that score, may be considered better or worse subjects for intensive analysis. (The one exception, as noted, is the influential case.)

Of all the problems besetting case‐study analysis, perhaps the most persistent— and the most persistently bemoaned—is the problem of sample bias ( Achen and Snidal 1989 ; Collier and Mahoney 1996 ; Geddes 1990 ; King, Keohane, and Verba 1994 ; Rohlfing 2004 ; Sekhon 2004 ). Lisa Martin (1992 , 5) finds that the overemphasis of international relations scholars on a few well‐known cases of economic sanctions— most of which failed to elicit any change in the sanctioned country—“has distorted analysts view of the dynamics and characteristics of economic sanctions.” Barbara Geddes (1990) charges that many analyses of industrial policy have focused exclusively on the most successful cases—primarily the East Asian NICs—leading to biased inferences. Anna Breman and Carolyn Shelton (2001) show that case‐study work on the question of structural adjustment is systematically biased insofar as researchers tend to focus on disaster cases—those where structural adjustment is associated with very poor health and human development outcomes. These cases, often located in sub‐Saharan Africa, are by no means representative of the entire population. Consequently, scholarship on the question of structural adjustment is highly skewed in a particular ideological direction (against neoliberalism) (see also Gerring, Thacker, and Moreno 2005) .

These examples might be multiplied many times. Indeed, for many topics the most‐studied cases are acknowledged to be less than representative. It is worth reflecting upon the fact that our knowledge of the world is heavily colored by a few “big” (populous, rich, powerful) countries, and that a good portion of the disciplines of economics, political science, and sociology are built upon scholars' familiarity with the economics, political science, and sociology of one country, the United States. 23 Case‐study work is particularly prone to problems of investigator bias since so much rides on the researcher's selection of one (or a few) cases. Even if the investigator is unbiased, her sample may still be biased simply by virtue of “random” error (which may be understood as measurement error, error in the data‐generation process, or as an underlying causal feature of the universe).

There are only two situations in which a case‐study researcher need not be concerned with the representativeness of her chosen case. The first is the influential case research design, where a case is chosen because of its possible influence on a cross‐case model, and hence is not expected to be representative of a larger sample. The second is the deviant‐case method, where the chosen case is employed to confirm a broader cross‐case argument to which the case stands as an apparent exception. Yet even here the chosen case is expected to be representative of a broader set of cases—those, in particular, that are poorly explained by the extant model.

In all other circumstances, cases must be representative of the population of interest in whatever ways might be relevant to the proposition in question. Note that where a researcher is attempting to disconfirm a deterministic proposition the question of representativeness is perhaps more appropriately understood as a question of classification: Is the chosen case appropriately classified as a member of the designated population? If so, then it is fodder for a disconfirming case study.

If the researcher is attempting to confirm a deterministic proposition, or to make probabilistic arguments about a causal relationship, then the problem of representativeness is of the more usual sort: Is case A unit‐homogeneous relative to other cases in the population? This is not an easy matter to test. However, in a large‐ N context the residual for that case (in whatever model the researcher has greatest confidence in) is a reasonable place to start. Of course, this test is only as good as the model at hand. Any incorrect specifications or incorrect modeling procedures will likely bias the results and give an incorrect assessment of each case's “typicality.” In addition, there is the possibility of stochastic error, errors that cannot be modeled in a general framework. Given the explanatory weight that individual cases are asked to bear in a case‐study analysis, it is wise to consider more than just the residual test of representativeness. Deductive logic and an in‐depth knowledge of the case in question are often more reliable tools than the results of a cross‐case model.

In any case, there is no dispensing with the question. Case studies (with the two exceptions already noted) rest upon an assumed synecdoche: The case should stand for a population. If this is not true, or if there is reason to doubt this assumption, then the utility of the case study is brought severely into question.

Fortunately, there is some safety in numbers. Insofar as case‐study evidence is combined with cross‐case evidence the issue of sample bias is mitigated. Indeed, the suspicion of case‐study work that one finds in the social sciences today is, in my view, a product of a too‐literal interpretation of the case‐study method. A case study tout court is thought to mean a case study tout seul . Insofar as case studies and cross‐case studies can be enlisted within the same investigation (either in the same study or by reference to other studies in the same subfield), problems of representativeness are less worrisome. This is the virtue of cross‐level work, a.k.a. “triangulation.”

11 Ambiguities

Before concluding, I wish to draw attention to two ambiguities in case‐selection strategies in case‐study research. The first concerns the admixture of several case‐ selection strategies. The second concerns the changing status of a case as a study proceeds.

Some case studies follow only one strategy of case selection. They are typical , diverse , extreme , deviant , influential , crucial , pathway , most‐similar , or most‐different research designs, as discussed. However, many case studies mix and match among these case‐selection strategies. Indeed, insofar as all case studies seek representative samples, they are always in search of “typical” cases. Thus, it is common for writers to declare that their case is, for example, both extreme and typical; it has an extreme value on X   1 or Y but is not, in other respects, idiosyncratic. There is not much that one can say about these combinations of strategies except that, where the cases allow for a variety of empirical strategies, there is no reason not to pursue them. And where the same cases can serve several functions at once (without further effort on the researcher's part), there is little cost to a multi‐pronged approach to case analysis.

The second issue that deserves emphasis is the changing status of a case during the course of a researcher's investigation—which may last for years, if not decades. The problem is acute wherever a researcher begins in an exploratory mode and proceeds to hypothesis‐testing (that is, she develops a specific X   1 / Y proposition) or where the operative hypothesis or key control variable changes (a new causal factor is discovered or another outcome becomes the focus of analysis). Things change. And it is the mark of a good researcher to keep her mind open to new evidence and new insights. Too often, methodological discussions give the misleading impression that hypotheses are clear and remain fixed over the course of a study's development. Nothing could be further from the truth. The unofficial transcripts of academia— accessible in informal settings, where researchers let their guards down (particularly if inebriated)—are filled with stories about dead‐ends, unexpected findings, and drastically revised theory chapters. It would be interesting, in this vein, to compare published work with dissertation prospectuses and fellowship applications. I doubt if the correlation between these two stages of research is particularly strong.

Research, after all, is about discovery, not simply the verification or falsification of static hypotheses. That said, it is also true that research on a particular topic should move from hypothesis generating to hypothesis‐testing. This marks the progress of a field, and of a scholar's own work. As a rule, research that begins with an open‐ended ( X ‐ or Y ‐centered) analysis should conclude with a determinate X   1 / Y hypothesis.

The problem is that research strategies that are ideal for exploration are not always ideal for confirmation. The extreme‐case method is inherently exploratory since there is no clear causal hypothesis; the researcher is concerned merely to explore variation on a single dimension ( X or Y ). Other methods can be employed in either an open‐ ended (exploratory) or a hypothesis‐testing (confirmatory/disconfirmatory) mode. The difficulty is that once the researcher has arrived at a determinate hypothesis the originally chosen research design may no longer appear to be so well designed.

This is unfortunate, but inevitable. One cannot construct the perfect research design until (a) one has a specific hypothesis and (b) one is reasonably certain about what one is going to find “out there” in the empirical world. This is particularly true of observational research designs, but it also applies to many experimental research designs: Usually, there is a “good” (informative) finding, and a finding that is less insightful. In short, the perfect case‐study research design is usually apparent only ex post facto .

There are three ways to handle this. One can explain, straightforwardly, that the initial research was undertaken in an exploratory fashion, and therefore not constructed to test the specific hypothesis that is—now—the primary argument. Alternatively, one can try to redesign the study after the new (or revised) hypothesis has been formulated. This may require additional field research or perhaps the integration of additional cases or variables that can be obtained through secondary sources or through consultation of experts. A final approach is to simply jettison, or de‐emphasize, the portion of research that no longer addresses the (revised) key hypothesis. A three‐case study may become a two‐case study, and so forth. Lost time and effort are the costs of this downsizing.

In the event, practical considerations will probably determine which of these three strategies, or combinations of strategies, is to be followed. (They are not mutually exclusive.) The point to remember is that revision of one's cross‐case research design is normal and perhaps to be expected. Not all twists and turns on the meandering trail of truth can be anticipated.

12 Are There Other Methods of Case Selection?

At the outset of this chapter I summarized the task of case selection as a matter of achieving two objectives: representativeness (typicality) and variation (causal leverage). Evidently, there are other objectives as well. For example, one wishes to identify cases that are independent of each other. If chosen cases are affected by each other (sometimes known as Galton's problem or a problem of diffusion), this problem must be corrected before analysis can take place. I have neglected this issue because it is usually apparent to the researcher and, in any case, there are no simple techniques that might be utilized to correct for such biases. (For further discussion of this and other factors impinging upon case selection see Gerring 2001 , 178–81.)

I have also disregarded pragmatic/logistical issues that might affect case selection. Evidently, case selection is often influenced by a researcher's familiarity with the language of a country, a personal entrée into that locale, special access to important data, or funding that covers one archive rather than another. Pragmatic considerations are often—and quite rightly—decisive in the case‐selection process.

A final consideration concerns the theoretical prominence of a particular case within the literature on a subject. Researchers are sometimes obliged to study cases that have received extensive attention in previous studies. These are sometimes referred to as “paradigmatic” cases or “exemplars” ( Flyvbjerg 2004 , 427).

However, neither pragmatic/logistical utility nor theoretical prominence qualifies as a methodological factor in case selection. That is, these features of a case have no bearing on the validity of the findings stemming from a study. As such, it is appropriate to grant these issues a peripheral status in this chapter.

One final caveat must be issued. While it is traditional to distinguish among the tasks of case selection and case analysis, a close look at these processes shows them to be indistinct and overlapping. One cannot choose a case without considering the sort of analysis that it might be subjected to, and vice versa. Thus, the reader should consider choosing cases by employing the nine techniques laid out in this chapter along with any considerations that might be introduced by virtue of a case's quasi‐experimental qualities, a topic taken up elsewhere ( Gerring 2007 , ch. 6 ).

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Gujarati (2003) ; Kennedy (2003) . Interestingly, the potential of cross‐case statistics in helping to choose cases for in‐depth analysis is recognized in some of the earliest discussions of the case‐study method (e.g. Queen 1928 , 226).

This expands on Mill (1843/1872 , 253), who wrote of scientific enquiry as twofold: “either inquiries into the cause of a given effect or into the effects or properties of a given cause.”

This method has not received much attention on the part of qualitative methodologists; hence, the absence of a generally recognized name. It bears some resemblance to J. S. Mill's Joint Method of Agreement and Difference ( Mill 1843/1872 ), which is to say a mixture of most‐similar and most‐different analysis, as discussed below. Patton (2002 , 234) employs the concept of “maximum variation (heterogeneity) sampling.”

More precisely, George and Smoke (1974 , 534, 522–36, ch. 18 ; see also discussion in Collier and Mahoney 1996 , 78) set out to investigate causal pathways and discovered, through the course of their investigation of many cases, these three causal types. Yet, for our purposes what is important is that the final sample includes at least one representative of each “type.”

For further examples see Collier and Mahoney (1996) ; Geddes (1990) ; Tendler (1997) .

Traditionally, methodologists have conceptualized cases as having “positive” or “negative” values (e.g. Emigh 1997 ; Mahoney and Goertz 2004 ; Ragin 2000 , 60; 2004 , 126).

Geddes (1990) ; King, Keohane, and Verba (1994) . See also discussion in Brady and Collier (2004) ; Collier and Mahoney (1996) ; Rogowski (1995) .

The exception would be a circumstance in which the researcher intends to disprove a deterministic argument ( Dion 1998 ).

Geddes (2003 , 131). For other examples of casework from the annals of medicine see “Clinical reports” in the Lancet , “Case studies” in Canadian Medical Association Journal , and various issues of the Journal of Obstetrics and Gynecology , often devoted to clinical cases (discussed in Jenicek 2001 , 7). For examples from the subfield of comparative politics see Kazancigil (1994) .

For a discussion of the important role of anomalies in the development of scientific theorizing see Elman (2003) ; Lakatos (1978) . For examples of deviant‐case research designs in the social sciences see Amenta (1991) ; Coppedge (2004) ; Eckstein (1975) ; Emigh (1997) ; Kendall and Wolf (1949/1955) .

For examples of the crucial‐case method see Bennett, Lepgold, and Unger (1994) ; Desch (2002) ; Goodin and Smitsman (2000) ; Kemp (1986) ; Reilly and Phillpot (2003) . For general discussion see George and Bennett (2005) ; Levy (2002) ; Stinchcombe (1968 , 24–8).

A third position, which purports to be neither Popperian or Bayesian, has been articulated by Mayo (1996 , ch. 6 ). From this perspective, the same idea is articulated as a matter of “severe tests.”

It should be noted that Tsai's conclusions do not rest solely on this crucial case. Indeed, she employs a broad range of methodological tools, encompassing case‐study and cross‐case methods.

See also the discussion in Eckstein (1975) and Lijphart (1969) . For additional examples of case studies disconfirming general propositions of a deterministic nature see Allen (1965); Lipset, Trow, and Coleman (1956) ; Njolstad (1990) ; Reilly (2000–1) ; and discussion in Dion (1998) ; Rogowski (1995) .

Granted, insofar as case‐study analysis provides a window into causal mechanisms, and causal mechanisms are integral to a given theory, a single case may be enlisted to confirm or disconfirm a proposition. However, if the case study upholds a posited pattern of X/Y covariation, and finds fault only with the stipulated causal mechanism, it would be more accurate to say that the study forces the reformulation of a given theory, rather than its confirmation or disconfirmation. See further discussion in the following section.

Sometimes, the most‐similar method is known as the “method of difference,” after its inventor ( Mill 1843/1872 ). For later treatments see Cohen and Nagel (1934) ; Eggan (1954) ; Gerring (2001 , ch. 9 ); Lijphart (1971 ; 1975) ; Meckstroth (1975) ; Przeworski and Teune (1970) ; Skocpol and Somers (1980) .

For good introductions see Ho et al. (2004) ; Morgan and Harding (2005) ; Rosenbaum (2004) ; Rosenbaum and Silber (2001) . For a discussion of matching procedures in Stata see Abadie et al. (2001) .

The most‐different method is also sometimes referred to as the “method of agreement,” following its inventor, J. S. Mill (1843/1872) . See also De Felice (1986) ; Gerring (2001 , 212–14); Lijphart (1971 ; 1975) ; Meckstroth (1975) ; Przeworski and Teune (1970) ; Skocpol and Somers (1980) . For examples of this method see Collier and Collier (1991/2002) ; Converse and Dupeux (1962) ; Karl (1997) ; Moore (1966) ; Skocpol (1979) ; Yashar (2005 , 23). However, most of these studies are described as combining most‐similar and most‐different methods.

In the following discussion I treat the terms social capital, civil society, and civic engagement interchangeably.

E.g. Collier and Collier (1991/2002) ; Karl (1997) ; Moore (1966) ; Skocpol (1979) ; Yashar (2005 , 23). Karl (1997) , which affects to be a most‐different system analysis (20), is a particularly clear example of this. Her study, focused ostensibly on petro‐states (states with large oil reserves), makes two sorts of inferences. The first concerns the (usually) obstructive role of oil in political and economic development. The second sort of inference concerns variation within the population of petro‐states, showing that some countries (e.g. Norway, Indonesia) manage to avoid the pathologies brought on elsewhere by oil resources. When attempting to explain the constraining role of oil on petro‐states, Karl usually relies on contrasts between petro‐states and nonpetro‐states (e.g. ch. 10 ). Only when attempting to explain differences among petro‐states does she restrict her sample to petro‐states. In my opinion, very little use is made of the most‐different research design.

This was recognized, at least implicitly, by Mill (1843/1872 , 258–9). Skepticism has been echoed by methodologists in the intervening years (e.g. Cohen and Nagel 1934 , 251–6; Gerring 2001 ; Skocpol and Somers 1980 ). Indeed, explicit defenses of the most‐different method are rare (but see De Felice 1986 ).

Another way of stating this is to say that X is a “nontrivial necessary condition” of Y .

Wahlke (1979 , 13) writes of the failings of the “behavioralist” mode of political science analysis: “It rarely aims at generalization; research efforts have been confined essentially to case studies of single political systems, most of them dealing …with the American system.”

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Organizing Your Social Sciences Research Assignments

• Annotated Bibliography
• Analyzing a Scholarly Journal Article
• Group Presentations
• Dealing with Nervousness
• Using Visual Aids
• Grading Someone Else's Paper
• Types of Structured Group Activities
• Group Project Survival Skills
• Leading a Class Discussion
• Multiple Book Review Essay
• Reviewing Collected Works
• Writing a Case Analysis Paper
• Writing a Case Study
• About Informed Consent
• Writing Field Notes
• Writing a Policy Memo
• Writing a Reflective Paper
• Writing a Research Proposal
• Generative AI and Writing
• Acknowledgments

A case study research paper examines a person, place, event, condition, phenomenon, or other type of subject of analysis in order to extrapolate  key themes and results that help predict future trends, illuminate previously hidden issues that can be applied to practice, and/or provide a means for understanding an important research problem with greater clarity. A case study research paper usually examines a single subject of analysis, but case study papers can also be designed as a comparative investigation that shows relationships between two or more subjects. The methods used to study a case can rest within a quantitative, qualitative, or mixed-method investigative paradigm.

Case Studies. Writing@CSU. Colorado State University; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010 ; “What is a Case Study?” In Swanborn, Peter G. Case Study Research: What, Why and How? London: SAGE, 2010.

How to Approach Writing a Case Study Research Paper

General information about how to choose a topic to investigate can be found under the " Choosing a Research Problem " tab in the Organizing Your Social Sciences Research Paper writing guide. Review this page because it may help you identify a subject of analysis that can be investigated using a case study design.

However, identifying a case to investigate involves more than choosing the research problem . A case study encompasses a problem contextualized around the application of in-depth analysis, interpretation, and discussion, often resulting in specific recommendations for action or for improving existing conditions. As Seawright and Gerring note, practical considerations such as time and access to information can influence case selection, but these issues should not be the sole factors used in describing the methodological justification for identifying a particular case to study. Given this, selecting a case includes considering the following:

• The case represents an unusual or atypical example of a research problem that requires more in-depth analysis? Cases often represent a topic that rests on the fringes of prior investigations because the case may provide new ways of understanding the research problem. For example, if the research problem is to identify strategies to improve policies that support girl's access to secondary education in predominantly Muslim nations, you could consider using Azerbaijan as a case study rather than selecting a more obvious nation in the Middle East. Doing so may reveal important new insights into recommending how governments in other predominantly Muslim nations can formulate policies that support improved access to education for girls.
• The case provides important insight or illuminate a previously hidden problem? In-depth analysis of a case can be based on the hypothesis that the case study will reveal trends or issues that have not been exposed in prior research or will reveal new and important implications for practice. For example, anecdotal evidence may suggest drug use among homeless veterans is related to their patterns of travel throughout the day. Assuming prior studies have not looked at individual travel choices as a way to study access to illicit drug use, a case study that observes a homeless veteran could reveal how issues of personal mobility choices facilitate regular access to illicit drugs. Note that it is important to conduct a thorough literature review to ensure that your assumption about the need to reveal new insights or previously hidden problems is valid and evidence-based.
• The case challenges and offers a counter-point to prevailing assumptions? Over time, research on any given topic can fall into a trap of developing assumptions based on outdated studies that are still applied to new or changing conditions or the idea that something should simply be accepted as "common sense," even though the issue has not been thoroughly tested in current practice. A case study analysis may offer an opportunity to gather evidence that challenges prevailing assumptions about a research problem and provide a new set of recommendations applied to practice that have not been tested previously. For example, perhaps there has been a long practice among scholars to apply a particular theory in explaining the relationship between two subjects of analysis. Your case could challenge this assumption by applying an innovative theoretical framework [perhaps borrowed from another discipline] to explore whether this approach offers new ways of understanding the research problem. Taking a contrarian stance is one of the most important ways that new knowledge and understanding develops from existing literature.
• The case provides an opportunity to pursue action leading to the resolution of a problem? Another way to think about choosing a case to study is to consider how the results from investigating a particular case may result in findings that reveal ways in which to resolve an existing or emerging problem. For example, studying the case of an unforeseen incident, such as a fatal accident at a railroad crossing, can reveal hidden issues that could be applied to preventative measures that contribute to reducing the chance of accidents in the future. In this example, a case study investigating the accident could lead to a better understanding of where to strategically locate additional signals at other railroad crossings so as to better warn drivers of an approaching train, particularly when visibility is hindered by heavy rain, fog, or at night.
• The case offers a new direction in future research? A case study can be used as a tool for an exploratory investigation that highlights the need for further research about the problem. A case can be used when there are few studies that help predict an outcome or that establish a clear understanding about how best to proceed in addressing a problem. For example, after conducting a thorough literature review [very important!], you discover that little research exists showing the ways in which women contribute to promoting water conservation in rural communities of east central Africa. A case study of how women contribute to saving water in a rural village of Uganda can lay the foundation for understanding the need for more thorough research that documents how women in their roles as cooks and family caregivers think about water as a valuable resource within their community. This example of a case study could also point to the need for scholars to build new theoretical frameworks around the topic [e.g., applying feminist theories of work and family to the issue of water conservation].

Eisenhardt, Kathleen M. “Building Theories from Case Study Research.” Academy of Management Review 14 (October 1989): 532-550; Emmel, Nick. Sampling and Choosing Cases in Qualitative Research: A Realist Approach . Thousand Oaks, CA: SAGE Publications, 2013; Gerring, John. “What Is a Case Study and What Is It Good for?” American Political Science Review 98 (May 2004): 341-354; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Seawright, Jason and John Gerring. "Case Selection Techniques in Case Study Research." Political Research Quarterly 61 (June 2008): 294-308.

Structure and Writing Style

The purpose of a paper in the social sciences designed around a case study is to thoroughly investigate a subject of analysis in order to reveal a new understanding about the research problem and, in so doing, contributing new knowledge to what is already known from previous studies. In applied social sciences disciplines [e.g., education, social work, public administration, etc.], case studies may also be used to reveal best practices, highlight key programs, or investigate interesting aspects of professional work.

In general, the structure of a case study research paper is not all that different from a standard college-level research paper. However, there are subtle differences you should be aware of. Here are the key elements to organizing and writing a case study research paper.

I.  Introduction

As with any research paper, your introduction should serve as a roadmap for your readers to ascertain the scope and purpose of your study . The introduction to a case study research paper, however, should not only describe the research problem and its significance, but you should also succinctly describe why the case is being used and how it relates to addressing the problem. The two elements should be linked. With this in mind, a good introduction answers these four questions:

• What is being studied? Describe the research problem and describe the subject of analysis [the case] you have chosen to address the problem. Explain how they are linked and what elements of the case will help to expand knowledge and understanding about the problem.
• Why is this topic important to investigate? Describe the significance of the research problem and state why a case study design and the subject of analysis that the paper is designed around is appropriate in addressing the problem.
• What did we know about this topic before I did this study? Provide background that helps lead the reader into the more in-depth literature review to follow. If applicable, summarize prior case study research applied to the research problem and why it fails to adequately address the problem. Describe why your case will be useful. If no prior case studies have been used to address the research problem, explain why you have selected this subject of analysis.
• How will this study advance new knowledge or new ways of understanding? Explain why your case study will be suitable in helping to expand knowledge and understanding about the research problem.

Each of these questions should be addressed in no more than a few paragraphs. Exceptions to this can be when you are addressing a complex research problem or subject of analysis that requires more in-depth background information.

II.  Literature Review

The literature review for a case study research paper is generally structured the same as it is for any college-level research paper. The difference, however, is that the literature review is focused on providing background information and  enabling historical interpretation of the subject of analysis in relation to the research problem the case is intended to address . This includes synthesizing studies that help to:

• Place relevant works in the context of their contribution to understanding the case study being investigated . This would involve summarizing studies that have used a similar subject of analysis to investigate the research problem. If there is literature using the same or a very similar case to study, you need to explain why duplicating past research is important [e.g., conditions have changed; prior studies were conducted long ago, etc.].
• Describe the relationship each work has to the others under consideration that informs the reader why this case is applicable . Your literature review should include a description of any works that support using the case to investigate the research problem and the underlying research questions.
• Identify new ways to interpret prior research using the case study . If applicable, review any research that has examined the research problem using a different research design. Explain how your use of a case study design may reveal new knowledge or a new perspective or that can redirect research in an important new direction.
• Resolve conflicts amongst seemingly contradictory previous studies . This refers to synthesizing any literature that points to unresolved issues of concern about the research problem and describing how the subject of analysis that forms the case study can help resolve these existing contradictions.
• Point the way in fulfilling a need for additional research . Your review should examine any literature that lays a foundation for understanding why your case study design and the subject of analysis around which you have designed your study may reveal a new way of approaching the research problem or offer a perspective that points to the need for additional research.
• Expose any gaps that exist in the literature that the case study could help to fill . Summarize any literature that not only shows how your subject of analysis contributes to understanding the research problem, but how your case contributes to a new way of understanding the problem that prior research has failed to do.
• Locate your own research within the context of existing literature [very important!] . Collectively, your literature review should always place your case study within the larger domain of prior research about the problem. The overarching purpose of reviewing pertinent literature in a case study paper is to demonstrate that you have thoroughly identified and synthesized prior studies in relation to explaining the relevance of the case in addressing the research problem.

III.  Method

In this section, you explain why you selected a particular case [i.e., subject of analysis] and the strategy you used to identify and ultimately decide that your case was appropriate in addressing the research problem. The way you describe the methods used varies depending on the type of subject of analysis that constitutes your case study.

If your subject of analysis is an incident or event . In the social and behavioral sciences, the event or incident that represents the case to be studied is usually bounded by time and place, with a clear beginning and end and with an identifiable location or position relative to its surroundings. The subject of analysis can be a rare or critical event or it can focus on a typical or regular event. The purpose of studying a rare event is to illuminate new ways of thinking about the broader research problem or to test a hypothesis. Critical incident case studies must describe the method by which you identified the event and explain the process by which you determined the validity of this case to inform broader perspectives about the research problem or to reveal new findings. However, the event does not have to be a rare or uniquely significant to support new thinking about the research problem or to challenge an existing hypothesis. For example, Walo, Bull, and Breen conducted a case study to identify and evaluate the direct and indirect economic benefits and costs of a local sports event in the City of Lismore, New South Wales, Australia. The purpose of their study was to provide new insights from measuring the impact of a typical local sports event that prior studies could not measure well because they focused on large "mega-events." Whether the event is rare or not, the methods section should include an explanation of the following characteristics of the event: a) when did it take place; b) what were the underlying circumstances leading to the event; and, c) what were the consequences of the event in relation to the research problem.

If your subject of analysis is a person. Explain why you selected this particular individual to be studied and describe what experiences they have had that provide an opportunity to advance new understandings about the research problem. Mention any background about this person which might help the reader understand the significance of their experiences that make them worthy of study. This includes describing the relationships this person has had with other people, institutions, and/or events that support using them as the subject for a case study research paper. It is particularly important to differentiate the person as the subject of analysis from others and to succinctly explain how the person relates to examining the research problem [e.g., why is one politician in a particular local election used to show an increase in voter turnout from any other candidate running in the election]. Note that these issues apply to a specific group of people used as a case study unit of analysis [e.g., a classroom of students].

If your subject of analysis is a place. In general, a case study that investigates a place suggests a subject of analysis that is unique or special in some way and that this uniqueness can be used to build new understanding or knowledge about the research problem. A case study of a place must not only describe its various attributes relevant to the research problem [e.g., physical, social, historical, cultural, economic, political], but you must state the method by which you determined that this place will illuminate new understandings about the research problem. It is also important to articulate why a particular place as the case for study is being used if similar places also exist [i.e., if you are studying patterns of homeless encampments of veterans in open spaces, explain why you are studying Echo Park in Los Angeles rather than Griffith Park?]. If applicable, describe what type of human activity involving this place makes it a good choice to study [e.g., prior research suggests Echo Park has more homeless veterans].

If your subject of analysis is a phenomenon. A phenomenon refers to a fact, occurrence, or circumstance that can be studied or observed but with the cause or explanation to be in question. In this sense, a phenomenon that forms your subject of analysis can encompass anything that can be observed or presumed to exist but is not fully understood. In the social and behavioral sciences, the case usually focuses on human interaction within a complex physical, social, economic, cultural, or political system. For example, the phenomenon could be the observation that many vehicles used by ISIS fighters are small trucks with English language advertisements on them. The research problem could be that ISIS fighters are difficult to combat because they are highly mobile. The research questions could be how and by what means are these vehicles used by ISIS being supplied to the militants and how might supply lines to these vehicles be cut off? How might knowing the suppliers of these trucks reveal larger networks of collaborators and financial support? A case study of a phenomenon most often encompasses an in-depth analysis of a cause and effect that is grounded in an interactive relationship between people and their environment in some way.

NOTE:   The choice of the case or set of cases to study cannot appear random. Evidence that supports the method by which you identified and chose your subject of analysis should clearly support investigation of the research problem and linked to key findings from your literature review. Be sure to cite any studies that helped you determine that the case you chose was appropriate for examining the problem.

IV.  Discussion

The main elements of your discussion section are generally the same as any research paper, but centered around interpreting and drawing conclusions about the key findings from your analysis of the case study. Note that a general social sciences research paper may contain a separate section to report findings. However, in a paper designed around a case study, it is common to combine a description of the results with the discussion about their implications. The objectives of your discussion section should include the following:

Reiterate the Research Problem/State the Major Findings Briefly reiterate the research problem you are investigating and explain why the subject of analysis around which you designed the case study were used. You should then describe the findings revealed from your study of the case using direct, declarative, and succinct proclamation of the study results. Highlight any findings that were unexpected or especially profound.

Explain the Meaning of the Findings and Why They are Important Systematically explain the meaning of your case study findings and why you believe they are important. Begin this part of the section by repeating what you consider to be your most important or surprising finding first, then systematically review each finding. Be sure to thoroughly extrapolate what your analysis of the case can tell the reader about situations or conditions beyond the actual case that was studied while, at the same time, being careful not to misconstrue or conflate a finding that undermines the external validity of your conclusions.

Relate the Findings to Similar Studies No study in the social sciences is so novel or possesses such a restricted focus that it has absolutely no relation to previously published research. The discussion section should relate your case study results to those found in other studies, particularly if questions raised from prior studies served as the motivation for choosing your subject of analysis. This is important because comparing and contrasting the findings of other studies helps support the overall importance of your results and it highlights how and in what ways your case study design and the subject of analysis differs from prior research about the topic.

Consider Alternative Explanations of the Findings Remember that the purpose of social science research is to discover and not to prove. When writing the discussion section, you should carefully consider all possible explanations revealed by the case study results, rather than just those that fit your hypothesis or prior assumptions and biases. Be alert to what the in-depth analysis of the case may reveal about the research problem, including offering a contrarian perspective to what scholars have stated in prior research if that is how the findings can be interpreted from your case.

Acknowledge the Study's Limitations You can state the study's limitations in the conclusion section of your paper but describing the limitations of your subject of analysis in the discussion section provides an opportunity to identify the limitations and explain why they are not significant. This part of the discussion section should also note any unanswered questions or issues your case study could not address. More detailed information about how to document any limitations to your research can be found here .

Suggest Areas for Further Research Although your case study may offer important insights about the research problem, there are likely additional questions related to the problem that remain unanswered or findings that unexpectedly revealed themselves as a result of your in-depth analysis of the case. Be sure that the recommendations for further research are linked to the research problem and that you explain why your recommendations are valid in other contexts and based on the original assumptions of your study.

V.  Conclusion

As with any research paper, you should summarize your conclusion in clear, simple language; emphasize how the findings from your case study differs from or supports prior research and why. Do not simply reiterate the discussion section. Provide a synthesis of key findings presented in the paper to show how these converge to address the research problem. If you haven't already done so in the discussion section, be sure to document the limitations of your case study and any need for further research.

The function of your paper's conclusion is to: 1) reiterate the main argument supported by the findings from your case study; 2) state clearly the context, background, and necessity of pursuing the research problem using a case study design in relation to an issue, controversy, or a gap found from reviewing the literature; and, 3) provide a place to persuasively and succinctly restate the significance of your research problem, given that the reader has now been presented with in-depth information about the topic.

Consider the following points to help ensure your conclusion is appropriate:

• If the argument or purpose of your paper is complex, you may need to summarize these points for your reader.
• If prior to your conclusion, you have not yet explained the significance of your findings or if you are proceeding inductively, use the conclusion of your paper to describe your main points and explain their significance.
• Move from a detailed to a general level of consideration of the case study's findings that returns the topic to the context provided by the introduction or within a new context that emerges from your case study findings.

Note that, depending on the discipline you are writing in or the preferences of your professor, the concluding paragraph may contain your final reflections on the evidence presented as it applies to practice or on the essay's central research problem. However, the nature of being introspective about the subject of analysis you have investigated will depend on whether you are explicitly asked to express your observations in this way.

Problems to Avoid

Overgeneralization One of the goals of a case study is to lay a foundation for understanding broader trends and issues applied to similar circumstances. However, be careful when drawing conclusions from your case study. They must be evidence-based and grounded in the results of the study; otherwise, it is merely speculation. Looking at a prior example, it would be incorrect to state that a factor in improving girls access to education in Azerbaijan and the policy implications this may have for improving access in other Muslim nations is due to girls access to social media if there is no documentary evidence from your case study to indicate this. There may be anecdotal evidence that retention rates were better for girls who were engaged with social media, but this observation would only point to the need for further research and would not be a definitive finding if this was not a part of your original research agenda.

Failure to Document Limitations No case is going to reveal all that needs to be understood about a research problem. Therefore, just as you have to clearly state the limitations of a general research study , you must describe the specific limitations inherent in the subject of analysis. For example, the case of studying how women conceptualize the need for water conservation in a village in Uganda could have limited application in other cultural contexts or in areas where fresh water from rivers or lakes is plentiful and, therefore, conservation is understood more in terms of managing access rather than preserving access to a scarce resource.

Failure to Extrapolate All Possible Implications Just as you don't want to over-generalize from your case study findings, you also have to be thorough in the consideration of all possible outcomes or recommendations derived from your findings. If you do not, your reader may question the validity of your analysis, particularly if you failed to document an obvious outcome from your case study research. For example, in the case of studying the accident at the railroad crossing to evaluate where and what types of warning signals should be located, you failed to take into consideration speed limit signage as well as warning signals. When designing your case study, be sure you have thoroughly addressed all aspects of the problem and do not leave gaps in your analysis that leave the reader questioning the results.

Case Studies. Writing@CSU. Colorado State University; Gerring, John. Case Study Research: Principles and Practices . New York: Cambridge University Press, 2007; Merriam, Sharan B. Qualitative Research and Case Study Applications in Education . Rev. ed. San Francisco, CA: Jossey-Bass, 1998; Miller, Lisa L. “The Use of Case Studies in Law and Social Science Research.” Annual Review of Law and Social Science 14 (2018): TBD; Mills, Albert J., Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Putney, LeAnn Grogan. "Case Study." In Encyclopedia of Research Design , Neil J. Salkind, editor. (Thousand Oaks, CA: SAGE Publications, 2010), pp. 116-120; Simons, Helen. Case Study Research in Practice . London: SAGE Publications, 2009;  Kratochwill,  Thomas R. and Joel R. Levin, editors. Single-Case Research Design and Analysis: New Development for Psychology and Education .  Hilldsale, NJ: Lawrence Erlbaum Associates, 1992; Swanborn, Peter G. Case Study Research: What, Why and How? London : SAGE, 2010; Yin, Robert K. Case Study Research: Design and Methods . 6th edition. Los Angeles, CA, SAGE Publications, 2014; Walo, Maree, Adrian Bull, and Helen Breen. “Achieving Economic Benefits at Local Events: A Case Study of a Local Sports Event.” Festival Management and Event Tourism 4 (1996): 95-106.

Writing Tip

At Least Five Misconceptions about Case Study Research

Social science case studies are often perceived as limited in their ability to create new knowledge because they are not randomly selected and findings cannot be generalized to larger populations. Flyvbjerg examines five misunderstandings about case study research and systematically "corrects" each one. To quote, these are:

Misunderstanding 1 :  General, theoretical [context-independent] knowledge is more valuable than concrete, practical [context-dependent] knowledge. Misunderstanding 2 :  One cannot generalize on the basis of an individual case; therefore, the case study cannot contribute to scientific development. Misunderstanding 3 :  The case study is most useful for generating hypotheses; that is, in the first stage of a total research process, whereas other methods are more suitable for hypotheses testing and theory building. Misunderstanding 4 :  The case study contains a bias toward verification, that is, a tendency to confirm the researcher’s preconceived notions. Misunderstanding 5 :  It is often difficult to summarize and develop general propositions and theories on the basis of specific case studies [p. 221].

While writing your paper, think introspectively about how you addressed these misconceptions because to do so can help you strengthen the validity and reliability of your research by clarifying issues of case selection, the testing and challenging of existing assumptions, the interpretation of key findings, and the summation of case outcomes. Think of a case study research paper as a complete, in-depth narrative about the specific properties and key characteristics of your subject of analysis applied to the research problem.

Flyvbjerg, Bent. “Five Misunderstandings About Case-Study Research.” Qualitative Inquiry 12 (April 2006): 219-245.

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Writing a Case Study

What is a case study?

A Case study is: 

• An in-depth research design that primarily uses a qualitative methodology but sometimes​​ includes quantitative methodology.
• Used to examine an identifiable problem confirmed through research.
• Used to investigate an individual, group of people, organization, or event.
• Used to mostly answer "how" and "why" questions.

What are the different types of case studies?

Note: These are the primary case studies. As you continue to research and learn

about case studies you will begin to find a robust list of different types. 

Who are your case study participants?

What is triangulation ? 

Validity and credibility are an essential part of the case study. Therefore, the researcher should include triangulation to ensure trustworthiness while accurately reflecting what the researcher seeks to investigate.

How to write a Case Study?

When developing a case study, there are different ways you could present the information, but remember to include the five parts for your case study.

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Research Article

Spatial analysis of digital economy and its driving factors: A case study of the Yangtze River Delta City Cluster in China

Roles Conceptualization, Funding acquisition, Methodology, Writing – original draft

* E-mail: [email protected]

Affiliation School of Economics and Management, Ningbo University of Technology, Ningbo, Zhejiang, China

Roles Formal analysis, Investigation

Roles Data curation, Resources

Affiliation College of Information and Intelligence Engineering, Zhejiang Wanli University, Ningbo, China

• Haidong Zhong, 
• Bifeng Wang, 
• Shaozhong Zhang

• Published: May 29, 2024
• https://doi.org/10.1371/journal.pone.0300443
• Reader Comments

The digital economy (DE) has become a major breakthrough in promoting industrial upgrading and an important engine for high-quality economic growth. However, most studies have neglected the important driving effect of regional economic and social (RES) development on DE. In this paper, we discuss the mechanism of RES development promoting the development of DE, and establish a demand-driven regional DE development model to express the general idea. With the help of spatial analysis toolbox in ArcGIS software, the spatial development characteristics of DE in the Yangtze River Delta City Cluster (YRDCC) is explored. We find the imbalance of spatial development is very significant in YRDCC, no matter at the provincial level or city level. Quantitative analysis reveals that less than 1% likelihood that the imbalanced or clustered pattern of DE development in YRDCC could be the result of random chance. Geographically weighted regression (GWR) analysis with publicly available dataset of YRDCC indicates RES development significantly promotes the development of DE.

Citation: Zhong H, Wang B, Zhang S (2024) Spatial analysis of digital economy and its driving factors: A case study of the Yangtze River Delta City Cluster in China. PLoS ONE 19(5): e0300443. https://doi.org/10.1371/journal.pone.0300443

Editor: Liang Zhuang, East China Normal University, CHINA

Received: October 22, 2023; Accepted: February 28, 2024; Published: May 29, 2024

Copyright: © 2024 Zhong et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The RES development related indicators for the cities in YRDCC are collected from Shanghai Statistical Yearbook ( https://tjj.sh.gov.cn/tjnj/index.html ) Zhejiang Statistical Yearbook ( https://tjj.zj.gov.cn/col/col1525563/index.html ), Jiangsu Statistical Yearbook ( http://tj.jiangsu.gov.cn/col/col89815/index.html ), and Anhui Statistical Yearbook ( http://tjj.ah.gov.cn/ssah/qwfbjd/tjnj/index.html ). Maps of administrative divisions and urban boundaries in China are downloaded from GaryBikini (ChinaAdminDivisonSHP:v23.01.04, 2023, DOI: 10.5281/zenodo.7503181 ) All the data used in the manuscript is publicly available and the URLs are annotated accordingly. CCCDEI data is included in Supporting Information files.

Funding: The Scientific Research Startup Fund of Ningbo University of Technology in 2022 (Grant No. 2022KQ32), the Zhejiang Soft Science Research Program (Grant No. 2023C35112) and the National Statistical Science Research Program of China (Grant No. 2022LY069). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

1. Introduction

With the wide application of information technologies, such as the Internet, wireless communication and artificial intelligence, the importance of DE is being promoted to a very high level. Early in 1998, the U.S. Department of Commerce released a report called the Emerging Digital Economy [ 1 ]. Subsequently, the U. S., Japan, Singapore, France and many other countries around the world have introduced DE strategies. For example, in 2016, the United States released the National Artificial Intelligence Research and Development Strategic Plan, and Germany released the Digital Strategy 2025 [ 2 ]. In 2022, the total DE of the top five economies in the world was 31 trillion US dollars, account for 58% of Gross Domestic Product (GDP), and an increase of about 11 percentage points over 2016 [ 3 ]. At present, DE has become an important strategic direction for many countries and a key force driving global economic growth.

In 2017, the Chinese government officially put forward the concept of DE in the Government Work Report, and then it booms in the nation. In recent years, the government departments at all levels in China have issued many policies and regulations to support the development of DE, and basically formed a sound policy system that combines the long-term planning goals of DE with detailed local promotion measures. According the report released by the China Communications Academy in 2023, the total amount of DE in China was 50.2 trillion yuan in the former year, and the nominal growth rate year-on-year reached up to 10.3%, which was significantly higher than GDP growth rate for 11 consecutive years [ 4 ]. Meanwhile, the proportion of DE in GDP is equivalent to the proportion of secondary industry in the national economy, reaching 41.5%. All these indicate the significant role of DE in driving China’s economic development.

Through the deep integration of DE and real economy with digital technology, most scholars believe that the overall economy and society can achieve continuous improvement and development in cost, efficiency, quality and scope [ 5 , 6 ]. There are lots of research results on the positive role of the DE in boosting the mobility of production factors, reducing transaction costs, stimulating consumption potential, promoting innovation, and RES development [ 7 , 8 ]. However, there are still the following two aspects need to be further explored: first, most scholars have paid much attention to the driving effect of DE on RES development, but little effort has been placed on the impact of the latter on the former, and second, YRDCC is a leading region in the development of DE in China, however, few studies have focused on spatial pattern and its driving factors of DE development in the region.

In this paper, we discuss the internal logic that RES development promoting the development of DE, and establish a conceptual model to represent the whole idea in detail. Possible contribution of the paper lies in the following three aspects:

• The mechanism of RES development promoting the development of DE is explored, and a demand-driven regional DE development model is proposed.
• Based on publicly available and authoritative DE development evaluation indicators, the spatial pattern of DE development in YRDCC is analyzed intensively.
• With the help of GWR analysis tools in ArcGIS software, driving factors of DE development in YRDCC is investigated quantitatively, and the promoting effect of RES development on DE is verified accordingly.

The rest of the paper is structured as follows: In the following chapter, prior literature, such as the concept, connotation and evaluation index system of DE, spatial analysis of DE, and factors affecting the development of DE are reviewed. In Chapter 3, we establish and explain the theoretical model of RES development promoting the development of DE. Chapter 4 describes study area, data sources and research methods in detail. In Chapter 5, we investigate the spatial pattern of DE development in YRDCC. In Chapter 6, we take YRDCC as an example to conduct the empirical study on the relationship between RES and DE development with spatial analysis. Finally, we conclude the paper with shortcomings and future work in the last chapter.

2. Literature review

2.1. definition and connotation of de.

The statement DE first appears in a book named Digital Economy [ 9 ]. In the book, DE is described as an all-encompassing lifestyle created by the advances in human communication, computing (computers, software, services), and content (publishing, entertainment, and information providers) in the Internet age. Up to now, there is no consensus among academics on the definition of DE. Some scholars define it as an economic form that uses modern information technology to digitize business processes and business activities in various industries [ 10 ]. And other scholars believe that DE is a new economic format based on network communication, artificial intelligence, big data, etc., taking data as the core production factor to realizing the collaboration and integration between data and traditional production factors [ 8 , 11 ]. Currently, the most widely accepted definition of DE appears in the set out of the G20 Digital Economy Development and Cooperation Initiative : “ A series of economic activities that use digital knowledge and information as key production factors, modern information networks as an important carrier, and the effective use of information and communication technologies as an important driving force for improving efficiency and optimizing economic structure” [ 12 ].

Compared with the traditional economy, DE is regarded as a new economic form which is based on information technology. With the help of different information technologies, various resource elements can flow freely and quickly, market players can restructure their organizational models, and a large number of market players can accelerate their integration to achieve cross-border development [ 11 ]. DE has undergone comprehensive changes in production factors, production relations and productivity. The changes that DE is likely to bring lies in the following three aspects [ 10 , 13 ]: (1) Digitalization. DE excavates social and economic activities through information systems, the Internet of Things (IoT) sensing, machine vision and other digital ways to form data, information and knowledge that can be recorded, stored and interactive. In this process, data becomes a new means of production and a key factor of production. (2) Networking. The collected data, information and knowledge can flow freely, seamlessly and comprehensively through the Internet, IoT and other network carriers. This may greatly change the traditional production relations, and (3) Intelligence. Realize automatic and intelligent data processing with IT systems, big data, cloud computing, artificial intelligence and other advanced information and communication technologies. This can make the efficiency of social and economic activities improve rapidly, and the social productivity increase exponentially.

2.2. Development evaluation of DE

At present, scholars have not reached a consensus, to evaluate the development level of DE, and many international organizations, government statistical agencies and scholars have proposed many different measurement methods. However, most of them measure the scale of DE by calculating its added value and construct digital economy index (DEI) based on other comprehensive evaluation indicators. Typically, the European Union published the Digital Economy and Society Index (DESI) annually to evaluate DE development for countries within the EU since 2014. DESI is calculated by thirty-one secondary indicators within five main aspects, such as broadband access, Internet application and so on [ 14 ]. The United States Department of Commerce Digital Economy Measurement Framework that includes the degree of digitalization in various sectors of the economy, the impact of digitalization in economic activities and output, the comprehensive influence of economic and social development related factors, and the monitoring of emerging digitalization areas [ 15 ]. The Organization for Economic Cooperation and Development DE measurement indicator, which includes 38 indicators with international comparability, such as broadband penetration, ICT equipment and applications [ 16 ].

In China, most of the DE development evaluations are issued by well-known enterprises or scientific research institutes. They usually refer to DE index released by China Academy of Information and Communications Technology ( http://www.caict.ac.cn/ ) and the "Internet +" DE index published by Tencent Group ( https://www.tencent.com/en-us/index.html ) [ 17 ]. For example, it is the case for the Global Digital Economy Competitiveness Index released by Shanghai Social Science Development Research ( https://english.sass.org.cn/ ), the China Central City Digital Economy Index (CCCDEI) released by H3C Group ( http://www.h3c.com/ ), and the China Digital Economy Index (CDEI) released the Caixin Insight Group ( https://www.caixinglobal.com/company-info/caixin-insight-group-172.html ) [ 18 ]. These kind of DE development evaluations usually utilize a lot of indicators that are not publically available or difficult to obtain. Also, there still many other published literatures evaluate the development level of the DE just based on publically available panel data. For example, DE evaluation indexes proposed by Ting, C. [ 19 ], Shuofeng, G. [ 20 ] and Bing⁃jie, S. [ 21 ]. However, compared with research institutions and government departments, the coverage of the DE evaluation index system established by scholars in academic papers is not so perfect. Data availability limitations may be one of the biggest challenges.

2.3 Spatial characteristics of DE development in China

In recent years, research on DE has become increasingly mature, more and more scholars pay attention to the spatial characteristics of DE development in China. With the extension of the connotation of DE, the studies are also expanding. At the regional level, Liu C., et al. analyzed the regional differences and dynamic evolution process of DE development through methods such as Kernel density and Dagum Gini coefficient [ 22 ]. They found that there were significant differences within and between the five major urban agglomerations, and there were gradient and multipolar development trends, showing an overall uneven distribution in China. At the provincial level, Wang B., et al. used interpolation simulation, Zipf order scale method, and geographic detector methods to analyze the spatial differentiation characteristics and influencing factors of DE in China. They found significant DE development differences exist in the eastern, central, western, and northeastern areas of the nation [ 23 ]; Zhang X. and Wu T. studied the spatial pattern of DE development in China with entropy and natural breakpoint methods. They found the development level of DE in the eastern area of China is much higher than the western area, and the unbalanced situation in provincial scale is also very significant [ 24 ]. At the municipal level, Zhong Y. and Mao W. explored the spatial distribution characteristics of DE development in China with spatial econometric models, and found there were significant differences between cities located in upstream and downstream of the Yangtze River Economic Belt [ 25 ]; Tian J., et al. analyzed the spatial differentiation pattern of DE development in Northeast China with multiple methods, such as the Thiel index and geographic detectors, and found that the overall development level of DE in Northeast China was relatively low, and the polarization of internal urban development was significant [ 26 ].

2.4. Relationship between RES and DE development

With the emergence of the digital wave in recent years, both academia and industry have realized that the rapid development of the DE has not only brought new growth points and driving forces to the global economy, but also played an increasingly important role in RES development [ 27 ]. A large number of studies have analyzed the positive effects of DE on RES development. Most of them believe that the development of DE can accelerate the cross-border integration of the local economy and enhance the overall competitiveness of the regional economy [ 28 , 29 ]. First of all, the development of information technology makes traditional industries more efficient, intelligent and automated, and promotes the upgrading and transformation of regional economies. Secondly, the development of DE is conducive to the advancement of urbanization process, and the popularization of digital technology and e-commerce can accelerate the speed of urbanization and promote the rapid development of urban economy and society. Finally, the development of DE can promote the development of education, technology and other industries, and improving the population quality and technical ability of the entire region [ 30 ]. In China, the development of DE is not only related to the economic and social development of the nation, but also an important means to promote the construction of a modern economic system and build a new national competitive advantage [ 28 ].

Most studies start from spatial perspective to find the factors that influence the spatial pattern of DE. The investigations reveal that information technology foundation, geographical region, economic level, and human capital have a significant impact on the spatial pattern and evolution of DE [ 20 ]. Over time, the impact of information technology foundation and human capital has become increasingly important, while the impact of geographical regions on DE has gradually weakened [ 31 – 33 ]. Still some other studies have shown that economic growth, foreign investment dependence, industrial structure optimization, government behavior, urbanization, and human capital have significant impact on regional DE development [ 11 , 34 , 35 ]. Overall, there are various indicators affecting the development of DE, however, relatively a few of them come from the perspective RES development.

3 The mechanism of RES development promoting the development of DE

There is very close relationship between RES development and the development of DE. Generally, the higher the level of RES development and the more efficient the governance of a region, the more perfect its digital infrastructure construction, the stronger policy support, and the higher the level of DE development. On the contrary, the lower the level of RES development and the less efficient governance in a region, the lower the level of information industry development and the fewer DE activities [ 36 ].

First of all, the development of RES directly contributes to consumption upgrading, industrial upgrading and technology upgrading [ 37 ]. Secondly, with the development of RES, people’s demands, such as efficiency improvement, individuation, precise matching, sustainable development, efficiency improving and cost saving will continue to emerge and upgrade [ 38 ]. And these will ultimately promote the development of DE. Following this approach, we establish a RES development promoting the development of DE model (as shown in Fig 1 ) based on the demand-driven theory [ 39 , 40 ]. In this model, we select commonly used indicators, such as retail sales of consumer goods, GDP, per capita GDP, industrial added value, household disposable income of urban residents, general public budget revenue, social investment in fixed assets, etc. to represent the development level of RES quantitatively. Meanwhile, industrial digitization, digital industrialization, DE development policy, digitization of urban governance, digitization of urban services, digital infrastructure development, etc. are selected as indicators to represent the level of DE development.

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https://doi.org/10.1371/journal.pone.0300443.g001

3.1 RES development promote consumption upgrading

As China moves toward high-quality development in recent years, the contribution of consumption to economic growth is increasing day by day [ 27 ]. However, most researches neglect the promoting effect of RES development on consumption upgrading. The promoting effect falls into the following two aspects: Firstly, RES development inevitably leads to an increase in product output and labor services, leading to the emergence of new industrial sectors and new commodities. This will expand consumers’ demand and the scope of consumption. Secondly, with the growth of RES and the increase of the GDP, per capita disposable income, household disposable income of urban residents, etc., people’s living standards and purchasing power will increase continuously, leading to an increase in the level of consumer demand. In the past, the commodities that may have been consumed were of relatively poor quality and low grade. Nevertheless, with the development of RES, people’s consumption of commodities will upgrade, which is manifested in higher demands for the commodities quality and optimization of the consumption structure.

3.2 RES development promote technology upgrading

It is generally believed that scientific and technological progress plays a very important role in RES development [ 41 ]. But the role of the latter in boosting the former has been underestimated for a long time. Firstly, RES development can bring a great many high-leveled skilled labor to gather and improve the overall regional human resource level. And the level of human capital somewhat determines the optimal allocation ability of labor force among industries and the type of technological progress. A lot of empirical evidence shows that different types of human capital have different effects on technological upgrading [ 27 , 42 ]. The more workers in a region with high labor proficiency, high technical and education levels, the more significant the effect of human capital on technological progress. Secondly, RES development provides capital for technological upgrading. The more developed a country’s economy, the more financial resources it can afford to support and promote technological progress. The experience of scientific and technological development of countries around the world shows that the regional distribution of research and development funds is closely related to a country’s level of economic and social development. In the early 1970s, developed countries, e.g., the UK, Germany, the former Soviet Union, former West Germany, Japan, the US, and France accounted for 85% of the world’s research and development expenditure, while developing countries in Africa and other regions only accounted for 3% [ 43 ].

3.3 RES development promote industrial upgrading

RES development provides the basic guarantee for the technological innovation of regional enterprises, the expansion of industrial scale, the adjustment of industrial structure and the necessary material basis for industrial upgrading. Firstly, regional economic development can prompt the government to enhance efficiency and introduce more policies conducive to enterprise innovation and upgrading, such as tax incentives and financial subsidies. This provides a good policy environment for the transformation and upgrading of enterprises. Secondly, economic growth triggers the promotion and improvement of regional education, medical care and infrastructure construction, and attract more high-end talents to gather. This provides an important human resource guarantee for industrial upgrading. Thirdly, with the development of economy, consumers’ demand for products and services continues to increase, and enterprises must improve product quality, reduce costs and optimize services through technological innovation, management innovation and other means to meet market demand. This provides a direct impetus for the transformation and upgrading of enterprises. Finally, RES development leads to the formation of a gradient development pattern between central cities and surrounding cities in the process of industrial transfer and docking, which promotes the optimal allocation of resources and the upgrading of industries [ 44 ]. The faster the regional economy develops, the faster the speed of technological progress and innovation, providing more opportunities for enterprises to transform and upgrade.

4. Study area, data sources and research methods

4.1. study area.

YRDCC lies at the heart of China’s eastern coast, where the Yangtze and Huai Rivers meet at the mouth of the sea (as shown in Fig 2 ). It is one of the six major city clusters, an important birthplace of China’s industry and commerce, famous manufacturing center in the world, and one of the regions with the most dynamic economy and the greatest growth potential in China [ 45 ]. YRDCC contains a total of 26 cities in three provinces and one city, covering an area of 21,700 square kilometers. Meanwhile, YRDCC is one of the regions in China with the best urbanization foundation, and rich natural and cultural resources. It is one of the important centers of China’s economic, cultural and social development, and a pioneering demonstration zone for China’s modernization and opening-up. YRDCC is also deemed as one of the main portals of Western culture into China, and the most international and modern regions in China [ 46 ].

https://doi.org/10.1371/journal.pone.0300443.g002

YRDCC is the most economically developed and urban agglomeration area in China. The overall economy of the region is large, with many strong enterprises and industrial clusters. There is also a relatively obvious hierarchical structure and functional division of labor among cities, such as Shanghai’s status as an international financial center and scientific and technological innovation center as a core city, Nanjing, Suzhou and other cities’ manufacturing and scientific and technological innovation capabilities, and Hangzhou’s DE and high-tech industrial advantages [ 47 ]. The economic hinterland of YRDCC is vast, with modern river and sea port clusters and airport clusters. The highway network is very sound, and the density of railway transportation trunk lines is leading in the country. In addition, YRDCC has about 1/4 of the country’s "double first-class" construction universities, and a large number of high-level scientific and technological talents [ 48 ].

4.2. Data sources

The dataset used in the research falls into the following four categories, their names and sources are detailed as follows:

• Basic geographic information data of YRDCC and China. This data is downloaded from GaryBikini (GaryBikini/ChinaAdminDivisonSHP:v23.01.04, 2023, DOI: 10.5281/zenodo.7503181 ). In this paper national, provincial, and municipal boundaries of the country are used to show the location of YRDCC (as shown in Fig 2 ).
• RES development related indicators for the cities in YRDCC. These indicators include permanent population, GDP, total retail sales of consumer goods, general budget revenue, per capita disposable income of urban residents, per capita GDP, etc. The data is collected from Shanghai Statistical Yearbook ( https://tjj.sh.gov.cn/tjnj/index.html ), Zhejiang Statistical Yearbook ( https://tjj.zj.gov.cn/col/col1525563/index.html ), Jiangsu Statistical Yearbook ( http://tj.jiangsu.gov.cn/col/col89815/index.html ), and Anhui Statistical Yearbook ( http://tjj.ah.gov.cn/ssah/qwfbjd/tjnj/index.html ).
• DE development index of cities in YRDCC. Based on the comprehensive considerations of authoritative and data availability, the paper uses CCCDEI, released by H3C Group ( http://www.h3c.com/cn/d_202011/1355635_30008_1.htm ), to measure the level of DE development of cities in YRDCC. CCCDEI consists of four primary indicators: data and information infrastructure, urban services, urban governance, and industrial integration; twelve secondary indicators, including information infrastructure, data infrastructure, and operational infrastructure, and so on; forty six tertiary indicators, including the penetration rate of fixed network broadband applications, the number of policies covering people’s livelihoods, the comprehensive index of industrial integration, etc. [ 49 ].

4.3. Research methods

A large number of existing studies have shown that geographical analysis has unique advantages in ecology, soil science, regional economics and other fields [ 50 , 51 ]. In this paper, global spatial autocorrelation (GSA) analysis method is used to explore the general regularity of spatial distribution of DE development in YRDCC, and local spatial autocorrelation (LSA) analysis approach is utilized to conduct an in-depth study. In addition, GWR analysis is utilized to find out the influencing factors of DE development in the region.

4.3.1 GSA analysis.

GSA focuses on analyzing the spatial distribution state and pattern of attribute values of spatial objects in the whole region, and the commonly used statistics is Moran’s I. It can reflect the similarity degree of the attribute values of units in adjacent or adjacent regions of space, and deemed as one of the most widely used statistics at present. There are two hypothesis testing methods for Moran’s I statistics: random distribution and approximate normal distribution [ 52 ].

4.3.2 LSA analysis.

The test premise of GSA is the hypothesis of regional homogeneity, but in reality, heterogeneity is more common. Additionally, the global optimal generally does not represent the local optimal. Similarly, the macro conclusions, cannot cover up some micro problems, and a high degree of global autocorrelation does not mean a high degree of local correlation. Therefore, we need a model that can explore and analyze spatial distribution on a more microscopic scale. LSA improves the Moran’s I model by breaking down the overall relationship to make each component can be calculated. Compared with GSA, LSA can better grasp the clustering and differentiation characteristics of local spatial elements by comparing the relationship between observed values and adjacent values, and the global [ 51 ]. LSA analysis can be used to test the cluster region, and verify the hot and cold spots where observations are clustered.

4.3.3 GWR analysis.

5. Spatial pattern of DE development in YRDCC

To reveal the spatial distribution characteristics of DE development in YRDCC, the research conducts a spatial analysis with 2018–2021 CCCDEI of YRDCC in ArcGIS pro 2.5.

5.1 DE development evaluation in YRDCC

To achieve regional collaborative progress and narrow regional differences, the 14th Five Year Plan for National Economic and Social Development of the People’s Republic of China and the Outline of Long Range Goals for 2035 ( https://www.ndrc.gov.cn/xxgk/zcfb/ghwb/202103/t20210323_1270124.html ) clearly point out "improving the level of integrated development in the Yangtze River Delta". As one of the regions with the most reasonable urban hierarchical structure, close external cooperation, leading digital transformation and innovative ecological in China, the Yangtze River Delta region open its arms to welcomes new opportunities for integrated development. However, due to the imbalanced development of policy orientation and resource endowment, the development level of DE in YRDCC varies significantly [ 57 ].

The CCCDEI does not provide provincial level DE development evaluation. We measure the DE development level of each province by averaging the CCCDEI of the cities under its jurisdiction, and the result is shown in Fig 3 . Overall, DE grows in all four provinces (provincial-level city) between 2018 and 2021, and DE development level in Shanghai is the highest, while Anhui province is the lowest. However, evaluating from the growth rate of the average CCCDEI for 2018–2021, the situation is quite different. Specifically, the growth rates in Anhui province is highest 39.9%, while Zhejiang province is the lowest 14.2%, during the same period. In recent years, China has been implementing the Yangtze River Delta integration strategy. However, there is a lot of room for improvement of DE development in Zhejiang, Anhui and Jiangsu provinces, and it is still urgent to narrow the regional gap to avoid the widening of the "digital divide".

https://doi.org/10.1371/journal.pone.0300443.g003

5.2 Spatiotemporal evolution of DE development in YRDCC

As can be seen from Fig 4 , the unbalanced and inadequate development of DE is a prominent problem, which is reflected in the low CCCDEI in most regions. The average value of Shanghai’s CCCDEI is nearly three times than that of Huaibei, Zhoushan, Quzhou and other cities. From 2018 to 2021, CCCDEI in four cities, Suqian, Huaibei, Tongling and Lianyungang, saw a growth rate of more than 70%. Although the four cities have large growth rates, the gap between them still significant.

https://doi.org/10.1371/journal.pone.0300443.g004

From the city level perspective, cities with high CCCDEI growth rate are mostly concentrated in the east of the Yangtze River Delta and coastal areas, while cities with low CCCDEI average growth rate are mostly concentrated in the western region. All these imply that the difference of DE development in YRDCC is difficult to be closed in a short time, and there is an obvious "Matthew effect" [ 58 ].

Fig 5 shows the spatial distribution of DE development in YRDCC displayed in graduated colors with the same color scheme and intervals. It indicates that the development level of DE in YRDCC has significant spatial heterogeneity from 2018 to 2021. On the whole, DE development level of cities in the east of YRDCC is relatively high, while in the west it is relatively low. Specifically, most cities under the jurisdiction of Anhui province have low DE development level. These cities include Bozhou city, Huaibei city, Xuancheng city, Fuyang city, Suzhou city, Chizhou city, Lu’an city, Huainan city, Huangshan city, Maanshan city, Chuzhou city, Bengbu city and Anqing city. Shanghai’s DE development has maintained at a relatively high level from 2018 to 2021, and this is also the case in most cities in Zhejiang province. However, there still many cities, such as Suzhou city, Huaibei city, Huainan city, Lishui city, Quanzhou city, Bozhou city, etc. have experienced a relative decline of DE development in the same period.

https://doi.org/10.1371/journal.pone.0300443.g005

5.3 Spatial correlation of DE development in YRDCC

To check whether spatial autocorrelation exists in the development of DE in YRDCC, we conduct the Global Moran’s I analysis with the help spatial analysis toolbox in ArcGIS pro, and the results are shown in Table 1 . The main parameters’ settings for the analysis are as follows: (1) Conceptualization of Spatial Relationships: Contiguity edges corners; (2) Distance method: Euclidean, and (3) Standardization: Row. It can be seen from Table 1 that the z-score values are greater than 2.58 in all years, while the p-value values less than 0.01. According to the spatial autocorrelation determination rules [ 59 ], there is a less than 1% likelihood that the clustered pattern of DE development in YRDCC could be the result of random chance.

https://doi.org/10.1371/journal.pone.0300443.t001

Based on the overall clustered pattern of DE development conclusion of the Global Moran’s I analysis, we try to conduct the Anselin Local Moran I analysis to find more accurate and specific results. The main parameters are set the same as the Global Moran’s I analysis in ArcGIS software, and the results are shown in Fig 6 . The results demonstrate that CCCDEI of cities in YRDCC presents a highly concentrated pattern in space. Specifically, there are two High-High clusters, where are DE well-developed hot places in the east of YDRCC from 2018 to 2021. One of the clusters is located in the northeast that contains four cities in Jiangsu province. They are Hangzhou city and Huzhou city in Zhejiang province, and Taizhou city and Suzhou city. The other cluster contains only one city, Shaoxing city in Zhejiang province.

https://doi.org/10.1371/journal.pone.0300443.g006

In 2018, 2019 and 2021, there are two Low-Low clusters, where are DE development cold places, and the clusters contain almost the same cities in the three years. From the analysis result of 2021, one of the Low-Low clusters in the northwest contains four cities in Anhui province. They are Bozhou city, Huaibei city, Bengbu city, Huainan city, and Fuyang city. While the other Low-Low cluster contains only one city, Chizhou city of the same province. Additionally, the High-High and Low-Low cluster areas have changed little between 2018 and 2021. It is still necessary to improve the market mechanism, cooperation mechanism, mutual assistance mechanism and support mechanism to narrow DE development gap between cities in the Yangtze River Delta at present.

There are few High-Low cluster areas, including only Hefei city in 2018 and 2019, which shows the level of DE development in the city is high, but its neighbor cities are low. The phenomenon of "polarization" is easily generated in High-Low cluster region. However, in the following two years, the agglomeration characteristics of Hefei city is not significant, showing an overall good DE development tendency.

6 Driving factors of DE development in YRDCC

6.1 construction of gwr analysis model.

To verify the rationality of the proposed demand-driven regional DE development model and explore the driving factors for the spatial pattern of DE development in YRDCC, we select city-level CCCDEI and RES development related indicators to establish the following GWR model (as shown in Formula ( 4 )). The analysis is completed with the help of GWR analysis toolkit in ArcGIS software. We set the model type to Continuous (Gaussian) and the local weighting scheme to Gaussian. The parameters in the model are explained in the Table 2 .

https://doi.org/10.1371/journal.pone.0300443.t002

Due to the impact of the COVID-19, from January 2020 to the end of 2022, many cities in the Yangtze River Delta region have implemented nucleic acid tests for all inhabitants and even closed down the city for many times. This had undoubtedly interrupted the normal operation of the economy and society to a certain extent, and lead to the distortion of various statistical data. Therefore, we select RES development related indicators and CCCDEI of YRDCC in 2019 to conduct the regression analysis, and the results are shown in Table 2 and Fig 7 .

https://doi.org/10.1371/journal.pone.0300443.g007

It can be found from Table 3 that AICc is greater than 3, R 2 is 0.8780 and the adjusted goodness of fit reaches 84.4%. These indicators reveal an overall reliability of the established GWR model, and significant impact of RES development of a city and its neighbors on the DE development in YRDCC.

https://doi.org/10.1371/journal.pone.0300443.t003

In addition, the standardized residual values of all the cities are within the range -2,5 to 2.5, except Suzhou city (as shown in Fig 7 ). It indicates the development level of DE in YRDCC not only has agglomeration characteristics in geographical space, but also the impact of RES development on DE development is geographically different. These are most likely caused by the factors such as differences in GDP, total retail sales of consumer goods, per capita gross regional product, general budget revenue, household disposable income of urban residents and added value of the tertiary industry between the cities in YRDCC.

When GWR analysis is performed in ArcGIS, an association coefficient report between the dependent variable and each independent variable is also generated. The association coefficient is identified by R 2 , and the result is shown in Table 4 . From this table, we can see that the R 2 values between CCCDEI and the independent indicators are all greater than 0.6, which proves RES development has significant role in promoting DE development from another side. However, the influence of each RES development related indicator on the development of DE is different. Measured by R 2 , general budget revenue has the highest goodness of fit, and total retail sales of consumer goods ranks the second. This could be because general budget revenue directly determines how much to invest in infrastructure related to DE, and the DE industry is an important part of the DE and the total retail sales of consumer goods. Relatively, added value of the tertiary industry has the least goodness of fit. The reason may be that tertiary industry includes many industries, for example, commerce, finance, services, agriculture and culture, and the added value created by DE accounts for only a small part of the added value of the tertiary industry.

https://doi.org/10.1371/journal.pone.0300443.t004

6.2 Analysis of spatial heterogeneity of influencing factors

With the help of ArcGIS for GWR analysis tool, regression analysis coefficients for each influencing factor can also be obtained. Based on the coefficients, the paper analyzes the spatial heterogeneity of the impact of various explanatory variables on the development of the DE in YRDCC, and we find there are significant spatial differences.

6.2.1. Gross domestic product.

Fig 8(A) indicates a significant positive correlation tendency between DE development and GDP in all the cities of YRDCC and the overall structure shows a decreasing circle structure from the outside to the inside. From the perspective of spatial heterogeneity, high and medium GDP coefficient values are concentrated in the south, north and east regions, and the cities with the highest GDP coefficient are Wenzhou city, Taizhou city, Lishui city, Quzhou city, Jinhua city, etc. While GDP coefficient low values are concentrated in the center area of YRDCC, and the cities with the lowest GDP coefficient values are Chuzhou city, Hefei city, Tongling city, Wuhu city, Xuancheng city, etc. Due to the differences in the economic bases, the increase in GDP of cities in the central region of YRDCC is more conducive to reduce the coefficient difference.

https://doi.org/10.1371/journal.pone.0300443.g008

6.2.2. Added value of the tertiary industry.

Fig 8(B) reveals an overall positive correlation tendency between DE development and added value of the tertiary industry, and the spatial distribution of added value of the tertiary industry coefficients is somewhat similar to Fig 8(A) . Specifically, high and medium coefficient values of added value of the tertiary industry are concentrated in the top and bottom of cities in YRDCC, while low coefficient values are located on the left and right sides. The lowest coefficient cities are Liuan city, Anqing city, Chizhou city, etc. Therefore, reducing the development level of the tertiary industry in YRDCC is one of the effective means to promote the coordinated development of DE in the region.

6.2.3. Per capita gross regional product.

Fig 8(C) also shows a significant positive correlation tendency between per capita gross regional product and DE development in all the cities of YRDCC. It implies the higher per capita gross regional product, the higher development level of DE, and this is consistent with existing research findings. On the whole, the spatial distribution of the per capita gross regional product coefficients reveals a gradually increasing trend from south to north. The highest per capita gross regional product coefficient values appear in the northwest region of YRDCC, where the lowest values appear in the southeast. Specifically, the lowest per capita gross regional product coefficient values are located in Lishui city, Wenzhou city, Taizhou city, Jinhua city, etc., and the highest values are located in Suzhou city, Suqian city, Bengbu city, Huaian city, etc. Therefore, vigorously developing regional economy to improve per capita gross regional product level is very important for the development of DE in YRDCC.

6.2.4. General budget revenue.

The impact of general budget revenue on the development of DE in YRDCC shows a negative correlation tendency in 19.51% of the cities (as shown in Fig 9(A)) . The cities include Quzhou city, Lishui city, Wenzhou city, Taizhou city, etc., which are mainly located in Zhejiang province. Meanwhile, there are 80.49% of cities with positive general budget revenue coefficient values, and the highest values appear in Xuzhou city, Lianyungang city, Suzhou city, Huaibei city, Suqian city, etc. The cities are mainly concentrated in Jiangsu province, and their CCCDEIs are relatively low. Therefore, improving general budget revenue level can also promote the development of DE for cities in YRDCC to a certain extent.

https://doi.org/10.1371/journal.pone.0300443.g009

6.2.5. Household disposable income of urban residents.

As can be found in Fig 9(B) , household disposable income of urban residents’ coefficient values of most cities are positively related to the development of DE in YRDCC. Specifically, 65.86% of the cities shows a positive correlation tendency, while the case for the other 34.14% cities is the opposite. This explains from another perspective that increase the per capita disposable income of urban residents leads to an increase development of DE. The cities with the lowest household disposable income of urban residents’ coefficient values mainly appear in northwest of Jiangsu province and northeast of Anhui province, such as Xuzhou city, Lianyungang city, Huaibei city, Bozhou city, etc. While the cities with the highest values are mainly located in Zhejiang province. These cities include Quzhou city, Lishui city, Taizhou city, Wenzhou city, etc.

6.2.6. Total retail sales of consumer goods.

The distribution of total retail sales of consumer goods coefficient values shows a gradually increasing trend from west to east (as shown in Fig 9(C)) . Concretely, the impact of total retail sales of consumer goods on DE development in 73.17% of cities indicates a positively tendency. On the whole, the cities with high of total retail sales of consumer goods coefficient values are mainly located in Anqing city, huangshan city, Quzhou city, Lishui city, etc. It implies the development level of DE in these cities is relatively significantly influenced by total retail sales of consumer goods. While the other 26.83% of cities with negative total retail sales of consumer goods coefficient values are generally concentrated in Yancheng city, Taizhou city, Nantong city, Suqian city, etc., which belongs to Jiangsu province.

7. Conclusions and future work

Based the existing research findings, the paper investigates the mechanism of RES development promoting the development of DE. To reveal their relationship, we propose a demand-driven regional DE development model. With publicly available dataset, we conduct spatial pattern analysis of DE development in YRDCC, and explore its driving factors. The specific conclusions of this paper are as follows:

First, the spatial imbalance of DE development in YRDCC is very obvious. At provincial scale, DE development level in Shanghai is the highest, while Anhui province is the lowest between 2018 and 2021. At city scale, cities with high DE indices are mostly concentrated in the east of the Yangtze River Delta and coastal areas, while cities with high average annual growth rates are mostly concentrated in the western region.

Second, there are DE development clusters in YRDCC. LSA analysis results indicate that there are two High-High clusters, where are DE well-developed hot places in YDRCC from 2018 to 2021, and two Low-Low clusters, where are DE development cold places at the same time. And GSA analysis results imply there is a less than 1% likelihood that the clustered pattern of DE development in YRDCC could be the result of random chance.

Third, RES development significantly affect DE development in YRDCC. The GWR analysis diagnostics report shows R 2 values between CCCDEI and the six RES development related indicators are all greater than 0.6. However, the influence of each indicator on the development of DE is geographically different. The quantitative spatial analysis proves RES development is a critical factor that promote the development of DE in YRDCC.

Due to data availability limitation, we collect CCCDEI and RES development related indicators of cities in YRDCC from 2018 to 2021 to conduct the spatial pattern analysis of DE development. The results may not fully represent the diversity of factors influencing the DE at a national or global scale. In the future, we plan to collect more data for consecutive years to carry out spatiotemporal evolution analysis of DE development in YRDCC. In addition, it is worth to collecting other district or county level DE development index to examine its driving factors in finer scale, and make the results more concrete and credible.

Supporting information

https://doi.org/10.1371/journal.pone.0300443.s001

Acknowledgments

We would like to thank the editors, the anonymous reviewers for their help and meaningful remarks.

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Distinguishing case study as a research method from case reports as a publication type

The purpose of this editorial is to distinguish between case reports and case studies. In health, case reports are familiar ways of sharing events or efforts of intervening with single patients with previously unreported features. As a qualitative methodology, case study research encompasses a great deal more complexity than a typical case report and often incorporates multiple streams of data combined in creative ways. The depth and richness of case study description helps readers understand the case and whether findings might be applicable beyond that setting.

Single-institution descriptive reports of library activities are often labeled by their authors as “case studies.” By contrast, in health care, single patient retrospective descriptions are published as “case reports.” Both case reports and case studies are valuable to readers and provide a publication opportunity for authors. A previous editorial by Akers and Amos about improving case studies addresses issues that are more common to case reports; for example, not having a review of the literature or being anecdotal, not generalizable, and prone to various types of bias such as positive outcome bias [ 1 ]. However, case study research as a qualitative methodology is pursued for different purposes than generalizability. The authors’ purpose in this editorial is to clearly distinguish between case reports and case studies. We believe that this will assist authors in describing and designating the methodological approach of their publications and help readers appreciate the rigor of well-executed case study research.

Case reports often provide a first exploration of a phenomenon or an opportunity for a first publication by a trainee in the health professions. In health care, case reports are familiar ways of sharing events or efforts of intervening with single patients with previously unreported features. Another type of study categorized as a case report is an “N of 1” study or single-subject clinical trial, which considers an individual patient as the sole unit of observation in a study investigating the efficacy or side effect profiles of different interventions. Entire journals have evolved to publish case reports, which often rely on template structures with limited contextualization or discussion of previous cases. Examples that are indexed in MEDLINE include the American Journal of Case Reports , BMJ Case Reports, Journal of Medical Case Reports, and Journal of Radiology Case Reports . Similar publications appear in veterinary medicine and are indexed in CAB Abstracts, such as Case Reports in Veterinary Medicine and Veterinary Record Case Reports .

As a qualitative methodology, however, case study research encompasses a great deal more complexity than a typical case report and often incorporates multiple streams of data combined in creative ways. Distinctions include the investigator’s definitions and delimitations of the case being studied, the clarity of the role of the investigator, the rigor of gathering and combining evidence about the case, and the contextualization of the findings. Delimitation is a term from qualitative research about setting boundaries to scope the research in a useful way rather than describing the narrow scope as a limitation, as often appears in a discussion section. The depth and richness of description helps readers understand the situation and whether findings from the case are applicable to their settings.

CASE STUDY AS A RESEARCH METHODOLOGY

Case study as a qualitative methodology is an exploration of a time- and space-bound phenomenon. As qualitative research, case studies require much more from their authors who are acting as instruments within the inquiry process. In the case study methodology, a variety of methodological approaches may be employed to explain the complexity of the problem being studied [ 2 , 3 ].

Leading authors diverge in their definitions of case study, but a qualitative research text introduces case study as follows:

Case study research is defined as a qualitative approach in which the investigator explores a real-life, contemporary bounded system (a case) or multiple bound systems (cases) over time, through detailed, in-depth data collection involving multiple sources of information, and reports a case description and case themes. The unit of analysis in the case study might be multiple cases (a multisite study) or a single case (a within-site case study). [ 4 ]

Methodologists writing core texts on case study research include Yin [ 5 ], Stake [ 6 ], and Merriam [ 7 ]. The approaches of these three methodologists have been compared by Yazan, who focused on six areas of methodology: epistemology (beliefs about ways of knowing), definition of cases, design of case studies, and gathering, analysis, and validation of data [ 8 ]. For Yin, case study is a method of empirical inquiry appropriate to determining the “how and why” of phenomena and contributes to understanding phenomena in a holistic and real-life context [ 5 ]. Stake defines a case study as a “well-bounded, specific, complex, and functioning thing” [ 6 ], while Merriam views “the case as a thing, a single entity, a unit around which there are boundaries” [ 7 ].

Case studies are ways to explain, describe, or explore phenomena. Comments from a quantitative perspective about case studies lacking rigor and generalizability fail to consider the purpose of the case study and how what is learned from a case study is put into practice. Rigor in case studies comes from the research design and its components, which Yin outlines as (a) the study’s questions, (b) the study’s propositions, (c) the unit of analysis, (d) the logic linking the data to propositions, and (e) the criteria for interpreting the findings [ 5 ]. Case studies should also provide multiple sources of data, a case study database, and a clear chain of evidence among the questions asked, the data collected, and the conclusions drawn [ 5 ].

Sources of evidence for case studies include interviews, documentation, archival records, direct observations, participant-observation, and physical artifacts. One of the most important sources for data in qualitative case study research is the interview [ 2 , 3 ]. In addition to interviews, documents and archival records can be gathered to corroborate and enhance the findings of the study. To understand the phenomenon or the conditions that created it, direct observations can serve as another source of evidence and can be conducted throughout the study. These can include the use of formal and informal protocols as a participant inside the case or an external or passive observer outside of the case [ 5 ]. Lastly, physical artifacts can be observed and collected as a form of evidence. With these multiple potential sources of evidence, the study methodology includes gathering data, sense-making, and triangulating multiple streams of data. Figure 1 shows an example in which data used for the case started with a pilot study to provide additional context to guide more in-depth data collection and analysis with participants.

Key sources of data for a sample case study

VARIATIONS ON CASE STUDY METHODOLOGY

Case study methodology is evolving and regularly reinterpreted. Comparative or multiple case studies are used as a tool for synthesizing information across time and space to research the impact of policy and practice in various fields of social research [ 9 ]. Because case study research is in-depth and intensive, there have been efforts to simplify the method or select useful components of cases for focused analysis. Micro-case study is a term that is occasionally used to describe research on micro-level cases [ 10 ]. These are cases that occur in a brief time frame, occur in a confined setting, and are simple and straightforward in nature. A micro-level case describes a clear problem of interest. Reporting is very brief and about specific points. The lack of complexity in the case description makes obvious the “lesson” that is inherent in the case; although no definitive “solution” is necessarily forthcoming, making the case useful for discussion. A micro-case write-up can be distinguished from a case report by its focus on briefly reporting specific features of a case or cases to analyze or learn from those features.

DATABASE INDEXING OF CASE REPORTS AND CASE STUDIES

Disciplines such as education, psychology, sociology, political science, and social work regularly publish rich case studies that are relevant to particular areas of health librarianship. Case reports and case studies have been defined as publication types or subject terms by several databases that are relevant to librarian authors: MEDLINE, PsycINFO, CINAHL, and ERIC. Library, Information Science & Technology Abstracts (LISTA) does not have a subject term or publication type related to cases, despite many being included in the database. Whereas “Case Reports” are the main term used by MEDLINE’s Medical Subject Headings (MeSH) and PsycINFO’s thesaurus, CINAHL and ERIC use “Case Studies.”

Case reports in MEDLINE and PsycINFO focus on clinical case documentation. In MeSH, “Case Reports” as a publication type is specific to “clinical presentations that may be followed by evaluative studies that eventually lead to a diagnosis” [ 11 ]. “Case Histories,” “Case Studies,” and “Case Study” are all entry terms mapping to “Case Reports”; however, guidance to indexers suggests that “Case Reports” should not be applied to institutional case reports and refers to the heading “Organizational Case Studies,” which is defined as “descriptions and evaluations of specific health care organizations” [ 12 ].

PsycINFO’s subject term “Case Report” is “used in records discussing issues involved in the process of conducting exploratory studies of single or multiple clinical cases.” The Methodology index offers clinical and non-clinical entries. “Clinical Case Study” is defined as “case reports that include disorder, diagnosis, and clinical treatment for individuals with mental or medical illnesses,” whereas “Non-clinical Case Study” is a “document consisting of non-clinical or organizational case examples of the concepts being researched or studied. The setting is always non-clinical and does not include treatment-related environments” [ 13 ].

Both CINAHL and ERIC acknowledge the depth of analysis in case study methodology. The CINAHL scope note for the thesaurus term “Case Studies” distinguishes between the document and the methodology, though both use the same term: “a review of a particular condition, disease, or administrative problem. Also, a research method that involves an in-depth analysis of an individual, group, institution, or other social unit. For material that contains a case study, search for document type: case study.” The ERIC scope note for the thesaurus term “Case Studies” is simple: “detailed analyses, usually focusing on a particular problem of an individual, group, or organization” [ 14 ].

PUBLICATION OF CASE STUDY RESEARCH IN LIBRARIANSHIP

We call your attention to a few examples published as case studies in health sciences librarianship to consider how their characteristics fit with the preceding definitions of case reports or case study research. All present some characteristics of case study research, but their treatment of the research questions, richness of description, and analytic strategies vary in depth and, therefore, diverge at some level from the qualitative case study research approach. This divergence, particularly in richness of description and analysis, may have been constrained by the publication requirements.

As one example, a case study by Janke and Rush documented a time- and context-bound collaboration involving a librarian and a nursing faculty member [ 15 ]. Three objectives were stated: (1) describing their experience of working together on an interprofessional research team, (2) evaluating the value of the librarian role from librarian and faculty member perspectives, and (3) relating findings to existing literature. Elements that signal the qualitative nature of this case study are that the authors were the research participants and their use of the term “evaluation” is reflection on their experience. This reads like a case study that could have been enriched by including other types of data gathered from others engaging with this team to broaden the understanding of the collaboration.

As another example, the description of the academic context is one of the most salient components of the case study written by Clairoux et al., which had the objectives of (1) describing the library instruction offered and learning assessments used at a single health sciences library and (2) discussing the positive outcomes of instruction in that setting [ 16 ]. The authors focus on sharing what the institution has done more than explaining why this institution is an exemplar to explore a focused question or understand the phenomenon of library instruction. However, like a case study, the analysis brings together several streams of data including course attendance, online material page views, and some discussion of results from surveys. This paper reads somewhat in between an institutional case report and a case study.

The final example is a single author reporting on a personal experience of creating and executing the role of research informationist for a National Institutes of Health (NIH)–funded research team [ 17 ]. There is a thoughtful review of the informationist literature and detailed descriptions of the institutional context and the process of gaining access to and participating in the new role. However, the motivating question in the abstract does not seem to be fully addressed through analysis from either the reflective perspective of the author as the research participant or consideration of other streams of data from those involved in the informationist experience. The publication reads more like a case report about this informationist’s experience than a case study that explores the research informationist experience through the selection of this case.

All of these publications are well written and useful for their intended audiences, but in general, they are much shorter and much less rich in depth than case studies published in social sciences research. It may be that the authors have been constrained by word counts or page limits. For example, the submission category for Case Studies in the Journal of the Medical Library Association (JMLA) limited them to 3,000 words and defined them as “articles describing the process of developing, implementing, and evaluating a new service, program, or initiative, typically in a single institution or through a single collaborative effort” [ 18 ]. This definition’s focus on novelty and description sounds much more like the definition of case report than the in-depth, detailed investigation of a time- and space-bound problem that is often examined through case study research.

Problem-focused or question-driven case study research would benefit from the space provided for Original Investigations that employ any type of quantitative or qualitative method of analysis. One of the best examples in the JMLA of an in-depth multiple case study that was authored by a librarian who published the findings from her doctoral dissertation represented all the elements of a case study. In eight pages, she provided a theoretical basis for the research question, a pilot study, and a multiple case design, including integrated data from interviews and focus groups [ 19 ].

We have distinguished between case reports and case studies primarily to assist librarians who are new to research and critical appraisal of case study methodology to recognize the features that authors use to describe and designate the methodological approaches of their publications. For researchers who are new to case research methodology and are interested in learning more, Hancock and Algozzine provide a guide [ 20 ].

We hope that JMLA readers appreciate the rigor of well-executed case study research. We believe that distinguishing between descriptive case reports and analytic case studies in the journal’s submission categories will allow the depth of case study methodology to increase. We also hope that authors feel encouraged to pursue submitting relevant case studies or case reports for future publication.

Editor’s note: In response to this invited editorial, the Journal of the Medical Library Association will consider manuscripts employing rigorous qualitative case study methodology to be Original Investigations (fewer than 5,000 words), whereas manuscripts describing the process of developing, implementing, and assessing a new service, program, or initiative—typically in a single institution or through a single collaborative effort—will be considered to be Case Reports (formerly known as Case Studies; fewer than 3,000 words).

Reservoir Rock Discrimination Based on Integrated Image Logs and Petrographic Analysis: A Case Study from the Early Miocene Nukhul Carbonate, Southern Gulf of Suez, Egypt

• Research Article-Earth Sciences
• Open access
• Published: 29 May 2024

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• Ahmed A. Kassem 1 ,
• Mohsen Abdel Fattah 2 ,
• Zakaria Hassan 2 &
• Ahmed E. Radwan   ORCID: orcid.org/0000-0002-3011-5832 3  

The discrimination of rock types within the limestones and dolostones of the Nukhul Formation in the West Younis Field (Gulf of Suez Basin, Egypt) presents significant challenges due to their multi-scale compositional and diagenetic heterogeneity, diverse pore types, complex microstructures, and limited core data. This study aims to characterize the carbonate reservoir of the Early Miocene sediments and establish distinct reservoir rock types by employing textural analysis, geological interpretations (i.e., structural interpretation, fracture analysis, reservoir characteristics) using advanced imaging tools, and petrophysical measurements to model porosity/permeability profiles across the reservoir. A new dataset was obtained from the latest exploratory well in the West Younis Field, incorporating microresistivity and acoustic image logs, well logs, nuclear magnetic resonance (NMR) tools, and drill cutting petrographic analysis. The integration of these datasets provided a comprehensive understanding of the properties of the Early Miocene carbonate reservoir. Based on image logs, the carbonate facies were divided into four reservoir units. Petrographic evaluation further classified two facies (A and B) based on diagenetic factors controlling reservoir quality. The results revealed the occurrence of multiple phases of dolomitization, which influenced the reservoir quality. Early-stage dolomitization enhanced reservoir quality, while late-stage idiotopic dolomite crystal growth diminished it. The study also provided comprehensive information on the original rock fabric/texture, diagenetic processes, porosity types and origins, as well as the spatial distribution of pores (permeability index) within this complex carbonate reservoir. By employing an integrated technique, this study successfully differentiated the carbonate reservoir into distinct rock types, leading to improved reservoir characterization and field development. Additionally, the findings contribute valuable insights for the development and exploration of the Early Miocene carbonate section in the southern Gulf of Suez.

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1 Introduction

The carbonate reservoirs in the early Miocene Nukhul Formation in the southern Gulf of Suez, Egypt, often exhibit complex and heterogeneous rock properties, including variations in pore types, pore sizes, and rock textures [ 1 , 2 , 3 , 4 , 5 ]. These heterogeneity poses challenges in accurately characterizing the reservoir and predicting fluid flow behavior [ 6 , 7 , 8 , 9 , 10 ]. Carbonate reservoir heterogeneity can occur at various scales, ranging from well to regional scales. Integrating data from different scales and understanding the relationships between them is essential for reservoir characterization and modeling [ 3 , 5 ]. Carbonate depositional fabrics undergo modifications through biological, chemical, and physical processes during deposition and subsequent diagenesis [ 8 , 11 , 12 ]. These modifications have a significant influence on pore system characterization and the physical properties of limestones and dolomites, ultimately impacting porosity and permeability [ 7 , 13 , 14 , 15 ]. Rock typing schemes have been developed to establish a framework for rock property modeling using integrated borehole data and 3D static reservoir models [ 16 , 17 , 18 , 19 , 20 ].

The optimum carbonate reservoir characterization requires integration of multiple datasets, including core samples, petrophysical measurements, and logs [ 3 , 8 ]. Traditional rock typing methods such as Leverett's J-function, Winland's R35, and flow zone indicators are commonly used in conjunction with cored reservoirs [ 21 ]. However, in the absence of core data, capturing the heterogeneity of carbonate reservoirs becomes more challenging, necessitating the integration of available data for improved rock classification. In this study, an integration of image analysis, thin section analysis, and borehole logging is employed to enhance our understanding of the pore network characteristics of the Nukhul Formation in Younis Field. The Younis Field, also known as GS 347, is located in the southern part of the Gulf of Suez, less than 3 km from the coast of the Sinai Peninsula (Fig.  1 ). Discovered in 1981 and brought into production in 1983, the main reservoir in Younis Field is the Lower Miocene Lower Rudeis Formation, which hydraulically connects with the Kareem Formation reservoir in the adjacent SB 339 Field via a non-sealing fault [ 22 ]. Minor production has also been observed from the Coniacian–Santonian Matulla Formation and the Lower Miocene (Aquitanian) carbonates of the Nukhul Formation, which are the primary focus of this paper.

Map showing the oil fields in the Gulf of Suez (EGPC, 1996). The Younis and SB 339 Fields lie in the east-central part of the Gulf of Suez. The first oil in Egypt was found in the Gemsa area, on the coast of the Eastern Desert

The main challenge facing the Nukhul exploration is the reservoir heterogeneity and the lack of understanding the depositional and diagenetic controls on the reservoir properties. This study aims to highlights the tools and workflow that may use to unlock these heterogeneities. Recent exploratory wells drilled in the western part of Younis Field have renewed interest in the exploration and characterization of this carbonate reservoir section, which has previously received limited attention. Despite previous studies investigating the petrographic and sedimentological characteristics of the Nukhul Formation reservoir [ 4 , 23 , 24 , 25 , 26 , 27 ], little is known about the reservoir characterization, reservoir compositional and diagenetic heterogeneity, relationship between petrographic characteristics and geophysical log signatures, pore system network, and reservoir quality in the Nukhul Formation of Younis Field, especially with the limited core data.

This research aims to: (i) establish distinct reservoir rock types within the Nukhul Formation carbonates; (ii) perform petrophysical and pore network evaluations to study the impact of diagenetic controls on reservoir quality; (iii) model the porosity/permeability profile along the entire reservoir using textural analysis of advanced image logs, and petrophysical measurements; and (iv) integrate ditch cutting petrographic descriptions and geophysical logs to differentiate the carbonate reservoir into various rock types, enhancing reservoir characterization and field development. To achieve these objectives, specialized petrophysical techniques, including microresistivity and acoustic borehole imaging, nuclear magnetic resonance (NMR), as well as petrographic analysis of original rock fabric/texture, diagenetic processes, and pore network evaluations, were employed. Production logging techniques have also been utilized to explore the carbonate rocks of the Nukhul Formation in the western part of Younis Field and further enhance reservoir development strategies. This research endeavors to contribute valuable insights into the pore network heterogeneity and reservoir characterization of the Nukhul Formation carbonates. The integration of various techniques and datasets will advance our understanding of reservoir properties, aid in accurate reservoir modeling, and facilitate improved field development strategies in carbonate reservoirs.

2 Geological Setting

The Gulf of Suez is a rift basin, approximately 350 km long and 50–80 km wide, trending NNW-SSE (Fig.  1 ). It is part of the Red Sea rift system, which formed when the African and Arabian plates separated in the late Eocene to Oligocene. The basin's fill, ranging from 10,000 to 16,000 ft (3048–4876.8 m) thick, consists of clastics, carbonates, and evaporites (Fig.  2 ) [ 28 , 29 , 30 , 31 ].

General stratigraphy of the Gulf of Suez (Schütz, 1994). The main Younis Field reservoir is in the Lower Rudeis Formation and Nukhul in West Younis block. Secondary reservoirs are in the Nubia, Matulla-Wata formations

Structurally, the Gulf of Suez is divided into three sub-basins with varying dips and fault directions (Fig.  1 ) [ 30 , 31 , 32 , 33 , 34 ]. The strata in the Darag sub-basin and the Amal-Zeit province in the north and south, respectively, dip to the SW, while faults dip to the NE [ 8 , 35 ]. In contrast, the Belayim province in the central region has strata dipping to the NE and faults dipping to the SW. The Zaafarana and Morgan accommodation zones separate these sub-basins. A Miocene biostratigraphic framework has been established, and sequence boundaries have been identified throughout the basin's sedimentary section (Fig.  3 ) [ 1 , 2 , 36 , 37 , 38 ]. The rifting process began around 22–24 million years ago (Aquitanian) with volcanic activity in the Lower Miocene.

Sequence stratigraphy of the Miocene section in the Central and Southern Gulf of Suez [ 1 ]. Sequences (S10, S20 etc.) are separated by major, biostratigraphically-defined breaks (T10, T20 etc.). Arrows indicate the main reservoirs in the Younis and SB 339 fields

The basin experienced a transgression during the Miocene, leading to an unconformable contact with rocks from the Precambrian to the Upper Eocene. The earliest synrift sediments consisted of fluvial and shallow marine sandstones, followed by shallow marine limestones, evaporites, and marine marls (Nukhul Formation). Also, deeper marine conditions developed during the Early Miocene due to rapid subsidence and fault block rotation, resulting in the deposition of marls and shales of the Rudeis Formation [ 5 ]. The rift margins contain sandstones and turbidites, reflecting the uneven topography. The Younis Field, located in the South Amal-Zeit province, has a stratigraphy that begins with a Precambrian basement overlain by the Nubia Sandstone (Fig.  3 ). The Nezzazat Group, including the Matulla Formation, overlies the Nubia Formation and has produced small oil volumes from Younis wells A2 and A6 [ 39 ]. The Younis Field also contains reefal carbonate sediments and a developed Lower Rudeis clastic reservoir. The lowest synrift unit, the Nukhul Formation, consists of siliciclastic, anhydrite, and highly dolomitic limestone that has produced minor oil in Younis well A2 and is being explored in the west Nukhul block. The ‘G’ horst, where the Younis and SB 339 Fields are situated, was formed during the Miocene rifting of the Gulf of Suez. The horst overlies a NNW-SSE trending high at Precambrian basement level and is characterized by bounding faults and numerous faults within (Figs. 4 , 1 ) [ 22 , 40 ]. The bounding faults have throws of > 4000 ft (1219.2 m) at pre- Miocene level, and the horst is cut by numerous faults (Fig.  4 ). The principal source rocks in the vicinity of the fields are the Senonian Brown Limestone and the Eocene Thebes Formation, which were deposited under marine, anoxic conditions and contain abundant kerogen. Oil migration occurred along the bounding faults that formed after the Mid-Rudeis tectonic event in the late Lower Miocene. The Younis Field has a significant oil reserve, with the Lower Rudeis interval being the main oil producer. The field has experienced fluctuations in production over the years, with water injection and other measures implemented to maintain and increase oil recovery [ 41 , 42 , 43 ].

Structure map of the Younis Field at the top of the Lower Rudeis reservoir, showing well locations (EGPC, 1996; Clark and Hanafy, 1994). E–E′ is the location of seismic section shown in Fig.  7

3 Materials and Methods

3.1 samples analysis.

Six wells distributed across the Younis Field were studied in this work (Fig.  4 ). The drill cuttings of the Nukhul Formation have been analyzed for petrographic investigation.

The drilled wet samples were dried and washed to eliminate the drilling mud and filtrates. Thirty polished thin sections were prepared from selected cuttings, using a suitable slab size. The slabs were impregnated with blue dye epoxy for porosity investigation. The samples were studied under Olympus BX 51 microscope [ 44 ]. Descriptive petrographic reservoir characteristics are point counted to assess the mineral composition, textural and compositional maturity, and porosity. To reconstruct the paragenetic sequence and establish the impact of diagenesis on the reservoir potential of the examined facies, the distinct diagenetic features, cement types and their morphologies, mineral replacement, and cross-cutting relationships of fractures were researched in detail. For petrographic description and facies, nomenclature was used classifications of Folk [ 45 , 46 ], Dunham [ 47 ], and Flügel and Munnecke [ 48 ].

A comprehensive analysis of point counting data from 12 thin sections was done on a random grid of 250 points for each photograph of the thin section. Points were assigned to one of four classes: sparite, micrite, Fe-oxides, and porosity (Table  1 ). We employed a systematic and standardized approach to gather mineralogical and textural information from the thin sections, ensuring the accuracy and consistency of our measurements. Subsequently, the collected data were processed and statistically evaluated to derive meaningful insights into the geological characteristics of the studied samples.

3.2 Image Log Tools and Analysis

Image logs have played a critical role in reservoir characterization, by providing high-resolution characteristics of carbonates and siliciclastic reservoirs [ 49 , 50 , 51 , 52 ]. The Circumferential Acoustic Scanner Tool (CAST™) and the Oil Mud Reservoir Imager (OMRI™) tools were run from the top of the Nukhul Formation covering the total depth (TD) of the exploratory well (well#5).

3.2.1 Acoustic Logs

The CAST tool delivers an ultrasonic (acoustic) image scan of the borehole walls by measuring the amplitude and travel-time of return pulses, which are transmitted 200 times per scanner rotation. Thus, this tool has two image modes: one is the amplitude image, which depends on the acoustic impedance of the formation and the fluid, while the travel-time image mainly depends on the distance between the transmitter and the borehole wall, making it perfect for evaluating hole (or casing) conditions. As the signal is bounced back from the borehole wall, the quality of both image types is very dependent on a smooth and round hole, as well as the tool being perfectly centered. One advantage of this tool is that it provides a complete image of the oil-based mud, which other tools do not support. In this work, the borehole image logs (i.e., CAST) were used to interpret some structural features (i.e., fractures, dip) within the target area, and picking the boundaries and reservoir features followed [ 53 , 54 ].

3.2.2 Electrical Imager Tool

The image tool in this work was used for identifying structural and stratigraphic dips, borehole stresses, fluid profiles, sedimentary geometry, and texture that are beyond the resolution of conventional logs. In this work, the image logs have been used to pick bedding planes and give information about the structural dip attitude of the picked mudstone/siltstone bed boundary and lamination planes of the studied facies, which is then displayed in the dip azimuth vector.

The OMRI tool is intended for the acquisition of microresistivity borehole images in non-conductive muds [ 53 , 55 ]. The OMRI™ is an electrical imager tool possessing six arms positioned as 2 sets of 3 arms vertically displaced by approx. 94 cm. Arms 1, 3, and 5 exist at the top, while arms 2, 4, and 6 are located at the bottom. Each arm is affixed to a pad of approx. 30 cm in length that has two transmitter electrodes at each end with six pairs of monitoring electrodes positioned symmetrically between them. A high-frequency measuring current is transmitted to capacitive couple the survey current through the mud and into the wall of the formation. The monitoring electrode pairs then measure the potential difference (due to voltage drop) between them, and Ohm’s law subsequently determines the formation resistivity. This high-resolution image tool is the optimum tool for carbonate reservoir discrimination, where it imaged the reservoir characteristics of pore system types, sedimentological and depositional characteristics that control the reservoir connectivity and deliverability. The two image tools (OMRI and CAST) have been used to investigate the structural features and reservoir characteristics along the studied intervals. Drilling-induced fractures, faults, natural fractures, and breakouts are structural discontinuity-related features in this investigation. The dip angle and azimuth of the aforementioned structural features were measured, and faults and natural fractures were identified in the acoustic image logs based on their continuous sharp edges and distinct dip and azimuth values in comparison with the sedimentary beddings.

3.2.3 Nuclear Magnetic Resonance (NMR)

Nuclear magnetic resonance (NMR) logging measures the magnetic moment induction of protons (hydrogen nuclei) that are preserved in the pores of the reservoir rock. The NMR responses to the rocks and fluid properties show mineralogy dependence [ 3 , 56 , 57 ]. Time-based metrics for reservoir properties, T1 and T2 cutoffs, are utilized as indicators. The NMR equipment combines magnetic fields that are acting directly on the protons in the formation fluid (T2) to detect the protons' polarization time or relaxation time (T1) [ 2 , 57 ]. For about 350 feet (107 m) of the reservoir section, between 6180 feet (1884 m) and 6530 feet (1990 m), NMR data were available.

4.1 Petrographic Analysis

The petrographic analysis of drilling ditch cuttings extracted from six wells revealed that the Nukhul Formation is composed of dolomite and highly dolomitized recrystallized lime-mudstone, varying in thickness from 100 to 150 ft. The Late Aquitanian and Early Burdigalian age of Nukhul Formation in the Younis field is confirmed by the presence of benthic foraminifera Miogypsinoides and nannoplankton zone Triquetrohabdulus carinatus ( NN2 Zone), which are correlated with age data of the Nukhul Formation type locality at Gebel el Zeit [ 58 ].

According to the petrographic description of the studied thin sections, the carbonate facies are discriminated into two distinctive lithofacies (A and B) (Fig.  5 ).

Petrographic description of ditch cutting in Well 5 in West Younis field block represents different stages of dolomitization in Facies A and B and its effect on the reservoir quality. ) Facies A: Micritized, idiotopic to hypidiotopic dolostone rhombs (red arrow). The outer rim is outlined by lime mud (black arrow) and traces of iron oxides (white arrow). b Facies A: Photomicrograph present multiphase of dolomitization (yellow arrows). Note that the late phase of dolomitization reduced the porosity ( P ) due to excessive crystal growth. Also, the outer rim is outlined by lime mud (black arrow). c Facies B: dolomitized vuggy dissolution mudstone with dominant vuggy porosity (blue dye). d Facies B: Intercrystalline and vuggy porosity ( P ) within the sparry calcite limestone (green arrow). Note that the enhancement in reservoir quality in Facies B that lie above the Paleocene/Eocene major unconformity. The log response reflects the facies variation along the well logs. GR = gamma ray. NPHI = neutron log. RHOB = density log

Facies A is composed of micritized, idiotopic to hypidiotopic dolostone rhombs (Fig.  5 ). The outer rim is outlined by lime mud and traces of iron oxides. The high percentage of argillaceous micrite has affected the GR log response and increased the shale volume content, while decreasing density log readings (Fig.  5 ). Facies A in the upper part of the Nukhul Formation lies below the Lower Rudeis unconformity (T10) (Fig.  3 ).

Facies B represents the lower part of the Nukhul Formation, and it lies above the Paleocene/Eocene major unconformity (T00) (Fig.  3 ). This facies is dolomitized, vuggy, and crystallized mudstone with dominant vuggy and intercrystalline porosity.

4.2 Reservoir Pore Systems

According to the microscopic characteristics of thin section castings, four main pore types have been identified: interparticle, intraparticle, intercrystalline, and vuggy (Figs. 5 , 6 , 7 ).

Thin section petrography of six wells represents the Nukhul carbonates reservoir characters around the exploratory well (well 5), showing that the rate of dolomitization is syntectonic character. Lower right is a location map

Paragenesis of the Nukhul carbonate Formation

Interparticle pores are used to describe the pores formed between grains (intergrain), which agrees with the definition provided by Choquette and Pray [ 59 ]. Interparticle pores, which primarily occur in Facies A and B, are mostly irregular polygonal shapes. Intraparticle pores are formed by the selective dissolution of interparticle cements. These pores are locally filled with cement, suggesting that they probably formed during early dolomitization [ 48 ]. The fine to medium-crystalline dolomite in both Facies A and B exhibits varying degrees of dolomitization, resulting in the observation of intercrystalline pores under the microscope [ 48 ]. Within the studied dataset, intercrystalline pores are observed to develop between euhedral dolomite crystals, as illustrated in Fig.  7 . Vuggy pores, which are secondary solution pores formed through the dissolution of cement, matrix, and grains, are predominantly present in Facies A and B, with an increased occurrence in Facies B (Fig.  8 ).

A stacked bar chart of the 12-point counted thin sections (Table  1 ) show how the porosity changes across the Facies A and B

4.3 Image and NMR Log Analysis

4.3.1 structural features analysis.

The image logs picked bedding planes and give information about the structural dip attitude of the picked mudstone/siltstone bed boundary and lamination planes of the studied facies, which is then displayed in the dip azimuth vector (Fig.  9 ).

Rose and dip azimuth plots representing the dip attitude of the mudstone bed-boundaries and lamination planes picked from the processed imaged rock interval; 6140–7660 ft (1871.5–2334.8 m). They strike generally NNE–SSW and dip mostly due ESE; swinging from SSE to ENE with a calculated mean dip attitude measuring 12°/S69°E

The image structural interpretation included determining the main structural dip attitude (dip magnitude/azimuth) of the study succession; identifying the distribution, orientation, and type of faults and fractures; and assigning the stress field orientation from drilling induced fractures and breakouts. All over the processed imaged interval (6140–7660 ft) (1871.5–7334.8 m), a total of 323 depositional planes of bedded/laminated mud facies (mudstone/siltstone) were picked. They generally strike NNE-SSW and dip mostly due ESE, swinging from SSE to ENE with a calculated mean dip attitude of 12°/S69°E. The dip azimuth vector plot for these picked mud facies planes displays one zone dipping generally due ESE (Fig.  9 ). In the Nukhul Formation, the structural dip attitude of the picked carbonate and mudstone bed boundary and lamination planes is generally striking NE-SW with a dip attitude of about 12°/S53°E (Fig.  10 ), and there are also ENE-trending cross-faults, which are parallel to the main bounding faults of the southern part of the Gulf of Suez [ 60 ].

Representative snapshots of massive limestone rock unit within the imaged interval of Nukhul Formation (zones 1 and 2). This limestone rock unit interval (6195–6213ft) (1888.2–1893.7 m) is characterized by 6 resistive steeply dipping natural fractures from the OMRI, and they are commonly striking NW–SE and dip mostly due the SW. Two fractures of these analyzed 6 natural resistive fractures show high acoustic impedance contrast (Blue Fracpole), while the rest of these fractures show partial acoustic contrast (Magenta Fracpole). Zone 2 shows the higher permeability with demonstrated vuggy porosity

4.3.2 Fracture Analysis

Fractures picked from the image include the following types of fractures: open, closed, partial open, and induced fractures. The picked fractures were categorized based on the following criteria: (a) natural open fractures are conductive because they are typically filled with drilling mud and appear as darker traces than the formation rock surrounding them. (b) Natural closed fractures have been filled by secondary mineralization, making them more resistant than open fractures, which are typically filled with drilling mud (Figs.  10 , 11 , 12 ).

The CAST image log showing the variation in the fracture intensity and permeabilities in zones 3 and 4

Integration of well logs, images, NMR and petrology for Nukhul carbonate evaluation. The density/neutron and the magnetic resonance porosity logs show crossover effect and hydrocarbon bearing zones

Closed fractures generally appear as traces that are brighter than the surrounding rock and sometimes demonstrate a "halo" appearance due to the resistivity of the secondary mineralization. (c) Natural partially open fractures are closed or partially mineralized. On image logs, they appear as traces that are partially bright and partially dark. (d) Induced fractures occur at various stages of the drilling process. Induced fractures are open fractures, so they will be conductive and show a dark fracture trace. There are different types of induced fractures. Petal and centerline fractures can form ahead of the bit while drilling and are caused by the weight of the bit and/or mud pressure. Tensile fractures can form from hydraulic fracturing with mud behind the bit. Since tensile fractures develop after the wellbore is cut, they develop in isolation and will be asymmetrical.

In the case of imaging holes drilled by oil base mud fluid (as in this study case), the differentiation between open, partially open, and closed fractures is generally very difficult due to the high resistivity of both the invaded drilling fluid in the case of open fractures and the healing occurring by resistive minerals such as quartz and calcite in the closed fractures. That’s why, in such cases, the acoustic image (CAST-open hole mode) in combination with OMRI was run in this studied reservoir since open fractures (fluid-filled) will be easily differentiated with their lower acoustic impedance and slower time relative to closed cemented fractures (calcium or siliceous cement filled). In addition, the petrographic analysis of the drill cuttings has differentiated between the cemented and open fractures. In the studied well, the carbonate section was investigated using the combination of OMRI and CAST for better fracture identification and classification, where the identified fractures could be classified using CAST into fractures with complete/partial acoustic impedance contrast or no acoustic impedance contrast, (closed). Based on the above criteria, along the entire logged interval from 6140 to 7660 ft (1871.5–2334.8 m), 92 natural resistive fractures were identified from the OMRI image (Fig.  9 ).

In the upper carbonate succession of the Nukhul Formation, the CAST and OMRI were run in combination, and a total of 37 natural fractures were identified (Figs. 10 , 11 ). They are commonly striking NW–SE and dip mostly due SW, with a wide range of dip angle magnitudes that lie between 21° and 85°. The fracture characterization along the Nukhul Formation reveals that the total number of 37 natural resistive fractures comprises five natural resistive fractures with no acoustic impedance contrast, commonly striking NW–SE and dipping mostly due SW, with dip angle magnitudes ranging between 71° and 78°. Twenty-five natural fractures with partial lower acoustic impedance contrast commonly striking NW–SE and dip mostly due SW, with a wide range of dip angle magnitudes that lie between 19° and 85°. Seven natural fractures with acoustic impedance contrast commonly striking NW–SE and dip mostly due SW, with dip angle magnitudes ranging between 55° and 79°.

5 Discussion

5.1 effects of sedimentary environment and tectonics on reservoir quality.

The rift initiation stage of the Nukhul Formation leads to variations in the depositional setting and regime of Nukhul from fluvial, fan delta, shallow marine, reefal carbonate, and dolomitized limestone, as discussed by [ 25 , 58 ]. The Miocene/Eocene unconformity T00 led to areal to sub-areal exposure of the limestone in Younis Field and the southern Gulf of Suez. Therefore, this sub-areal exposure has potential for magnesium-rich freshwater that caused the first phase of diagenesis, as evidenced by Facies B vuggy limestone and dolomitization [ 25 , 58 , 61 , 62 , 63 ]. Temraz and Dypvik [ 25 ] recorded significant changes in the southwest at Gebel el Zeit highly sandy dolostone in the early stage of rifting.

The findings of this study suggest that the unconformity potentially introduced freshwater into the lower carbonate of the Nukhul Formation, triggering a gradual process of dolomitization that ultimately improved the reservoir quality (Fig.  5 ), as mentioned in the work of Elshahat [ 64 ] and Shallaly and others [ 65 ]. Also, the work of Yang and others [ 63 ] established a quantification study for dolomitization and its effect on porosity and permeability. Their numerical modeling finds an increase in the effective porosity by 8.5% during dolomitization. These findings match the work of Carr et al. [ 24 ] and McClay et al. [ 23 ], which proposed the effect of the early rift faults on the deposition of the Nukhul Formation.

The acoustic and microresistivity OMRI and CAST images discriminate the Nukhul carbonate unit into four zones based on the lithological criteria and rock unit characterization. Zone 1 is composed of fractured dolomitic limestone that has an average fracture density of one open fracture per foot. It also has approximately twenty-five naturally occurring resistive fractures with low impedance, most of which dip largely toward the SW and typically have a NW–SE strike. These fractures may result from the Gulf of Suez extension regime and may indicate that they were initiated with the initiation stage of the Gulf of Suez rift, with a wide range of dip magnitudes of 20°–85° (Fig.  10 ). This zone shows low permeability and is matched with the petrology of Facies A. Zone 2 may be highly karistified dolostone due to T00 unconformity at the initial stage of rifting [ 66 , 67 ]. This rock unit interval is characterized by dissolution vugs pores, which appear as highly resistive patches with low acoustic impedance (Fig.  10 ). The dissolution vuggy pores are found to be connected at some intervals. This zone shows the same facies that is recognized by the ditch cutting petrology of Facies B, with a good permeability of 50–100 millidarcy. Zone 3 shows a massive interbedded limestone rock unit that is characterized by dissolution vugs with low acoustic impedance and high resistive patches. These dissolution vug pores are found to be connected to some natural resistive fractures, with an average fracture density of 1.5 open fractures per foot (Fig.  11 ). The permeability measured by CMR was less than 100 mD (Fig.  11 ). Zone 3 matched the petrographic description of Facies B. Zone 4 of the Nukhul carbonate unit is characterized by resistive fracture striking, generally due to the SW showing high acoustic contrast (blue flagpole). The presence of fractures filled with silica cement is notable, and their formation is attributed to precipitation in an acidic medium. This phenomenon may have contributed to the development of dissolution porosities within zones 3 and 2. The zone is composed of permeable, vuggy, and dolomitic limestone with a high mud content. Zone 2 and zone 3 show the same lithological criteria as recognized in Facies B (Fig.  12 ). Two main distinctive zones can be interpreted from the CAST image tool mainly based on the intensity of the vuggy limestone, which is reflected in the permeability derived from the CMR log (Fig.  10 ). The upper zone of the CAST image is correlated with the Facies A from the petrography analysis, where the permeability displays very low permeability and low mobility of 0–5 Md. On the other hand, the lower zone of the CAST image is correlated with Facies B, with a permeability of 50–100 mD (Fig.  10 ).

These two zones have the best quality intervals of the Nukhul carbonates. According to the production data, zone 2 is the only zone that contributes to oil production in the Nukhul reservoir, while zone 3 does not. In the case of a non-sealed fault, zone 3's hydrocarbon volume may be shared with another reservoir. The NMR integration with the density/neutron porosity logs shows the hydrocarbon bearing units exhibited at zones 2 and 3 (Fig.  12 ). These log integrations emphasize that zones 2 and 3 have the highest storage capacity and flow.

Facies B was presented as the best reservoir quality facies due to its intercrystalline and vuggy porosity (Fig.  5 ). In contrast, the reservoir quality is reduced in Facies A due to multiphase dolomitization (Figs. 5 , 6 ).

5.2 Diagenetic Controls on Reservoir Quality

5.2.1 effects of dolomitization.

The thin sections display the effect of the dolomitization processes in the Nukhul Formation, where two dolomitization phases affect the reservoir quality (Fig.  5 ). Dolomitization, calcite cementation, dissolution, and fracturing commonly exert a considerable impact on carbonate reservoir quality, as the major diagenetic processes in carbonate reservoir rocks [ 2 , 68 , 69 , 70 , 71 , 72 ].

Early dolomitization enhanced the reservoir's quality by creating intercrystalline porosity. Late stage dolomitization is characterized by the growth of another phase of dolomitization, which has reduced the reservoir quality by reducing the porosity due to crystal growth (Fig.  5 ). The vuggy porosity in Facies B of the Nukhul Formation demonstrates the dissolution diagenetic process. Furthermore, the selected fractures along Facies B appear to play a role in enhancing the pore system in the Nukhul Formation. Open, closed, partial open, and induced fractures were picked from the image logs in the Nukhul Formation. Therefore, the dolomitization, dissolution, and fracturing processes enhanced the reservoir quality of the Nukhul Facies B that are associated with rifting initiation. The interparticle pores are commonly related to the selective dissolution of cements and matrix, which is strongly controlled by fluid migration pathways and patchy cementation of both primary and secondary interparticle pores [ 48 ].

The identified characteristics must be closely monitored throughout the Gulf of Suez basin to effectively pinpoint high-quality reservoirs. On the other hand, a destructive dolomitization feature of diagenesis has been propagated by later stages of diagenesis, leading to more growth of dolomite crystals to reduce the reservoir quality and deliverability of Facies A at the upper part of the Nukhul Formation (Figs. 5 , 6 , 7 ) [ 73 , 74 , 75 ]. Calcite or siliceous cement filled some fractures in both Facies A and B, which led to a decrease in the pore system in some parts.

The study reveals a significant correlation between porosity and micrite content, as demonstrated by the point counting data (Table  1 ). Within the dataset (Table  1 and Fig.  8 ), it is evident that Facies A exhibits a pronounced decrease in porosity alongside a high micrite percentage, while Facies B exhibits an inverse trend, highlighting the intricate relationship between micrite and porosity in the Nukhul Formation. These findings underscore the critical role of micrite in governing the porosity variations observed in the investigated rock samples.

Dolomitization is the most important diagenetic process in the Early Miocene Nukhul Formation. Petrographic description of ditch cutting in the studied well 5 in the West Younis field block shows different stages of dolomitization in Facies A and B (Fig.  5 ). The vuggy pores are affected by near-surface meteoric waters and are related to deep-burial fluids mainly controlled by fractures and faults [ 76 , 77 ]. The petrographic analysis displays multiphase dolomitization (Fig.  5 ); the first dolomitization is most likely earlier of diagenesis processes (Fig.  7 ), which enhances the pore system of the Nukhul carbonate rocks. On the other hand, the late phase of dolomitization started at the late phase of diagenetic processes and reduced the porosity due to dense crystal growth. Thus, dolomitization has dual roles in controlling the reservoir quality of the Nukhul Formation.

5.2.2 Effects of Late Stage Cementation, Dissolution and Fracturing

Cementation is the second most important diagenetic process following dolomitization in the Early Miocene Nukhul Formation. In both Facies A and B, some fractures were filled with calcium or siliceous cement, which caused a reduction in porosity (Fig.  5 ). As a result, the Nukhul Formation could only accommodate fluid movement at specific moments in time. Pore-filling and fracture-filling cementation play a key role in reservoir quality [ 2 ].

Both dissolution and fracturing were recorded in the thin sections of the Early Miocene Nukhul Formation. In Figs. 5 , 6 , 7 , the dissolution resulted in various pores porosity in thin sections, while fracturing was recorded in both image logs and thin sections. Additionally, the late calcite dissolution is responsible for improving reservoir quality by dissolving most of the early calcite cementation and creating new pore spaces [ 72 ]. Dissolution and fracturing play a key role in reservoir quality [ 10 , 78 , 79 , 80 ], 2. They affect the pores by spreading within carbonates and considerably enhance reservoir porosity and permeability [ 3 , 79 ]. Facies B, which lie above the Paleocene/Eocene major unconformity, display enhanced reservoir quality, which is characterized by karistified carbonate at the initiation stage of rifting. This information provides insights about the syntectonic carbonate deposits that can be traced in the southern Gulf of Suez.

5.3 Pore Pressure and Connectivity

The formation pressure tool (RFT) of well 5 displays an initial pressure of about 1600 psi in zones 1 and 2. On the contrary, zones 3 and 4 show communication with Upper Sand at a lower Rudeis pressure of 1150 psi [ 41 , 42 ] on the down-thrown side of well 5 (Fig.  13 ). Pressure differences between the zones separated by the mudstone layer, which acts as a permeability barrier, may be correlative across Younis Field.

Structural cross section shows the development of carbonate platform in the west block with cartoon. Note the absence of the Lower Rudeis sandstone reservoir in the West block due to pinching out. In contrast, development of the Nukhul carbonates. Zones 1 and 2 show initial pressure while zones 3 and 4 may communicated with the upper part of Lower Rudeis reservoir and lead to depletion

Based on that, the hydrocarbon production from the carbonates in the West Younis explored block is coming from zone 2 only, which shows initial pressure and isolation from the higher permeability zone of Lower Rudeis sandstone on the down-thrown side of the main Younis area (Fig.  13 ). The volumetric calculations for zone 2 were done using a drainage radius of 500 m (point of communication with the main field), showing stock tank oil initially in place (STOIIP) of about 10–15 million barrels of oil and a production rate estimated to be 200 barrels of oil daily.

Stratigraphically, the analyzed imaged sedimentary rock succession in Well 5 belongs to the Late Cretaceous–Early Miocene age, and covers, from base to top; Nezzazat Group, Sudr Formation, Esna Shale, Thebes Formation, and Nukhul Formation (Figs. 3 , 14 ). The integrated suite of logs, combined with OMRI/CAST images, aided in the redrawing of a better reservoir understanding. The combination of OMRI/CAST was acquired along the upper carbonate succession for reservoir characterization and identifying the secondary porosities (fractures or/and vugs).

NNW–SSE 3-D seismic cross section through Younis well A9, used as example to show thick Lower Rudeis sand development in a syndepositional half-graben [ 1 ]. See Fig.  4 for location of section E–E′

The enhancing and destructive diagenetic features cannot be evaluated by using conventional logging tools. Petrographic analysis and discrimination based on the factors controlling the fluid capacity flow are favorable tools for optimum reservoir discrimination [ 8 , 81 , 82 ]. In the absence of Nukhul cores, the most recent image techniques, such as OMRI and CAST, are recommended for optimum reservoir characterization and discrimination in the oil-based mud condition. The image studies are clearly providing an excellent tool for discriminating the Nukhul carbonate reservoir, where the image tool aids in classifying the Facies B from petrographic description into three distinct reservoir zones (zones 2, 3, and 4). Therefore, we managed to identify the characteristics of each zone and delineate the most productive reservoir zone in the Nukhul carbonate reservoir by integrating the petrographic description, image, and production data. The facies A is characterized by massive/interbedded limestone rock units based on the imaged interval of the Nukhul Formation (Fig.  10 ). This facies is characterized by natural parallel resistive fractures striking generally NW–SE and mostly due to SW (Fig.  10 ). The limestone of Facies B is characterized by dissolution vugs that appear as highly resistive patches on OMRI and low acoustic impedance on the CAST, where these possible dissolution vugs are found to be connected at some intervals (Fig.  11 ). The main natural fractures with low impedance have a strike of NW–SE and dip mostly toward the SW. These fractures exhibit the main dipping regime of the southern area of the Gulf of Suez (Fig.  10 ).

The integrated suite of logs, combined with OMRI/CAST images, aided in the redrawing of a better reservoir understanding. The combination of OMRI/CAST has been acquired along the upper carbonate succession for reservoir characterization and identifying the secondary porosities (fractures or/and vugs).

5.4 Hydrocarbon Potentiality

The main hydrocarbon pool in the Younis Field is primarily trapped in the Lower Rudeis Formation, extending into the Kareem Formation in the SB 339 Field. The Younis Field also contains minor reserves in the Nubia Sandstone, Matulla Formation, and Nukhul Formation. The Lower Rudeis reservoir's architecture in the Younis Field resembles a layer-cake structure, consisting of two principal pay intervals: the Main Sand and a thinner Upper Sand separated by a shale barrier (Figs. 15 , 16 ).

Wireline log across the Lower Rudeis and Nukhul reservoirs in well GS 347-1 (Younis development well A1) (EGPC, 1996)

Wireline log from Younis well A3, showing the main sand and upper sand of the Lower Rudeis reservoir (Clark and Hanafy, 1994)

The Main Sand thickness varies due to pinching out, while the Upper Sand remains relatively constant. The net pay thickness ranges from 6 ft (1.9 m) in the northeast to 199 ft (60.7 m) in the southwest of Younis, with an average of 131 ft. The reservoir exhibits a Net/Gross ratio of approximately 0.6–0.8. The Lower Rudeis reservoir is affected by several faults, with the major NW-trending fault likely acting as a seal, and two ENE-trending faults near well A3 being non-sealing. Exploration in the west block of the main Younis Field revealed the pinching out of the Lower Rudeis Formation, with the development of carbonates and reefs related to the Nukhul Formation, indicating potential as a reservoir. Recent 3-D seismic data, along with improved processing techniques, have enabled the recognition of depositional features, such as fan geometry and subtle onlaps (Fig.  15 ), providing valuable insights for further evaluation and exploration activities.

6 Conclusions

This work shows how petrology data in integration with logging tools in the lack of cores can quantify the rock types into optimum producing zones, as well as provide insights into the karistified carbonate in the syntectonic carbonate deposits that can be traced in the south Gulf of Suez as high-quality hydrocarbon resources.

The Nukhul Formation shows a challenge in determining the reservoir rock type, reservoir quality, and the variation of quality along Younis field and Gulf of Suez using the conventional subsurface logging. Applying the advanced image logs was able to differentiate the reservoir facies and provide a better understanding the reservoir properties of the studied carbonate section.

The main conclusion from this work is the following:

Petrology of the drilling ditch cutting of six wells along the Younis field found two facies, namely Facies A and Facies B. According to petrographic analysis, four main pore types have been identified: interparticle, intraparticle, intercrystalline, and vuggy.

Dolomitization, calcite cementation, dissolution, and fracturing commonly exert a considerable impact on the carbonate reservoir quality. The dolomitization and tectonics propagated during the initiation stage of Suez rifting have a positive impact on reservoir development.

Integration of petrology with nuclear magnetic resonance (NMR) tool and high-resolution microresistivity acoustic imaging tools addressed hydrocarbon potential and overcame the challenge of distinguishing between various secondary porosities (i.e., vuggy and fractures).

Zone 1 and zone 2 in the West block of Younis Field show initial pressure and isolation from the main Younis Field block, which has a very high permeability reservoir in lower Rudeis sandstone. Integrating all the techniques reveals that zone 2 is the produced zone, which is separated from zones 3 and 4 by a permeability barrier layer of mudstone. The detection of a drainage area of 500 m in zone 2 from the point of communication with the main field and a sealed fault found a STOIIP of 15–20 million barrels of oil.

The Nukhul has the potential to act as a syntectonic karistified carbonate reservoirs in neighboring areas, where it deserves further exploration in the basin.

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Acknowledgements

Authors express their sincere gratitude to Dr. Bassam El Ali and the handling editor for the excellent editorial handling. The three anonymous reviewers are thanked for their constructive comments which benefited and enhanced our manuscript. The authors thank the Egyptian General Petroleum Corporation (EGPC) and Gulf of Suez Petroleum Company (GUPCO) for providing the samples in six wells, well logs and images for well 5. Dr. Radwan is thankful to the Priority Research Area Anthropocene under the program “Excellence Initiative—Research University” at the Jagiellonian University in Kraków, Poland.

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Ahmed A. Kassem

Geology Department, Faculty of Science, Cairo University, Giza, 12613, Egypt

Mohsen Abdel Fattah & Zakaria Hassan

Institute of Geological Sciences, Faculty of Geography and Geology, Jagiellonian University, Gronostajowa 3a, 30-387, Kraków, Poland

Ahmed E. Radwan

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Kassem, A.A., Abdel Fattah, M., Hassan, Z. et al. Reservoir Rock Discrimination Based on Integrated Image Logs and Petrographic Analysis: A Case Study from the Early Miocene Nukhul Carbonate, Southern Gulf of Suez, Egypt. Arab J Sci Eng (2024). https://doi.org/10.1007/s13369-024-09173-5

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Accepted : 09 May 2024

Published : 29 May 2024

DOI : https://doi.org/10.1007/s13369-024-09173-5

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