These general characteristics of research designs serve as a background for considering the specific designs for case studies. Four types of designs will be discussed, based on a 2 x 2 matrix (see Figure 2.4). The matrix first shows that every type of design will include the desire to analyze contextual conditions in relation to the “case,” with the dotted lines between the two signaling that the boundaries between the case and the context are not likely to be sharp. The matrix then shows that single- and multiple-case studies reflect different design situations and that, within these two variants, there also can be unitary or multiple units of analysis. The resulting four types of designs for case studies are (Type 1) single-case (holistic) designs, (Type 2) single-case (embedded) designs, (Type 3) multiple-case (holistic) designs, and (Type 4) multiple-case (embedded) designs. The rationale for these four types of designs is as follows.
1. What Are the Potential Single-Case Designs (Types 1 and 2)?
Rationale for single-case designs. A primary distinction in designing case studies is between single- and multiple-case designs. This means the need for a decision, prior to any data collection, on whether a single case or multiple cases are going to be used to address the research questions. The single-case study is an appropriate design under several circumstances, and five rationales are given below. Recall that a single-case study is analogous to a single experiment, and many of the same conditions that justify a single experiment also justify a single-case study.
One rationale for a single case is when it represents the critical case in testing a well-formulated theory (again, note the analogy to the critical experiment). The theory has specified a clear set of propositions as well as the circumstances within which the propositions are believed to be true. A single case, meeting all of the conditions for testing the theory, can confirm, challenge, or extend the theory. The single case can then be used to determine whether a theory’s propositions are correct or whether some alternative set of explanations might be more relevant. In this manner, like Graham Allison’s comparison of three theories and the Cuban missile crisis (described in Chapter 1, BOX 2), the single case can represent a significant contribution to knowledge and theory building. Such a study can even help to refocus future investigations in an entire field. (See BOX 7 for another example, in the field of organizational innovation.)
A second rationale for a single case is where the case represents an extreme case or a unique case. Either of these situations commonly occurs in clinical psychology, where a specific injury or disorder may be so rare that any single case is worth documenting and analyzing. For instance, one rare clinical syndrome is the inability of certain clinical patients to recognize familiar faces. Given visual cues alone, such patients are unable to recognize loved ones, friends, pictures of famous people, or (in some cases) their own image in a mirror. This syndrome appears to be due to some physical injury to the brain. Yet the syndrome occurs so rarely that scientists have been unable to establish any common patterns (Yin, 1970, 1978). In such circumstances, the single-case study is an appropriate research design whenever a new person with this syndrome—known as prosopagnosia—is encountered. The case study would document the person’s abilities and disabilities, determine the precise nature of the face recognition deficit, but also ascertain whether related disorders exist.
The Critical Case as a Single-Case Study
One rationale for selecting a single-case rather than a multiple-case design is that the single case can represent the critical test of a significant theory. Cross, Bernstein, and Giacquinta (1971) used such a design by focusing on a single school in their book. Implementing Organizational Innovations (also see BOX 19B, Chapter 3, p. 110).
The school was selected because it had a prior history of innovation and could not be claimed to suffer from “barriers to innovation.” In the prevailing theories, such barriers had been prominently cited as the major reason that innovations failed. Cross et al. (1971) showed that, in this school, an innovation also failed but that the failure could not be attributed to any barriers. Implementation processes, rather than barriers, appeared to account for the failure.
In this manner, the book, though limited to a single case, represented a watershed in organizational innovation theory. Prior to the study, analysts had focused on the identification of barriers to innovation; since the study, the literature has been much more dominated by studies of the implementation process.
Conversely, a third rationale for a single case is the representative or typical case. Here, the objective is to capture the circumstances and conditions of an everyday or commonplace situation (see BOX 8; also see BOX 14, p. 75). The case study may represent a typical “project” among many different projects, a manufacturing firm believed to be typical of many other manufacturing firms in the same industry, a typical urban neighborhood, or a representative school, as examples. The lessons learned from these cases are assumed to be informative about the experiences of the average person or institution.
A fourth rationale for a single-case study is the revelatory case. This situation exists when an investigator has an opportunity to observe and analyze a phenomenon previously inaccessible to social science inquiry, such as Whyte’s (1943/1955) Street Comer Society, previously described in Chapter 1, BOX 2A. Another example is Elliot Liebow’s (1967) famous case study of unemployed men, Tally’s Corner (see BOX 9). Liebow had the opportunity to meet the men in an African American neighborhood in Washington, D.C. and to learn about their everyday lives. His observations of and insights into the problems of unemployment formed a significant case study, because few social scientists had previously had the opportunity to investigate these problems, even though the problems were common across the country. When other investigators have similar types of opportunities and can uncover some prevalent phenomenon previously inaccessible to social scientists, such conditions justify the use of a single-case study on the grounds of its revelatory nature.
The Average Case as a Single-Case Study
A famous community case study in sociology, Middletown, is about an average American city. The investigators, Robert and Helen Lynd (1929), deliberately chose to study a small town in middle America during the early 20th century (also see BOX 14, p. 75). Their purpose was to show how the transition from an agricultural to an industrial economy occurred in the average town—and thereby to provide a case ^jstudy about a significant development in all of American history.
The Revelatory Case as in Single-Case Study
Another rationale for selecting a single-case rather than a multiple-case design is that the investigator has access to a situation previously inaccessible to scientific observation. The case study is therefore worth conducting because the descriptive information alone will be revelatory.
Such was the situation in Elliot Liebow’s (1967) sociological classic, Tally’s Comer. The book is about a single group of African American men living in a poor, inner-city neighborhood. By befriending these men, the author was able to learn about their lifestyles, their coping behavior, and in particular their sensitivity to unemployment and failure. The book provided insights into a subculture that has prevailed in many U.S. cities for a long period of time, but one that had been only obscurely understood. The single case showed how investigations of such topics could be done, thus stimulating much further research and eventually the development of policy actions.
A fifth rationale for a single-case study is the longitudinal case: studying the same single case at two or more different points in time. The theory of interest would likely specify how certain conditions change over time, and the desired time intervals would presumably reflect the anticipated stages at which the changes should reveal themselves.
These five serve as major reasons for conducting a single-case study. There are other situations in which the single-case study may be used as a pilot case that is the first of a multiple-case study. However, in these latter instances, the single-case study cannot be regarded as a complete study on its own.
Whatever the rationale for doing single-case studies (and there may be more than the five mentioned here), a potential vulnerability of the single-case design is that a case may later turn out not to be the case it was thought to be at the outset. Single-case designs therefore require careful investigation of the potential case to minimize the chances of misrepresentation and to maximize the access needed to collect the case study evidence. A fair warning is not to commit yourself to any single-case study until all of these major concerns have been covered.
Holistic versus embedded case studies. The same single-case study may involve more than one unit of analysis. This occurs when, within a single case, attention is also given to a subunit or subunits (see BOX 10). For instance, even though a case study might be about a single organization, such as a hospital, the analysis might include outcomes about the clinical services and staff employed by the hospital (and possibly even some quantitative analyses based on the employee records of the staff). In an evaluation study, the single case might be a public program that involves large numbers of funded projects— which would then be the embedded units. In either situation, these embedded units can be selected through sampling or cluster techniques (McClintock, 1985). No matter how the units are selected, the resulting design would be called an embedded case study design (see Figure 2.4, Type 2). In contrast, if the case study examined only the global nature of an organization or of a program, a holistic design would have been used (see Figure 2.4, Type 1).
These two variants of single-case studies both have their strengths and weaknesses. The holistic design is advantageous when no logical subunits can be identified or when the relevant theory underlying the case study is itself of a holistic nature. Potential problems arise, however, when a global approach allows an investigator to avoid examining any specific phenomenon in operational detail. Thus, a typical problem with the holistic design is that the entire case study may be conducted at an unduly abstract level, lacking sufficiently clear measures or data.
An Embedded, Single-Case Design
Union Democracy (1956) is a highly regarded case study by three eminent academicians— Seymour Martin Lipset, Martin Trow, and James Coleman. The case study is about the inside politics of the International Typographical Union and involves several units of analysis (see “Kinds of Data” table). The main unit was the organization as a whole, the smallest unit was the individual member, and several intermediary units also were important. At each level of analysis, different data collection techniques were used, ranging from historical to survey analysis.
A further problem with the holistic design is that the entire nature of the case study may shift, unbeknownst to the researcher, during the course of study. The initial study questions may have reflected one orientation, but as the case study proceeds, a different orientation may emerge, and the evidence begins to address different research questions. Although some people have claimed such flexibility to be a strength of the case study approach, in fact the largest criticism of case studies is based on this type of shift—in which the implemented research design is no longer appropriate for the research questions being asked (see COSMOS Corporation, 1983). Because of this problem, you need to avoid such unsuspected slippage; if the relevant research questions really do change, you should simply start over again, with a new research design. One way to increase the sensitivity to such slippage is to have a set of subunits. Thus, an embedded design can serve as an important device for focusing a case study inquiry.
An embedded design, however, also has its pitfalls. A major one occurs when the case study focuses only on the subunit level and fails to return to the larger unit of analysis. For instance, an evaluation of a program consisting of multiple projects may include project characteristics as a subunit of analysis. The project-level data may even be highly quantitative if there are many projects. However, the original evaluation becomes a project study (i.e., a multiple-case study of different projects) if no investigating is done at the level of the original case—that is, the program. Similarly, a study of organizational climate may involve individual employees as a subunit of study. However, if the data focus only on individual employees, the study will in fact become an employee and not an organizational study. In both examples, what has happened is that the original phenomenon of interest (a program or organizational climate) has become the context and not the target of study.
Summary. Single cases are a common design for doing case studies, and two variants have been described: those using holistic designs and those using embedded units of analysis. Overall, the single-case design is eminently justifiable under certain conditions—where the case represents (a) a critical test of existing theory, (b) a rare or unique circumstance, or (c) a representative or typical case, or where the case serves a (d) revelatory or (e) longitudinal purpose.
A major step in designing and conducting a single case is defining the unit of analysis (or the case itself). An operational definition is needed, and some caution must be exercised—before a total commitment to the whole case study is made— to ensure that the case in fact is relevant to the issues and questions of interest.
Within the single case may still be incorporated subunits of analyses, so that a more complex—or embedded—design is developed. The subunits can often add significant opportunities for extensive analysis, enhancing the insights into the
single case. However, if too much attention is given to these subunits, and if the larger, holistic aspects of the case begin to be ignored, the case study itself will have shifted its orientation and changed its nature. If the shift is justifiable, you need to address it explicitly and indicate its relationship to the original inquiry.
2. What Are the Potential Multiple-Case Designs (Types 3 and 4)?
The same study may contain more than a single case. When this occurs, the study has used a multiple-case design, and such designs have increased in frequency in recent years. A common example is a study of school innovations (such as the use of new curricula, rearranged school schedules, or a new educational technology), in which individual schools adopt some innovation. Each school might be the subject of an individual case study, but the study as a whole covers several schools and in this way uses a multiple-case design.
Multiple- versus single-case designs. In some fields, multiple-case studies have been considered a different “methodology” from single-case studies. For example, both anthropology and political science have developed one set of rationales for doing single-case studies and a second set for doing what have been considered “comparative” (or multiple-case) studies (see Eckstein, 1975; Lijphart, 1975). This book, however, considers single- and multiple-case designs to be variants within the same methodological framework—and no broad distinction is made between the so-called classic (that is, single) case study and multiple-case studies. The choice is considered one of research design, with both being included under the case study method.
Multiple-case designs have distinct advantages and disadvantages in comparison to single-case designs. The evidence from multiple cases is often considered more compelling, and the overall study is therefore regarded as being more robust (Herriott & Firestone, 1983). At the same time, the rationale for single-case designs cannot usually be satisfied by multiple cases. By definition, the unusual or rare case, the critical case, and the revelatory case all are likely to involve only single cases. Moreover, the conduct of a multiple-case study can require extensive resources and time beyond the means of a single student or independent research investigator. Therefore, the decision to undertake multiple- case studies cannot be taken lightly.
Selecting the multiple cases also raises a new set of questions. Here, a major insight is to consider multiple cases as one would consider multiple experiments—that is, to follow a “replication” design. This is far different from a mistaken analogy in the past, which incorrectly considered multiple cases to be similar to the multiple respondents in a survey (or to the multiple subjects within an experiment)—that is, to follow a “sampling” design. The methodological differences between these two views are revealed by the different rationales underlying the replication as opposed to sampling designs.
Replication, not sampling logic, for multiple-case studies. The replication logic is analogous to that used in multiple experiments (see Hersen & Barlow, 1976). For example, upon uncovering a significant finding from a single experiment, an ensuing and pressing priority would be to replicate this finding by conducting a second, third, and even more experiments. Some of the replications might attempt to duplicate the exact conditions of the original experiment. Other replications might alter one or two experimental conditions considered unimportant to the original finding, to see whether the finding could still be duplicated. Only with such replications would the original finding be considered robust.
The logic underlying the use of multiple-case studies is the same. Each case must be carefully selected so that it either (a) predicts similar results (a literal replication) or (b) predicts contrasting results but for anticipatable reasons (a theoretical replication). The ability to conduct 6 or 10 case studies, arranged effectively within a multiple-case design, is analogous to the ability to conduct 6 to 10 experiments on related topics; a few cases (2 or 3) would be literal replications, whereas a few other cases (4 to 6) might be designed to pursue two different patterns of theoretical replications. If all the cases turn out as predicted, these 6 to 10 cases, in the aggregate, would have provided compelling support for the initial set of propositions. If the cases are in some way contradictory, the initial propositions must be revised and retested with another set of cases. Again, this logic is similar to the way scientists deal with conflicting experimental findings.
An important step in all of these replication procedures is the development of a rich, theoretical framework. The framework needs to state the conditions under which a particular phenomenon is likely to be found (a literal replication) as well as the conditions when it is not likely to be found (a theoretical replication). The theoretical framework later becomes the vehicle for generalizing to new cases, again similar to the role played in cross-experiment designs. Furthermore, just as with experimental science, if some of the empirical cases do not work as predicted, modification must be made to the theory. Remember, too, that theories can be practical and not just academic.
For example, one might consider the initial proposition that an increase in using a new technology in school districts will occur when the technology is used for both administrative and instmctional applications, but not either alone. To pursue this proposition in a multiple-case study design, 3 or 4 cases might be selected in which both types of applications are present, to determine whether, in fact, technology use did increase over a period of time (the investigation would be predicting a literal replication in these 3 or 4 cases). Three or 4 additional cases might be selected in which only administrative applications are present, with the prediction being little increase in use (predicting a theoretical replication). Finally, 3 or 4 other cases would be selected in which only instructional applications are present, with the same prediction of little increase in use, but for different reasons than the administrative-only cases (another theoretical replication). If this entire pattern of results across these multiple cases is indeed found, the 9 to 12 cases, in the aggregate, would provide substantial support for the initial proposition.
Another example of a multiple-case replication design comes from the field of urban studies (see BOX 11). You also can find examples of three entire case studies, all following a replication design but covering HIV/AIDS prevention, university administration, and the transformation of business firms, in the companion text (Yin, 2003, chaps. 8-10).
This replication logic, whether applied to experiments or to case studies, must be distinguished from the sampling logic commonly used in surveys. The sampling logic requires an operational enumeration of the entire universe or pool of potential respondents and then a statistical procedure for selecting a specific subset of respondents to be surveyed. The resulting data from the sample that is actually surveyed are assumed to reflect the entire universe or pool, with inferential statistics used to establish the confidence intervals for which this representation is presumed accurate. The entire procedure is commonly used when an investigator wishes to determine the prevalence or frequency of a particular phenomenon.
A Multiple-Case, Replication Design
A common problem in the 1960s and 1970s was how to get good advice to city governments. Peter Szanton’s (1981) book, Not Well Advised, reviewed the experiences of numerous attempts by university and research groups to collaborate with city officials.
The book is an excellent example of a multiple-case, replication design. Szanton starts with eight case studies, showing how different university groups all failed to help cities. The eight cases are sufficient “replications” to convince the reader of a general phenomenon. Szanton then provides five more case studies, in which nonuniversity groups also failed, concluding that failure was therefore not necessarily inherent in the academic enterprise. Yet a third group of cases shows how university groups have successfully helped business, engineering firms, and sectors other than city government. A final set of three cases shows that those few groups able to help city government were concerned with implementation and not just with the production of new ideas, leading to the major conclusion that city governments may have peculiar needs in receiving but also then putting advice into practice.
Within each of the four groups of case studies, Szanton has illustrated the principle of literal replication. Across the four groups, he has illustrated theoretical replication. This potent case study design can and should be applied to many other topics.
Any application of this sampling logic to case studies would be misplaced. First, case studies are not the best method for assessing the prevalence of phenomena. Second, a case study would have to cover both the phenomenon of interest and its context, yielding a large number of potentially relevant variables. In turn, this would require an impossibly large number of cases—too large to allow any statistical consideration of the relevant variables.
Third, if a sampling logic had to be applied to all types of research, many important topics could not be empirically investigated, such as the following problem: Your investigation deals with the role of the presidency of the United States, and you are interested in doing a multiple-case study of a (few) presidents to test your theory about presidential leadership. However, the complexity of your topic means that your choice of a small number of cases could not adequately represent all the 44 presidents since the beginning of the Republic. Critics using a sampling logic might therefore deny the acceptability of your study. In contrast, if you use a replication logic, the study is eminently feasible.
The replication approach to multiple-case studies is illustrated in Figure 2.5. The figure indicates that the initial step in designing the study must consist of theory development, and then shows that case selection and the definition of specific measures are important steps in the design and data collection process. Each individual case study consists of a “whole” study, in which convergent evidence is sought regarding the facts and conclusions for the case; each case’s conclusions are then considered to be the information needing replication by other individual cases. Both the individual cases and the multiple-case results can and should be the focus of a summary report. For each individual case, the report should indicate how and why a particular proposition was demonstrated (or not demonstrated). Across cases, the report should indicate the extent of the replication logic and why certain cases were predicted to have certain results, whereas other cases, if any, were predicted to have contrasting results.
An important part of Figure 2.5 is the dashed-line feedback loop. The loop represents the situation where important discovery occurs during the conduct of one of the individual case studies (e.g., one of the cases did not in fact suit the original design). Such a discovery even may require you to reconsider one or more of the study’s original theoretical propositions. At this point, “redesign” should take place before proceeding further. Such redesign might involve the selection of alternative cases or changes in the case study (i.e., data collection) protocol (see Chapter 3). Without such redesign, you risk being accused of distorting or ignoring the discovery, just to accommodate the original design. This condition leads quickly to a further accusation—that you have been selective in reporting your data, to suit your preconceived ideas (i.e., the original theoretical propositions).
Overall, Figure 2.5 depicts a very different logic from that of a sampling design. The logic as well as its contrast with a sampling design may be difficult to follow and is worth extensive discussion with colleagues before proceeding with any multiple case study.
When using a multiple-case design, a further question you will encounter has to do with the number of cases deemed necessary or sufficient for your study. However, because a sampling logic should not be used, the typical criteria regarding sample size also are irrelevant. Instead, you should think of this decision as a reflection of the number of case replications—both literal and theoretical—that you need or would like to have in your study.
For the number of literal replications, an appropriate analogy from statistics is the selection of the criterion for establishing the sample size desired to detect an “effect.” Designating a “p < .05” or “p < .01” likelihood of detection as part of a power analysis is not based on any formula but is a matter of discretionary, judgmental choice. Analogously, designating the number of replications depends upon the certainty you want to have about your multiple-case results (as with the higher criterion for establishing the likelihood of detection, the greater certainty lies with the larger number of cases). For example, you may want to settle for two or three literal replications when your theory is straightforward and the issue at hand does not demand an excessive degree of certainty. However, if your theory is subtle or if you want a high degree of certainty, you may press for five, six, or more replications.
For the number of theoretical replications, the important consideration is related to your sense of the importance of rival explanations. The stronger the rivals, the more additional cases you might want, each case showing a different result when some rival explanation had been taken into account. For example, your original hypothesis might be that summer reading programs improve students’ reading scores, and you already might have shown this result through several cases that served as literal replications. A rival explanation might be that parents also work more closely with their children during the summer and that this circumstance can account for improved reading scores. You would then find another case, with parent participation but no summer reading program, and in this theoretical replication you would predict that the scores would not improve.
Rationale for multiple-case designs. In short, the rationale for multiple-case designs derives directly from your understanding of literal and theoretical replications. The simplest multiple-case design would be the selection of two or more cases that are believed to be literal replications, such as a set of cases with exemplary outcomes in relation to some evaluation questions, such as “how and why a particular intervention has been implemented smoothly.” Selecting such cases requires prior knowledge of the outcomes, with the multiple-case inquiry focusing on how and why the exemplary outcomes might have occurred and hoping for literal (or direct) replications of these conditions from case to case.5
More complicated multiple-case designs would likely result from the number and types of theoretical replications you might want to cover. For example, investigators have used a “two-tail” design in which cases from both extremes (of some important theoretical condition, such as good and bad outcomes) have been deliberately chosen. Multiple-case rationales also can derive from the prior hypothesizing of different types of conditions and the desire to have subgroups of cases covering each type. These and other similar designs are more complicated because the study should still have at least two individual cases within each of the subgroups, so that the theoretical replications across subgroups are complemented by literal replications within each subgroup.
Multiple-case studies: Holistic or embedded. The fact that a design calls for multiple-case studies does not eliminate the variation identified earlier with single cases: Each individual case may still be holistic or embedded. In other words, a multiple-case study may consist of multiple holistic cases (see Figure 2.4, Type 3) or of multiple embedded cases (see Figure 2.4, Type 4).
The difference between these two variants depends upon the type of phenomenon being studied and your research questions. In an embedded design, a study even may call for the conduct of a survey at each case study site. For instance, suppose a study is concerned with the impact of the same type of curriculum adopted by different schools. Each school may be the topic of a case study, with the theoretical framework dictating that nine such schools be included as case studies, three to replicate a direct result (literal replication) and six others to deal with contrasting conditions (theoretical replications).
For all nine schools, an embedded design is used because surveys of the students (or, alternatively, examination of students’ archival records) are needed to address research questions about the performance of the schools. However, the results of each survey will not be pooled across schools. Rather, the survey data will be part of the findings for each individual school, or case. These data may be highly quantitative, focusing on the attitudes and behavior of individual students, and the data will be used along with archival information to interpret the success and operations at the given school. If, in contrast, the survey data are pooled across schools, a replication design is no longer being used. In fact, the study has now become a single-case study, in which all nine schools and their students have now become part of some larger, main unit of analysis. Such a new case study would then require a complete redefinition of the main unit of analysis, with extensive revisions to the original theories and propositions of interest also a likely need.
Summary. This section has dealt with situations in which the same investigation may call for multiple-case studies. These types of designs are becoming more prevalent, but they are more expensive and time-consuming to conduct.
Any use of multiple-case designs should follow a replication, not a sampling logic, and an investigator must choose each case carefully. The cases should serve in a manner similar to multiple experiments, with similar results (a literal replication) or contrasting results (a theoretical replication) predicted explicitly at the outset of the investigation.
The individual cases within a multiple-case study design may be either holistic or embedded. When an embedded design is used, each individual case study may in fact include the collection and analysis of quantitative data, including the use of surveys within each case.
EXERCISE 2.4 Defining a Case Study Research Design
Select one of the case studies described in the BOXES of this book, reviewing the entire case study (not just the material in the BOX). Describe the research design of this case study. How did it justify the relevant evidence to be sought, given the basic research questions to be answered? What methods were used to draw conclusions, based on the evidence? Is the design a single- or multiple-case design? Is it holistic or does it have embedded units of analysis?
Source: Yin K Robert (2008), Case Study Research Designs and Methods, SAGE Publications, Inc; 4th edition.