hypothesis of case studies

Case Study Methods and Examples

By Janet Salmons, PhD Manager, Sage Research Methods Community

What is Case Study Methodology ?

Case studies in research are both unique and uniquely confusing. The term case study is confusing because the same term is used multiple ways. The term can refer to the methodology, that is, a system of frameworks used to design a study, or the methods used to conduct it. Or, case study can refer to a type of academic writing that typically delves into a problem, process, or situation.

Case study methodology can entail the study of one or more "cases," that could be described as instances, examples, or settings where the problem or phenomenon can be examined. The researcher is tasked with defining the parameters of the case, that is, what is included and excluded. This process is called bounding the case , or setting boundaries.

Case study can be combined with other methodologies, such as ethnography, grounded theory, or phenomenology. In such studies the research on the case uses another framework to further define the study and refine the approach.

Case study is also described as a method, given particular approaches used to collect and analyze data. Case study research is conducted by almost every social science discipline: business, education, sociology, psychology. Case study research, with its reliance on multiple sources, is also a natural choice for researchers interested in trans-, inter-, or cross-disciplinary studies.

The Encyclopedia of case study research provides an overview:

The purpose of case study research is twofold: (1) to provide descriptive information and (2) to suggest theoretical relevance. Rich description enables an in-depth or sharpened understanding of the case.

It is unique given one characteristic: case studies draw from more than one data source. Case studies are inherently multimodal or mixed methods because this they use either more than one form of data within a research paradigm, or more than one form of data from different paradigms.

A case study inquiry could include multiple types of data:

multiple forms of quantitative data sources, such as Big Data + a survey

multiple forms of qualitative data sources, such as interviews + observations + documents

multiple forms of quantitative and qualitative data sources, such as surveys + interviews

Case study methodology can be used to achieve different research purposes.

Robert Yin , methodologist most associated with case study research, differentiates between descriptive , exploratory and explanatory case studies:

Descriptive : A case study whose purpose is to describe a phenomenon. Explanatory : A case study whose purpose is to explain how or why some condition came to be, or why some sequence of events occurred or did not occur. Exploratory: A case study whose purpose is to identify the research questions or procedures to be used in a subsequent study.

Robert Yin’s book is a comprehensive guide for case study researchers!

You can read the preface and Chapter 1 of Yin's book here . See the open-access articles below for some published examples of qualitative, quantitative, and mixed methods case study research.

Mills, A. J., Durepos, G., & Wiebe, E. (2010). Encyclopedia of case study research (Vols. 1-0). Thousand Oaks, CA: SAGE Publications, Inc. doi: 10.4135/9781412957397

Yin, R. K. (2018). Case study research and applications (6th ed.). Thousand Oaks: SAGE Publications.

Open-Access Articles Using Case Study Methodology

As you can see from this collection, case study methods are used in qualitative, quantitative and mixed methods research.

Ang, C.-S., Lee, K.-F., & Dipolog-Ubanan, G. F. (2019). Determinants of First-Year Student Identity and Satisfaction in Higher Education: A Quantitative Case Study. SAGE Open. https://doi.org/10.1177/2158244019846689

Abstract. First-year undergraduates’ expectations and experience of university and student engagement variables were investigated to determine how these perceptions influence their student identity and overall course satisfaction. Data collected from 554 first-year undergraduates at a large private university were analyzed. Participants were given the adapted version of the Melbourne Centre for the Study of Higher Education Survey to self-report their learning experience and engagement in the university community. The results showed that, in general, the students’ reasons of pursuing tertiary education were to open the door to career opportunities and skill development. Moreover, students’ views on their learning and university engagement were at the moderate level. In relation to student identity and overall student satisfaction, it is encouraging to state that their perceptions of studentship and course satisfaction were rather positive. After controlling for demographics, student engagement appeared to explain more variance in student identity, whereas students’ expectations and experience explained greater variance in students’ overall course satisfaction. Implications for practice, limitations, and recommendation of this study are addressed.

Baker, A. J. (2017). Algorithms to Assess Music Cities: Case Study—Melbourne as a Music Capital. SAGE Open. https://doi.org/10.1177/2158244017691801

Abstract. The global Mastering of a Music City report in 2015 notes that the concept of music cities has penetrated the global political vernacular because it delivers “significant economic, employment, cultural and social benefits.” This article highlights that no empirical study has combined all these values and offers a relevant and comprehensive definition of a music city. Drawing on industry research,1 the article assesses how mathematical flowcharts, such as Algorithm A (Economics), Algorithm B (Four T’s creative index), and Algorithm C (Heritage), have contributed to the definition of a music city. Taking Melbourne as a case study, it illustrates how Algorithms A and B are used as disputed evidence about whether the city is touted as Australia’s music capital. The article connects the three algorithms to an academic framework from musicology, urban studies, cultural economics, and sociology, and proposes a benchmark Algorithm D (Music Cities definition), which offers a more holistic assessment of music activity in any urban context. The article concludes by arguing that Algorithm D offers a much-needed definition of what comprises a music city because it builds on the popular political economy focus and includes the social importance of space and cultural practices.

Brown, K., & Mondon, A. (2020). Populism, the media, and the mainstreaming of the far right: The Guardian’s coverage of populism as a case study. Politics. https://doi.org/10.1177/0263395720955036

Abstract. Populism seems to define our current political age. The term is splashed across the headlines, brandished in political speeches and commentaries, and applied extensively in numerous academic publications and conferences. This pervasive usage, or populist hype, has serious implications for our understanding of the meaning of populism itself and for our interpretation of the phenomena to which it is applied. In particular, we argue that its common conflation with far-right politics, as well as its breadth of application to other phenomena, has contributed to the mainstreaming of the far right in three main ways: (1) agenda-setting power and deflection, (2) euphemisation and trivialisation, and (3) amplification. Through a mixed-methods approach to discourse analysis, this article uses The Guardian newspaper as a case study to explore the development of the populist hype and the detrimental effects of the logics that it has pushed in public discourse.

Droy, L. T., Goodwin, J., & O’Connor, H. (2020). Methodological Uncertainty and Multi-Strategy Analysis: Case Study of the Long-Term Effects of Government Sponsored Youth Training on Occupational Mobility. Bulletin of Sociological Methodology/Bulletin de Méthodologie Sociologique, 147–148(1–2), 200–230. https://doi.org/10.1177/0759106320939893

Abstract. Sociological practitioners often face considerable methodological uncertainty when undertaking a quantitative analysis. This methodological uncertainty encompasses both data construction (e.g. defining variables) and analysis (e.g. selecting and specifying a modelling procedure). Methodological uncertainty can lead to results that are fragile and arbitrary. Yet, many practitioners may be unaware of the potential scale of methodological uncertainty in quantitative analysis, and the recent emergence of techniques for addressing it. Recent proposals for ‘multi-strategy’ approaches seek to identify and manage methodological uncertainty in quantitative analysis. We present a case-study of a multi-strategy analysis, applied to the problem of estimating the long-term impact of 1980s UK government-sponsored youth training. We use this case study to further highlight the problem of cumulative methodological fragilities in applied quantitative sociology and to discuss and help develop multi-strategy analysis as a tool to address them.

Ebneyamini, S., & Sadeghi Moghadam, M. R. (2018). Toward Developing a Framework for Conducting Case Study Research . International Journal of Qualitative Methods . https://doi.org/10.1177/1609406918817954

Abstract. This article reviews the use of case study research for both practical and theoretical issues especially in management field with the emphasis on management of technology and innovation. Many researchers commented on the methodological issues of the case study research from their point of view thus, presenting a comprehensive framework was missing. We try representing a general framework with methodological and analytical perspective to design, develop, and conduct case study research. To test the coverage of our framework, we have analyzed articles in three major journals related to the management of technology and innovation to approve our framework. This study represents a general structure to guide, design, and fulfill a case study research with levels and steps necessary for researchers to use in their research.

Lai, D., & Roccu, R. (2019). Case study research and critical IR: the case for the extended case methodology. International Relations , 33 (1), 67-87. https://doi.org/10.1177/0047117818818243

Abstract. Discussions on case study methodology in International Relations (IR) have historically been dominated by positivist and neopositivist approaches. However, these are problematic for critical IR research, pointing to the need for a non-positivist case study methodology. To address this issue, this article introduces and adapts the extended case methodology as a critical, reflexivist approach to case study research, whereby the case is constructed through a dynamic interaction with theory, rather than selected, and knowledge is produced through extensions rather than generalisation. Insofar as it seeks to study the world in complex and non-linear terms, take context and positionality seriously, and generate explicitly political and emancipatory knowledge, the extended case methodology is consistent with the ontological and epistemological commitments of several critical IR approaches. Its potential is illustrated in the final part of the article with reference to researching the socioeconomic dimension of transitional justice in Bosnia and Herzegovina.

Lynch, R., Young, J. C., Boakye-Achampong, S., Jowaisas, C., Sam, J., & Norlander, B. (2020). Benefits of crowdsourcing for libraries: A case study from Africa . IFLA Journal. https://doi.org/10.1177/0340035220944940

Abstract. Many libraries in the Global South do not collect comprehensive data about themselves, which creates challenges in terms of local and international visibility. Crowdsourcing is an effective tool that engages the public to collect missing data, and it has proven to be particularly valuable in countries where governments collect little public data. Whereas crowdsourcing is often used within fields that have high levels of development funding, such as health, the authors believe that this approach would have many benefits for the library field as well. They present qualitative and quantitative evidence from 23 African countries involved in a crowdsourcing project to map libraries. The authors find benefits in terms of increased connections between stakeholders, capacity-building, and increased local visibility. These findings demonstrate the potential of crowdsourced approaches for tasks such as mapping to benefit libraries and similarly positioned institutions in the Global South in multifaceted ways.

Mason, W., Morris, K., Webb, C., Daniels, B., Featherstone, B., Bywaters, P., Mirza, N., Hooper, J., Brady, G., Bunting, L., & Scourfield, J. (2020). Toward Full Integration of Quantitative and Qualitative Methods in Case Study Research: Insights From Investigating Child Welfare Inequalities. Journal of Mixed Methods Research, 14 (2), 164-183. https://doi.org/10.1177/1558689819857972

Abstract. Delineation of the full integration of quantitative and qualitative methods throughout all stages of multisite mixed methods case study projects remains a gap in the methodological literature. This article offers advances to the field of mixed methods by detailing the application and integration of mixed methods throughout all stages of one such project; a study of child welfare inequalities. By offering a critical discussion of site selection and the management of confirmatory, expansionary and discordant data, this article contributes to the limited body of mixed methods exemplars specific to this field. We propose that our mixed methods approach provided distinctive insights into a complex social problem, offering expanded understandings of the relationship between poverty, child abuse, and neglect.

Rashid, Y., Rashid, A., Warraich, M. A., Sabir, S. S., & Waseem, A. (2019). Case Study Method: A Step-by-Step Guide for Business Researchers . International Journal of Qualitative Methods . https://doi.org/10.1177/1609406919862424

Abstract. Qualitative case study methodology enables researchers to conduct an in-depth exploration of intricate phenomena within some specific context. By keeping in mind research students, this article presents a systematic step-by-step guide to conduct a case study in the business discipline. Research students belonging to said discipline face issues in terms of clarity, selection, and operationalization of qualitative case study while doing their final dissertation. These issues often lead to confusion, wastage of valuable time, and wrong decisions that affect the overall outcome of the research. This article presents a checklist comprised of four phases, that is, foundation phase, prefield phase, field phase, and reporting phase. The objective of this article is to provide novice researchers with practical application of this checklist by linking all its four phases with the authors’ experiences and learning from recently conducted in-depth multiple case studies in the organizations of New Zealand. Rather than discussing case study in general, a targeted step-by-step plan with real-time research examples to conduct a case study is given.

VanWynsberghe, R., & Khan, S. (2007). Redefining Case Study. International Journal of Qualitative Methods, 80–94. https://doi.org/10.1177/160940690700600208

Abstract. In this paper the authors propose a more precise and encompassing definition of case study than is usually found. They support their definition by clarifying that case study is neither a method nor a methodology nor a research design as suggested by others. They use a case study prototype of their own design to propose common properties of case study and demonstrate how these properties support their definition. Next, they present several living myths about case study and refute them in relation to their definition. Finally, they discuss the interplay between the terms case study and unit of analysis to further delineate their definition of case study. The target audiences for this paper include case study researchers, research design and methods instructors, and graduate students interested in case study research.

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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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A Beginner’s Guide to Hypothesis Testing in Business

Business professionals performing hypothesis testing

30 Mar 2021

Becoming a more data-driven decision-maker can bring several benefits to your organization, enabling you to identify new opportunities to pursue and threats to abate. Rather than allowing subjective thinking to guide your business strategy, backing your decisions with data can empower your company to become more innovative and, ultimately, profitable.

If you’re new to data-driven decision-making, you might be wondering how data translates into business strategy. The answer lies in generating a hypothesis and verifying or rejecting it based on what various forms of data tell you.

Below is a look at hypothesis testing and the role it plays in helping businesses become more data-driven.

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What Is Hypothesis Testing?

To understand what hypothesis testing is, it’s important first to understand what a hypothesis is.

A hypothesis or hypothesis statement seeks to explain why something has happened, or what might happen, under certain conditions. It can also be used to understand how different variables relate to each other. Hypotheses are often written as if-then statements; for example, “If this happens, then this will happen.”

Hypothesis testing , then, is a statistical means of testing an assumption stated in a hypothesis. While the specific methodology leveraged depends on the nature of the hypothesis and data available, hypothesis testing typically uses sample data to extrapolate insights about a larger population.

Hypothesis Testing in Business

When it comes to data-driven decision-making, there’s a certain amount of risk that can mislead a professional. This could be due to flawed thinking or observations, incomplete or inaccurate data , or the presence of unknown variables. The danger in this is that, if major strategic decisions are made based on flawed insights, it can lead to wasted resources, missed opportunities, and catastrophic outcomes.

The real value of hypothesis testing in business is that it allows professionals to test their theories and assumptions before putting them into action. This essentially allows an organization to verify its analysis is correct before committing resources to implement a broader strategy.

As one example, consider a company that wishes to launch a new marketing campaign to revitalize sales during a slow period. Doing so could be an incredibly expensive endeavor, depending on the campaign’s size and complexity. The company, therefore, may wish to test the campaign on a smaller scale to understand how it will perform.

In this example, the hypothesis that’s being tested would fall along the lines of: “If the company launches a new marketing campaign, then it will translate into an increase in sales.” It may even be possible to quantify how much of a lift in sales the company expects to see from the effort. Pending the results of the pilot campaign, the business would then know whether it makes sense to roll it out more broadly.

Related: 9 Fundamental Data Science Skills for Business Professionals

Key Considerations for Hypothesis Testing

1. alternative hypothesis and null hypothesis.

In hypothesis testing, the hypothesis that’s being tested is known as the alternative hypothesis . Often, it’s expressed as a correlation or statistical relationship between variables. The null hypothesis , on the other hand, is a statement that’s meant to show there’s no statistical relationship between the variables being tested. It’s typically the exact opposite of whatever is stated in the alternative hypothesis.

For example, consider a company’s leadership team that historically and reliably sees $12 million in monthly revenue. They want to understand if reducing the price of their services will attract more customers and, in turn, increase revenue.

In this case, the alternative hypothesis may take the form of a statement such as: “If we reduce the price of our flagship service by five percent, then we’ll see an increase in sales and realize revenues greater than $12 million in the next month.”

The null hypothesis, on the other hand, would indicate that revenues wouldn’t increase from the base of $12 million, or might even decrease.

Check out the video below about the difference between an alternative and a null hypothesis, and subscribe to our YouTube channel for more explainer content.

2. Significance Level and P-Value

Statistically speaking, if you were to run the same scenario 100 times, you’d likely receive somewhat different results each time. If you were to plot these results in a distribution plot, you’d see the most likely outcome is at the tallest point in the graph, with less likely outcomes falling to the right and left of that point.

With this in mind, imagine you’ve completed your hypothesis test and have your results, which indicate there may be a correlation between the variables you were testing. To understand your results' significance, you’ll need to identify a p-value for the test, which helps note how confident you are in the test results.

In statistics, the p-value depicts the probability that, assuming the null hypothesis is correct, you might still observe results that are at least as extreme as the results of your hypothesis test. The smaller the p-value, the more likely the alternative hypothesis is correct, and the greater the significance of your results.

3. One-Sided vs. Two-Sided Testing

When it’s time to test your hypothesis, it’s important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests , or one-tailed and two-tailed tests, respectively.

Typically, you’d leverage a one-sided test when you have a strong conviction about the direction of change you expect to see due to your hypothesis test. You’d leverage a two-sided test when you’re less confident in the direction of change.

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4. Sampling

To perform hypothesis testing in the first place, you need to collect a sample of data to be analyzed. Depending on the question you’re seeking to answer or investigate, you might collect samples through surveys, observational studies, or experiments.

A survey involves asking a series of questions to a random population sample and recording self-reported responses.

Observational studies involve a researcher observing a sample population and collecting data as it occurs naturally, without intervention.

Finally, an experiment involves dividing a sample into multiple groups, one of which acts as the control group. For each non-control group, the variable being studied is manipulated to determine how the data collected differs from that of the control group.

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Learn How to Perform Hypothesis Testing

Hypothesis testing is a complex process involving different moving pieces that can allow an organization to effectively leverage its data and inform strategic decisions.

If you’re interested in better understanding hypothesis testing and the role it can play within your organization, one option is to complete a course that focuses on the process. Doing so can lay the statistical and analytical foundation you need to succeed.

Do you want to learn more about hypothesis testing? Explore Business Analytics —one of our online business essentials courses —and download our Beginner’s Guide to Data & Analytics .

About the Author

The theory contribution of case study research designs

Original Research
Open access
Published: 16 February 2017
Volume 10 , pages 281–305, ( 2017 )

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Hans-Gerd Ridder 1

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The objective of this paper is to highlight similarities and differences across various case study designs and to analyze their respective contributions to theory. Although different designs reveal some common underlying characteristics, a comparison of such case study research designs demonstrates that case study research incorporates different scientific goals and collection and analysis of data. This paper relates this comparison to a more general debate of how different research designs contribute to a theory continuum. The fine-grained analysis demonstrates that case study designs fit differently to the pathway of the theory continuum. The resulting contribution is a portfolio of case study research designs. This portfolio demonstrates the heterogeneous contributions of case study designs. Based on this portfolio, theoretical contributions of case study designs can be better evaluated in terms of understanding, theory-building, theory development, and theory testing.

Case Study Research

Avoid common mistakes on your manuscript.

1 Introduction

Case study research scientifically investigates into a real-life phenomenon in-depth and within its environmental context. Such a case can be an individual, a group, an organization, an event, a problem, or an anomaly (Burawoy 2009 ; Stake 2005 ; Yin 2014 ). Unlike in experiments, the contextual conditions are not delineated and/or controlled, but part of the investigation. Typical for case study research is non-random sampling; there is no sample that represents a larger population. Contrary to quantitative logic, the case is chosen, because the case is of interest (Stake 2005 ), or it is chosen for theoretical reasons (Eisenhardt and Graebner 2007 ). For within-case and across-case analyses, the emphasis in data collection is on interviews, archives, and (participant) observation (Flick 2009 : 257; Mason 2002 : 84). Case study researchers usually triangulate data as part of their data collection strategy, resulting in a detailed case description (Burns 2000 ; Dooley 2002 ; Eisenhardt 1989 ; Ridder 2016 ; Stake 2005 : 454). Potential advantages of a single case study are seen in the detailed description and analysis to gain a better understanding of “how” and “why” things happen. In single case study research, the opportunity to open a black box arises by looking at deeper causes of the phenomenon (Fiss 2009 ). The case data can lead to the identification of patterns and relationships, creating, extending, or testing a theory (Gomm et al. 2000 ). Potential advantages of multiple case study research are seen in cross-case analysis. A systematic comparison in cross-case analysis reveals similarities and differences and how they affect findings. Each case is analyzed as a single case on its own to compare the mechanisms identified, leading to theoretical conclusions (Vaughan 1992 : 178). As a result, case study research has different objectives in terms of contributing to theory. On the one hand, case study research has its strength in creating theory by expanding constructs and relationships within distinct settings (e.g., in single case studies). On the other hand, case study research is a means of advancing theories by comparing similarities and differences among cases (e.g., in multiple case studies).

Unfortunately, such diverging objectives are often neglected in case study research. Burns ( 2000 : 459) emphasizes: “The case study has unfortunately been used as a ‘catch –all’ category for anything that does not fit into experimental, survey, or historical methods.”

Therefore, this paper compares case study research designs. Such comparisons have been conducted previously regarding their philosophical assumptions and orientations, key elements of case study research, their range of application, and the lacks of methodological procedures in publications. (Baxter and Jack 2008 ; Dooley 2002 ; Dyer and Wilkins 1991 ; Piekkari et al. 2009 ; Welch et al. 2011 ). This paper aims to compare case study research designs regarding their contributions to theory.

Case study research designs will be analyzed regarding their various strengths on a theory continuum. Edmondson and McManus ( 2007 ) initiated a debate on whether the stage of theory fits to research questions, style of data collection, and analyses. Similarly, Colquitt and Zapata-Phelan ( 2007 ) created a taxonomy capturing facets of empirical article’s theoretical contributions by distinguishing between theory-building and theory testing. Corley and Gioia ( 2011 ) extended this debate by focusing on the practicality of theory and the importance of prescience. While these papers consider the whole range of methodological approaches on a higher level, they treat case studies as relatively homogeneous. This paper aims to delve into a deeper level of analysis by solely focusing on case study research designs and their respective fit on this theory continuum. This approach offers a more fine-grained understanding that sheds light on the diversity of case study research designs in terms of their differential theory contributions. Such a deep level of analysis on case study research designs enables more rigor in theory contribution. To analyze alternative case study research designs regarding their contributions to theory, I engage into the following steps:

First, differences between case study research designs are depicted. I outline and compare the case study research designs with regard to the key elements, esp. differences in research questions, frameworks, sampling, data collection, and data analysis. These differences result in a portfolio of various case study research designs.

Second, I outline and substantiate a theory continuum that varies between theory-building, theory development, and testing theory. Based on this continuum, I analyze and discuss each of the case study research designs with regard to their location on the theory continuum. This analysis is based on a detailed differentiation of the phenomenon (inside or outside the theory), the status of the theory, research strategy, and methods.

As a result, the contribution to the literature is a portfolio of case study research designs explicating their unique contributions to theory. The contribution of this paper lies in a fine-grained analysis of the interplay of methods and theory (van Maanen et al. 2007 ) and the methodological fit (Edmondson and McManus 2007 ) of case study designs and the continuum of theory. It demonstrates that different designs have various strengths and that there is a fit between case study designs and different points on a theory continuum. If there is no clarity as to whether a case study design aims at creating, elaborating, extending, or testing theory, the contribution to theory is difficult to identify for authors, reviewers, and readers. Consequently, this paper aims to clarify at which point of the continuum of theory case study research designs can provide distinct contributions that can be identified beyond their traditionally claimed exploratory character.

2 Differences across case study design: a portfolio approach

Only few papers have compared case study research designs so far. In all of these comparisons, the number of designs differs as well as the issues under consideration. In an early debate between Dyer and Wilkins ( 1991 ) and Eisenhardt ( 1991 ), Dyer and Wilkins compared the case study research design by Eisenhardt ( 1989 ) with “classical” case studies. The core of the debate concerns a difference between in-depth single case studies (classical case study) to a focus on the comparison of multiple cases. Dyer and Wilkins ( 1991 : 614) claim that the essence of a case study lies in the careful study of a single case to identify new relationships and, as a result, question the Eisenhardt approach which puts a lot of emphasis on comparison of multiple cases. Eisenhardt, on the contrary, claims that multiple cases allow replication between cases and is, therefore, seen as a means of corroboration of propositions (Eisenhardt 1991 ). Classical case studies prefer deep descriptions of a single case, considering the context to reveal insights into the single case and by that elaborate new theories. The comparison of multiple cases, therefore, tends—in the opinion of Dyer and Wilkens—to surface descriptions. This weakens the possibility of context-related, rich descriptions. While, in classic case study, good stories are the aim, the development of good constructs and their relationships is aimed in Eisenhardt’s approach. Eisenhardt ( 1991 : 627) makes a strong plea on more methodological rigor in case study research, while Dyer and Wilkins ( 1991 : 613) criticize that the new approach “… includes many of the attributes of hypothesis-testing research (e.g., sampling and controls).”

Dooley ( 2002 : 346) briefly takes the case study research designs by Yin (1994) and Eisenhardt ( 1989 ) as exemplars of how the processes of case study research can be applied. The approach by Eisenhardt is seen as an exemplar that advances conceptualization and operationalization in the phases of theory-building, while the approach by Yin is seen as exemplar that advances minimally conceptualized and operationalized existing theory.

Baxter and Jack ( 2008 ) describe the designs by Yin (2003) and Stake ( 1995 ) to demonstrate key elements of qualitative case study. The authors outline and carefully compare the approaches by Yin and Stake in conducting the research process, neglecting philosophical differences and theoretical goals.

Piekkari et al. ( 2009 ) outline the methodological richness of case study research using the approaches of Yin et al. (1998), and Stake. They specifically exhibit the role of philosophical assumptions, establishing differences in conventionally accepted practices of case study research in published papers. The authors analyze 135 published case studies in four international business journals. The analysis reveals that, in contrast to the richness of case study approaches, the majority of published case studies draw on positivistic foundations and are narrowly declared as explorative with a lack of clarity of the theoretical purpose of the case study. Case studies are often designed as multiple case studies with cross-sectional designs based on interviews. In addition to the narrow use of case study research, the authors find out that “… most commonly cited methodological literature is not consistently followed” (Piekkari et al. 2009 : 567).

Welch et al. ( 2011 ) develop a typology of theorizing modes in case study methods. Based on the two dimensions “contextualization” and “causal explanation”, they differentiate in their typology between inductive theory-building (Eisenhardt), interpretive sensemaking (Stake), natural experiment (Yin), and contextualised explanation (Ragin/Bhaskar). The typology is used to analyze 199 case studies from three highly ranked journals over a 10-year period for whether the theorizing modes are exercised in the practice of publishing case studies. As a result, the authors identify a strong emphasis on the exploratory function of case studies, neglecting the richness of case study methods to challenge, refine, verify, and test theories (Welch et al. 2011 : 755). In addition, case study methods are not consistently related to theory contribution: “By scrutinising the linguistic elements of texts, we found that case researchers were not always clear and consistent in the way that they wrote up their theorising purpose and process” (Welch et al. 2011 : 756).

As a result, the comparisons reveal a range of case study designs which are rarely discussed. In contrast, published case studies are mainly introduced as exploratory design. Explanatory, interpretivist, and critical/reflexive designs are widely neglected, narrowing the possible applications of case study research. In addition, comparisons containing an analysis of published case studies reveal a low degree in accuracy when applying case study methods.

What is missing is a comparison of case study research designs with regard to differences in the contribution to theory. Case study designs have different purposes in theory contribution. Confusing these potential contributions by inconsistently utilizing the appropriate methods weakens the contribution of case studies to scientific progress and, by that, damages the reputation of case studies.

To conduct such a comparison, I consider the four case study research approaches of Yin, Eisenhardt, Burawoy, and Stake for the following reasons.

These approaches are the main representatives of case study research design outlined in the comparisons elaborated above (Baxter and Jack 2008 ; Dooley 2002 ; Dyer and Wilkins 1991 ; Piekkari et al. 2009 ; Welch et al. 2011 ). I follow especially the argument by Piekkari et al. ( 2009 ) that these approaches contain a broad spectrum of methodological foundations of exploratory, explanatory, interpretivist, and critical/reflexive designs. The chosen approaches have an explicit and detailed methodology which can be reconstructed and compared with regard to their theory contribution. Although there are variations in the application of the designs, to the best of my knowledge, the designs represent the spectrum of case study methodologies. A comparison of these methodologies revealed main distinguishable differences. To highlight these main differences, I summarized these differences into labels of “no theory first”; “gaps and holes”; “social construction of reality”; and “anomalies”.

I did not consider descriptions of case study research in text books which focus more or less on general descriptions of the common characteristics of case studies, but do not emphasize differences in methodologies and theory contribution. In addition, I did not consider so-called “home grown” designs (Eisenhardt 1989 : 534) which lack a systematic and explicit demonstration of the methodology and where “… the hermeneutic process of inference—how all these interviews, archival records, and notes were assembled into a coherent whole, what was counted and what was discounted—remains usually hidden from the reader” (Fiss 2009 : 425).

Finally, although often cited in the methodological section of case studies, books are not considered which concentrate on data analysis in qualitative research per se (Miles et al. 2014 ; Corbin and Strauss 2015 ). Therefore, to analyze the contribution of case study research to the scientific development, it needs to compare explicit methodology. This comparison will be outlined in the following sections with regard to main methodological steps: the role of the case, the collection of data, and the analysis of data.

2.1 Case study research design 1: no theory first

A popular template for building theory from case studies is a paper by Eisenhardt ( 1989 ). It follows a dramaturgy with a precise order of single steps for constructing a case study and is one of the most cited papers in methods sections (Ravenswood 2011 ). This is impressive for two reasons. On the one hand, Eisenhardt herself has provided a broader spectrum of case study research designs in her own empirical papers, for example, by combining theory-building and theory elaboration (Bingham and Eisenhardt 2011 ). On the other hand, she “updated” her design in a paper with Graebner (Eisenhardt and Graebner 2007 ), particularly by extending the range of inductive theory-building. These developments do not seem to be seriously considered by most authors, as differences and elaborations of this spectrum are rarely found in publications. Therefore, in the following, I focus on the standards provided by Eisenhardt ( 1989 ) and Eisenhardt and Graebner ( 2007 ) as exemplary guidelines.

Eisenhardt follows the ideal of ‘no theory first’ to capture the richness of observations without being limited by a theory. The research question may stem from a research gap meaning that the research question is of relevance. Tentative a priori constructs or variables guide the investigation, but no relationships between such constructs or variables are assumed so far: “Thus, investigators should formulate a research problem and possibly specify some potentially important variables, with some reference to extant literature. However, they should avoid thinking about specific relationships between variables and theories as much as possible, especially at the outset of the process” (Eisenhardt 1989 : 536).

Cases are chosen for theoretical reasons: for the likelihood that the cases offer insights into the phenomenon of interest. Theoretical sampling is deemed appropriate for illuminating and extending constructs and identifying relationships for the phenomenon under investigation (Eisenhardt and Graebner 2007 ). Cases are sampled if they provide an unusual phenomenon, replicate findings from other cases, use contrary replication, and eliminate alternative explanations.

With respect to data collection, qualitative data are the primary choice. Data collection is based on triangulation, where interviews, documents, and observations are often combined. A combination of qualitative data and quantitative data is possible as well (Eisenhardt 1989 : 538). Data analysis is conducted via the search for within-case patterns and cross-case patterns. Systematic procedures are conducted to compare the emerging constructs and relationships with the data, eventually leading to new theory.

A good exemplar for this design is the investigation of technology collaborations (Davis and Eisenhardt 2011 ). The purpose of this paper is to understand processes by which technology collaborations support innovations. Eight technology collaborations among ten firms were sampled for theoretical reasons. Qualitative and quantitative data were used from semi-structured interviews, public and private data, materials provided by informants, corporate intranets, and business publications. The data was measured, coded, and triangulated. Writing case histories was a basis for within-case and cross-case analysis. Iteration between cases and emerging theory and considering the relevant literature provided the basis for the development of a theoretical framework.

Another example is the investigation of what is learned in organizational processes (Bingham and Eisenhardt 2011 ). This paper demonstrates that the case study design is not only used for theory-building, but can also be combined with theory elaboration. Based on the lenses of the organizational knowledge literature, organizational routines literature, and heuristics literature, six technology-based ventures were chosen for theoretical reasons. Several data sources were used, especially quantitative and qualitative data from semi-structured interviews, archival data, observations, e-mails, phone calls, and follow-up interviews. Within-case analysis revealed what each firm has learned from process experience. Cross-case analysis revealed emerging patterns from which tentative constructs and propositions were formed. In replication logic constructs and propositions were refined across the cases. When mirroring the findings with the literature, both the emergences of the constructs were compared and unexpected types were considered. The iteration of theory and data as well as the consideration of related research sharpened the theoretical arguments, eventually leading to a theoretical framework. “Thus, we combined theory elaboration (Lee 1999 ) and theory generation (Eisenhardt 1989 )” (Bingham and Eisenhardt 2011 : 1448).

2.2 Case study research design 2: gaps and holes

Contrary to “No Theory First”, case study research design can also aim at specifying gaps or holes in existing theory with the ultimate goal of advancing theoretical explanations (Ridder 2016 ). A well-known template for this case study research design is the book by Yin ( 2014 ). It is a method-orientated handbook of how to design single and multiple case studies with regard to this purpose. Such a case study research design includes: “A ‘how’ and ‘why’ question” (Yin 2014 : 14). Research questions can be identified and shaped using literature to narrow the interest in a specific topic, looking for key studies and identifying questions in these studies. According to Yin’s design, existing theory is the starting point of case study research. In addition, propositions or frameworks provide direction, reflect the theoretical perspective, and guide the search for relevant evidence.

There are different rationales for choosing a single case design (Yin 2014 : 51). Purposeful sampling is conducted if an extreme case or an unusual case is chosen and if rarely observable phenomena can be investigated with regard to unknown matters and their relationships. Common cases allow conclusions for a broader class of cases. Revelatory cases provide the opportunity to investigate into a previously inaccessible inquiry, and the longitudinal study enables one to investigate a single case at several points in time. A rationale for multiple case designs has its strength in replication logic (Yin 2014 : 56). In the case of literal replication, cases are selected to predict similar results. In the case of theoretical replication, cases are selected to predict contrasting results but for theoretical reasons. Yin provides several tactics to increase the reliability (protocol; data base) of the study.

Yin ( 2014 : 103) emphasizes that interviews are one of the most important sources of data collection but considers other sources of qualitative data as well. Data triangulation is designed to narrow problems of construct validity, as multiple sources of data provide multiple measures of the same phenomenon. Yin ( 2014 : 133) offers a number of data analysis strategies (e.g., case description; examining rival explanations) and analytic techniques which are apt to compare the proposed relationships with empirical patterns. Pattern-matching logic compares empirically based patterns with predicted patterns, enabling further data analysis techniques (explanation building, time series analysis, logic models, and cross-case synthesis). In analytical generalization, the theory is compared with the empirical results, leading to the modification or extension of the theory.

An appropriate model for this case study design can be identified in a paper by Ellonen et al. ( 2009 ). The paper is based on the emerging dynamic capability theory. The four cases were chosen for theoretical reasons to deliver an empirical contribution to the dynamic capability theory by investigating the relationship of dynamic capabilities and innovation outcomes. The authors followed a literal replication strategy and identified patterns between dynamic capabilities of the firms and their innovation outcomes.

Shane ( 2000 ) is an author who developed specific propositions from a framework and examined the propositions in eight entrepreneurial cases. Using several sources of interviews and archival data, the author compared the data with the propositions using the pattern-matching logic, which concluded in developing entrepreneurship theory.

2.3 Case study research design 3: social construction of reality

So far, the outlined case study research designs are based on positivist roots, but there is richness and variety in case study research stemming from different philosophical realms. The case study research design by Stake ( 1995 , 2000 , 2005 ), for example, is based on constructivist assumptions and aims to investigate the social construction of reality and meaning (Schwandt 1994 : 125).

According to this philosophical assumption, there is no unique “real world” that preexists independently of human mental activity and symbolic language. The world is a product of socially and historically related interchanges amongst people (social construction). The access to reality is given through social constructions, such as language and shared meanings: “The meaning-making activities themselves are of central interest to social constructionists/constructivists, simply because it is the meaning-making/sense making attributional activities that shape action or (inaction)” (Guba and Lincoln 2005 : 197). Therefore, the researcher is not looking for objective “facts”, nor does he aim at identifying and measuring patterns which can be generalized. Contrarily, the constructivist is researching into specific actions, in specific places, at specific times. The scientist tries to understand the construction and the sharing of meaning (Schwandt 1994 ).

According to Stake ( 2005 ), the direction of the case study is shaped by the interest in the case. In an intrinsic case study, the case itself is of interest. The purpose is not theory-building but curiosity in the case itself. In an instrumental case study, the case itself is of secondary interest. It plays a supportive role, as it facilitates the understanding of a research issue. The case can be typical of other cases. Multiple or collective case study research designs extend the instrumental case study. It is assumed that a number of cases will increase the understanding and support theorizing by comparison of the cases.

The differentiation by Stake ( 1995 , 2005 ) into intrinsic and instrumental cases guides the purposive sampling strategy. In intrinsic case studies, the case is, by definition, already selected. The researcher looks for specific characteristics, aiming for thick descriptions with the opportunity to learn. Representativeness or generalization is not considered. In instrumental case study design, purposive sampling leads to the phenomenon under investigation. In multiple case study designs, the ability to compare cases enhances the opportunity to theorize.

A case study requires an integrated, holistic comprehension of the case complexity. According to Stake ( 2005 ), the case study is constructed by qualitative data, such as observations, interviews, and documents. Triangulation first serves as clarification of meaning. Second, the researcher is interested in the diversity of perceptions.

Two methods of data analysis are considered in such qualitative case study design: direct interpretation and categorical aggregation (Stake 1995 : 74). The primary task of an intrinsic case study is to understand the case. This interpretation is offered to the reader, but the researcher has to provide the material in a sufficient way (thick descriptions), so that the reader can learn from the case as well as draw his or her own conclusions. Readers can thus make some generalizations based on personal and vicarious experiences (“naturalistic generalization”). In instrumental case studies, the understanding of phenomena and relationships leads to categorical aggregation, and the focus is on how the phenomenon exists across several cases.

Greenwood and Suddaby ( 2006 ), for example, used the instrumental case study design by Stake, combining network location theory and dialectical theory. They identified new dynamics creating a process model of elite institutional entrepreneurship.

Ituma et al. ( 2011 ) highlighted the social construction of reality in their study of career success. The majority of career studies have been conducted in Western countries and findings have been acknowledged as universally applicable. The authors demonstrated that realities of managers in other areas are constructed differently. As a result of their study, they provided a contextually sensitive frame for the analysis of career outcomes.

2.4 Case study research design 4: anomalies

Identifying anomalies as a basis for further research is common in management and organization research (Gilbert and Christensen 2005 ). In case study research, the extended case study method is used for this case study research design (Ridder 2016 ). Following Burawoy ( 1991 , 1998 , 2009 ), the research question derives from curiosity. Researchers normally look at what is “interesting” and what is “surprising” in a social situation that existing theory cannot explain. Initially, it is not important whether the expectations develop from some popular belief, stereotype, or from an academic theory. The extended case study research design is guided by anomalies that the previous theory was not able to explain through internal contradictions of theory, theoretical gaps, or silences. An anomaly does not reject theory, but rather demonstrates that the theory is incomplete. Theory is aimed to be improved by “… turning anomalies into exemplars” (Burawoy 1991 : 10).

The theoretical sampling strategy in this case study research design stems from the theoretical failure in confrontation with the site. According to the reflexive design, such cases do not favour individuals or isolated phenomena, but social situations in which a comparative strategy allows the tracing of differences across the cases to external forces.

In the extended case study, the researcher deals with qualitative data, but also considers the broader complex social situation. The researcher engages into a dialogue with the respondents (Burawoy ( 1991 , 1998 , 2009 ). An interview is an intervention into the life of a respondent. By means of mutual interaction it is possible to discover the social order under investigation. The observer has to unpack those situational experiences by means of participant observation and mutual interpretation. This situational comprehension aims at understanding divergent “voices”, reflecting the variety of respondents’ understandings of the social situation.

As in other sciences, these voices have to be aggregated. This aggregation of multiple readings of a single case is conducted by turning the aggregation into social processes: “The move from situation to process is accomplished differently in different reflexive methods, but it is always reliant on existing theory” (Burawoy 2009 : 41). Social processes are now traced to the external field as the conditions of the social processes. Consequently, this leads to the question concerning “… how those micro situations are shaped by wider structures” (Burawoy 1991 : 282). “Reflexive science insists, therefore, on studying the everyday world from the standpoint of its structuration, that is, by regarding it as simultaneously shaped by and shaping an external field of forces” (Burawoy 2009 : 42). Such social fields cannot be held constant, which undermines the idea of replication. The external field is in continuous flux. Accordingly, social forces that influence the social processes are identified, shaping the phenomenon under investigation. Extension of theory does not target representativeness as a relationship of sample and population. Generality in reflexive science is to reconstruct an existing theory: “We begin with our favorite theory but seek not confirmations but refutations that inspire us to deepen that theory. Instead of discovering grounded theory, we elaborate existing theory. We do not worry about the uniqueness of our case, since we are not as interested in its representativeness as its contribution to reconstructing theory. Our theoretical point of departure can range from the folk theory of participants to any abstract law. We consider only that the scientist consider it worth developing” (Burawoy 2009 : 43). Such elaboration stems from the identification of anomalies and offers new predictions with regard to the theory.

It is somewhat surprising that the extended case study design has been neglected in the management literature so far, and it appears that critical reflexive principles have to be resurrected as they have been in other disciplines (see the overview at Wadham and Warren 2014 ). Examples in the management and organization literature are rare. Danneels ( 2011 ) used the extended case study design to extend the dynamic capabilities theory. In his famous Smith Corona case, Danneels shows how a company tried to change its resource base. Based on detailed data, the Smith Corona case provides insights into the resource alteration processes and how dynamic capabilities operate. As a result, the paper fills a process gap in dynamic capability theory. Iterating between data collection and analysis, Danneels revealed resource cognition as an element not considered so far in dynamic capability theory. The use of the extended case study method is limited to the iteration of data and theory. First, there is “running exchange” (Burawoy 1991 : 10) between field notes and analysis. Second, there is iteration between analysis and existing theory. Unlike Burawoy, who aims to reconstruct existing theory on the basis of “emergent anomalies” (Burawoy 1991 : 11) considering social processes and external forces, Danneels confronts the dynamic capabilities literature with the Smith Corona case to extend the theory of dynamic capabilities.

2.5 A comparison of case study research processes

Commonalities and differences emerged from the comparison of the designs. Table 1 provides a brief summary of these main differences and the resulting portfolio of case study research designs which will be discussed in more detail.

There is an extensive range between the different designs regarding the research processes. In “no theory first”, there is a broad and tentative research question with some preliminary variables at the outset. The research question may be modified during the study as well as the variables. This design avoids any propositions regarding relationships.

On the contrary, the research question in “gaps and holes” is strongly related to existing theory, focusing on “how and why” questions. The existing theory contains research gaps which, once identified within the existing theory, lead accordingly to assumed relationships which are the basis for framework and propositions to be matched by empirical data. This broad difference is even more elaborated by a design that aims the “social construction of reality”. There is no research question at the outset, but a curiosity in the case or the case is a facilitator to understand a research issue. This is far away from curiosity in the “anomaly approach”. Here, the research question is inspired by questioning why an anomaly cannot be explained by the existing theory. What kind of gaps, silences, or internal contradictions demonstrates the insufficiency of the existing theory?

Various sampling strategies are used across these case study research designs, including theoretical sampling and purposeful sampling, which serve different objectives. Theoretical sampling in “no theory first” aims at selecting a case or cases that are appropriate to highlight new or extend preliminary constructs and reveal new relationships. There is a distinct difference from theoretical sampling in the “anomalies” approach. Such a sampling strategy aims to choose a case that is a demonstration of the failure of the theory. In “gaps and holes” sampling is highly focused on the purpose of the case study. Extreme and unusual cases have other purposes compared to common cases or revelatory cases. A single case may be chosen to investigate deeply into new phenomena. A multiple case study may serve a replication logic by which the findings have relevance beyond the cases under investigation. In “social construction of reality”, the sampling is purposeful as well, but for different reasons. Either the case is of interest per se or the case represents a good opportunity to understand a theoretical issue.

Although qualitative data are preferred in all of the designs, quantitative data are seen as a possible opportunity to strengthen cases by such data. Nevertheless, in “social construction of reality”, there is a strong emphasis on thick descriptions and a holistic understanding of the case. This is in contrast to a more construct- and variable- oriented collection of data in “no theory first” and “gaps and holes”. In addition, in contrast to that, the “anomaly” approach is the only design that receives data from dialogue between observer and participants and participant observation.

Finally, data analysis lies within a wide range. In “no theory first”, the research process is finalized by inspecting the emerging constructs within the case or across cases. Based on a priory constructs, systematic comparisons reveal patterns and relationships resulting in a tentative theory. On the contrary, in “gaps and holes”, a tentative theory exists. The final analysis concentrates on the matching of the framework or propositions with patterns from the data. While both of these approaches condense data, the approach of “social construction of reality” ends the research process with thick descriptions of the case to learn from the case or with categorical comparisons. In the “anomaly” approach, the data analysis is aggregation of data, but these aggregated data are related to its external field and their pressures and influences by structuration to reconstruct the theory.

As a result, it is unlikely that the specified case study designs contribute to theory in a homogeneous manner. This result will be discussed in light of the question regarding how these case study designs can inform theory at several points of a continuum of theory. This analysis will be outlined in the following sections. In a first step, I review the main elements of a theory continuum. In a second step, I discuss the respective contribution of the previously identified case study research designs to the theory continuum.

3 Elements of a theory continuum

What a theory is and what a theory is not is a classic debate (Sutton and Staw 1995 ; Weick 1995 ). Often, theories are described in terms of understanding relationships between phenomena which have not been or were not well understood before (Chiles 2003 ; Edmondson and McManus 2007 ; Shah and Corley 2006 ), but there is no overall acceptance as to what constitutes a theory. Theory can be seen as a final product or as a continuum, and there is an ongoing effort to define different stages of this continuum (Andersen and Kragh 2010 ; Colquitt and Zapata-Phelan 2007 ; Edmondson and McManus 2007 ; Snow 2004 ; Swedberg 2012 ). In the following section, basic elements of the theory and the construction of the theory continuum are outlined.

3.1 Basic elements of a theory

Most of the debate concerning what a theory is comprises three basic elements (Alvesson and Kärreman 2007 ; Bacharach 1989 ; Dubin 1978 ; Kaplan 1998 ; Suddaby 2010 ; Weick 1989 , 1995 ; Whetten 1989 ). A theory comprises components (concepts and constructs), used to identify the necessary elements of the phenomenon under investigation. The second is relationships between components (concepts and constructs), explaining the how and whys underlying the relationship. Third, temporal and contextual boundaries limit the generalizability of the theory. As a result, definitions of theory emphasize these components, relationships, and boundaries:

“It is a collection of assertions, both verbal and symbolic, that identifies what variables are important for what reasons, specifies how they are interrelated and why, and identifies the conditions under which they should be related or not related” (Campbell 1990 : 65).

“… a system of constructs and variables in which the constructs are related to each other by propositions and the variables are related to each other by hypotheses” (Bacharach 1989 : 498).

“Theory is about the connections among phenomena, a story about why acts, events, structure, and thoughts occur. Theory emphasizes the nature of causal relationships, identifying what comes first as well as the timing of such events” (Sutton and Staw 1995 : 378).

“… theory is a statement of concepts and their interrelationships that shows how and/or why a phenomenon occurs” (Corley and Gioia 2011 : 12).

The terms “constructs” and “concepts” are either used interchangeably or with different meanings. Positivists use “constructs” as a lens for the observation of a phenomenon (Suddaby 2010 ). Such constructs have to be operationalized and measured. Non-positivists often use the term “concept” as a more value neutral term in place of the term construct (Gioia et al. 2013 ; Suddaby 2010 : 354). Non-positivists aim at developing concepts on the basis of data that contain richness and complexity of the observed phenomenon instead of narrow definitions and operationalizations of constructs. Gioia et al. ( 2013 : 16) clarify the demarcation line between constructs and concepts as follows: “By ‘concept,’ we mean a more general, less well-specified notion capturing qualities that describe or explain a phenomenon of theoretical interest. Put simply, in our way of thinking, concepts are precursors to constructs in making sense of organizational worlds—whether as practitioners living in those worlds, researchers trying to investigate them, or theorists working to model them”.

In sum, theories are a systematic combination of components and their relationships within boundaries. The use of the terms constructs and concepts is related to different philosophical assumptions reflected in different types of case study designs.

3.2 Theory continuum

Weick ( 1995 ) makes an important point that theory is more a continuum than a product. In his view, theorizing is a process containing assumptions, accepted principles, and rules of procedures to explain or predict the behavior of a specified set of phenomena. In similar vein, Gilbert and Christensen ( 2005 ) demonstrate the process character of theory. In their view, a first step of theory building is a careful description of the phenomena. Having already observed and described the phenomena, researchers then classify the phenomena into similar categories. In this phase a framework defines categories and relationships amongst phenomena. In the third phase, researchers build theories to understand (causal) relationships, and in this phase, a model or theory asserts what factors drive the phenomena and under what circumstances. The categorization scheme enables the researchers to predict what they will observe. The “test” offers a confirmation under which circumstances the theory is useful. The early drafts of a theory may be vague in terms of the number and adequateness of factors and their relationships. At the end of the continuum, there may be more precise variables and predicted relationships. These theories have to be extended by boundaries considering time and space.

Across that continuum, different research strategies have various strengths. Several classifications in the literature intend to match research strategies to the different phases of a theory continuum (Andersen and Kragh 2010 ; Colquitt and Zapata-Phelan 2007 ; Edmondson and McManus 2007 ; Snow 2004 ; Swedberg 2012 ). These classifications, although there are differences in terms, comprise three phases with distinguishable characteristics.

3.2.1 Building theory

Here, the careful description of the phenomena is the starting point of theorizing. For example, Snow ( 2004 ) puts this phase as theory discovery, where analytic understandings are generated by means of detailed examination of data. Edmondson and McManus ( 2007 ) state the starting phase of a theory as nascent theory providing answers to new questions revealing new connections among phenomena. Therefore, research questions are open and researchers avoid hypotheses predicting relationships between variables. Swedberg ( 2012 ) highlights the necessity of observation and extensive involvement with the phenomenon at the early stage of theory-building. It is an attempt to understand something of interest by observing and interpreting social facts. Creativity and inspiration are necessary conditions to put observations into concepts and outline a tentative theory.

3.2.2 Developing theory

This tentative theory exists in the second phase of the continuum and has to be developed. Several possibilities exist. In theory extension, the preexisting constructs are extended to other groups or other contexts. In theoretical refinement, a modification of existing theoretical perspectives is conducted (Edmondson and McManus ( 2007 ). New antecedents, moderators, mediators, and outcomes are investigated, enhancing the explanation power of the tentative theory.

3.2.3 Test of theories

Constructs and relationships are well developed to a mature state; measures are precise and operationalized. Such theories are empirically tested with elaborate methods, and research questions are more precise. In the quantitative realm, testing of hypotheses is conducted and statistical analysis is the usual methodological foundation. Recently, researchers criticize that testing theories has become the major focus of scientists today (Delbridge and Fiss 2013 ); testing theories does not only happen to mature theory but to intermediate theory as well. The boundary between theory development and theory testing is not always so clear. While theory development is adding new components to a theory and elaborating the measures, testing a theory implies precise measures, variables, and predicted relationships considering time and space (Gilbert and Christensen ( 2005 ). It will be of interest whether case studies are eligible to test theories as well.

To summarize: there is a conversation as to where on a continuum of theory development, various methods are required to target different contributions to theory (methodological fit). In this discussion, case study research designs have been discussed as a homogeneous set that mostly contributes to theory-building in an exploratory manner. Hence, what is missing is a more differentiated analysis of how case study methodology fits into this conversation, particularly how case study research methodologically fits theory development and theory testing beyond its widely assumed explorative role. In the following section, the above types of case study research designs will be discussed with regard to their positions across the theory continuum.

This distinction adds to existing literature by demonstrating that case study research does not only contribute to theory-building, but also to the development of tentative theories and to the testing of theories. This distinction leads to the next question: is there any interplay between case study research designs and their contributions to the theory continuum? This paper aims at reconciling this interplay with regard to case study design by mirroring phases of a theory continuum with specific types of case study research designs as outlined above. The importance of the interplay between theory and method lies in the capacity to generate and shape theory, while theory can generate and shape method. “In this long march, theory and method surely matter, for they are the tools with which we build both our representations and understandings of organizational life and our reputations” (van Maanen et al. 2007 : 1145). Theory is not the same as methods, but a relationship of this interplay can broaden or restrict both parts of the equation (Swedberg 2012 : 7).

In the following, I discuss how the above-delineated case study research designs unfold their capacities and contribute differently to the theory continuum to build, develop, and test theory.

4 Discussion of the contribution of case study research to a theory continuum

Case study research is diverse with distinct contributions to the continuum of theory. The following table provides the main differences in terms of contributions to theory and specifically locates the case study research designs on the theory continuum (Table 2 ).

In the following, I outline how these specific contributions of case study designs provide better opportunities to enhance the rigor of building theory, developing theory, testing, and reconstructing theory.

4.1 Building theory

In building theory, the phenomenon is new or not understood so far. There is no theory which explains the phenomenon. At the very beginning of the theory continuum, there is curiosity in the phenomenon itself. I focus on the intrinsic case study design which is located in the social construction of reality approach on the very early phase of the theory continuum, as intrinsic case study research design is not theory-building per se but curiosity in the case itself. It is not the purpose of the intrinsic case study to identify abstract concepts and relationships; the specific research strategy lies in the observation and description of a case and the primary method is observation, enabling understanding from personal and vicarious experience. This meets long lasting complaints concerning the lack of (new) theory in management and organization research and signals that the gap between research and management practice is growing. It is argued that the complexity of the reality is not adequately captured (Suddaby et al. 2011 ). It is claimed that management and organization research systematically neglect the dialogue with practice and, as a result, miss new trends or recognize important trends with delay (Corley and Gioia 2011 ).

The specific case study research design’s contribution to theory is in building concrete, context-dependent knowledge with regard to the identification of new phenomena and trends. Openness with regard to the new phenomena, avoiding theoretical preconceptions but building insights out of data, enables the elaboration of meanings and the construction of realities in intrinsic case studies. Intrinsic case studies will enhance the understanding by researcher and reader concerning new phenomena.

The “No Theory First” case study research design is a classic and often cited candidate for building theory. As the phenomenon is new and in the absence of a theory, qualitative data are inspected for aggregation and interpretation. In instrumental case study design, a number of cases will increase the understanding and support building theories by description, aggregation, and interpretation (Stake 2000 ). New themes and concepts are revealed by case descriptions, interviews, documents, and observations, and the analysis of the data enables the specific contribution of the case study design through a constructivist perspective in theory-building.

Although the design by Eisenhardt ( 1989 ) stems from other philosophical assumptions and there are variations and developments in this design, there is still an overwhelming tendency to quote and to stick to her research strategy which aims developing new constructs and new relationships out of real-life cases. Data are collected mainly by interviews, documents, and observations. From within-site analysis and cross-case analysis, themes, concepts, and relationships emerge. Shaping hypotheses comprises: “… refining the definition of the construct and (…) building evidence which measures the construct in each case” (Eisenhardt 1989 : 541). Having identified the emerged constructs, the emergent relationships between constructs are verified in each case. The underlying logic is validation by replication. Cases are treated as experiments in which the hypotheses are replicated case by case. In replication logic cases that confirm the emergent relationships enhance confidence in the validity of the relationships. Disconfirmation of the relationships leads to refinement of the theory. This is similar to Yin’s replication logic, but targets the precision and measurement of constructs and the emerging relationships with regard to the emerging theory. The building of a theory concludes in an understanding of the dynamics underlying the relationship; the primary theoretical reasons for why the relationships exist (Huy 2012 ). Finally, a visual theory with “boxes and arrows” (Eisenhardt and Graebner 2007 ) may visually demonstrate the emerged theory. The theory-building process is finalized by iterating case data, emerging theory, and extant literature.

The “No Theory First” and “Social Construction of Reality” case study research designs, although they represent different philosophical assumptions, adequately fit the theory-building phase concerning new phenomena. The main contribution of case study designs in this phase of the theory continuum lies in the generation of tentative theories.

Case studies at this point of the theory continuum, therefore, have to demonstrate: why the phenomenon is new or of interest; that no previous theory that explains the phenomenon exists; how and why detailed descriptions enhance the understanding of the phenomenon; and how and why new concepts (constructs) and new relationships will enhance our understanding of the phenomenon.

As a result, it has to be demonstrated that the research strategy is in sync with an investigation of a new phenomenon, building a tentative theory.

4.2 Developing theory

In the “Gaps and Holes” case study research design, the phenomenon is partially understood. There is a tentative theory and the research strategy is theory driven. Compared to the theory-building phase, the existence and not the development of propositions differentiate this design along the continuum. The prediction comes first, out of an existing theory. The research strategy and the data have to be confronted by pattern-matching. Pattern-matching is a means to compare the theoretically based predictions with the data in the site: “For case study analysis, one of the most preferred techniques is to use a pattern-matching logic. Such a logic (…) compares an empirically based pattern–that is, one based on the findings from your case study–with a predicted one made before you collected your data (….)” (Yin 2014 : 143). The comparison of propositions and the rich case material is the ground for new elements or relationships within the tentative theory.

Such findings aim to enhance the scientific usefulness of the theory (Corley and Gioia 2011 ). To enhance the validity of the new elements or relationships of the tentative theory, literal replication is a means to confirm the new findings. By that, the theory is developed by new antecedents, moderators, mediators, or outcomes. This modification or extension of the theory contributes to the analytical generalization of the theory.

If new cases provide similar results, the search for regularities is based on more solid ground. Therefore, the strength of case study research in “Gaps and Holes” lies in search for mechanisms in their specific context which can reveal causes and effects more precisely.

The “Gaps and Holes” case study research design is an adequate candidate for this phase of the theory continuum. Case studies at this point of the theory continuum, therefore, have to outline the tentative theory; to demonstrate the lacks and gaps of the tentative theory; to specify how and why the tentative theory is aimed to be extended and/or modified; to develop theoretically based propositions which guide the investigation; and to evaluate new elements, relationships, and mechanisms related to the previous theory (analytical generalization).

As a result and compared to theory-building, a different research strategy exists. While in theory building the research strategy is based on the eliciting of concepts (constructs) and relationships out of data, in theory development, it has to be demonstrated that the research strategy aims to identify new elements and relationships within a tentative theory, identifying mechanisms which explain the phenomenon more precisely.

4.3 Test of theory

In “Gaps and Holes” and “Anomalies”, an extended theory exists. The phenomenon is understood. There is no search for additional components or relationships. Mechanisms seem to explain the functioning or processes of the phenomenon. The research strategy is focused on testing whether the theory holds under different circumstances or under different conditions. Such a test of theories is mainly the domain of experimental and quantitative studies. It is based on previously developed constructs and variables which are the foundation for stating specific testable hypotheses and testing the relations on the basis of quantitative data sets. As a result, highly sophisticated statistical tools enable falsification of the theory. Therefore, testing theory in “Gaps and Holes” is restricted on specific events.

Single case can serve as a test. There is a debate in case study research whether the test of theories is related to the falsification logic of Karl Popper (Flyvbjerg 2006 ; Tsang 2013 ). Another stream of the debate is related to theoretical generalizability (Hillebrand et al. 2001 ; Welch et al. 2011 ). More specifically, test in” Gaps and Holes” is analogous to a single experiment if a single case represents a critical case. If the theory has specified a clear set of propositions and defines the exact conditions within which the theory might explain the phenomena under investigation, a single case study, testing the theory, can confirm or challenge the theory. In sum Yin states: “Overall, the single-case design is eminently justifiable under certain conditions—where the case represents (a) a critical test of existing theory, …” (Yin 2014 : 56). In their survey in the field of International Business, Welch et al. conclude: “In addition, the widespread assumption that the role of the case study lies only in the exploratory, theory-building phase of research downplays its potential to propose causal mechanisms and linkages, and test existing theories” (Welch et al. 2011 : 755).

In multiple case studies, a theoretical replication is a test of theory by comparing the findings with new cases. If a series of cases have revealed pattern-matching between propositions and the data, theoretical replication can be revealed by new waves of cases with contrasting propositions. If the contrasting propositions reveal contrasting results, the findings of the first wave are confirmed. Several possibilities exist to test the initial findings of multiple case studies using different lenses from inside and outside the management realm (Corley and Gioia 2011 ; LePine and Wilcox-King 2010 ; Okhuysen and Bonardi 2011 ; Zahra and Newey 2009 ), but have not become a standard in case study research.

In rival explanations, rival theoretical propositions are developed as a test of the previous theory. This can be distinguished from theoretical replication where contrasting propositions aim to confirm the initial findings. This can, as well, be distinguished from developing theory where rival explanations might develop theory by the elimination of possible influences (interventions, implementations). The rich data enable one to identify internal and external interventions that might be responsible for the findings. Alternative explanations in a new series of cases enable to test, whether a theory “different from the original theory explains the results better (…)” (Yin 2014 : 141).

As a result, it astonishes that theoretical replication and rival explanations, being one of the strengths of case study research, are rarely used. Although the general debate about “lenses” has informed the discussion about theory contributions, this paper demonstrates that there is a wide range of possible integration of vertical or horizontal lenses in case study research design. Case study research designs aiming to test theories have to outline modes of replication and the elimination of rival explanations.

The “anomaly approach” is placed in the final phase of the theory testing, as well. In this approach, a theory exists, but the theory fails to explain anomalies. Burawoy goes a step further. While Yin ( 2014 ) sees a critical case as a test that challenges or contradicts a well formulated theory, in Burawoy’s approach, in contrast to falsification logic (Popper 2002 ), the theory is not rejected but reconstructed. Burawoy relates extended case study design to society and history. Existing theory is challenged by intervention into the social field. Identifying processes of historical roots and social circumstances and considering external forces by structuration lead to the reconstruction of the theory.

It is surprising that this design has been neglected so far in management research. Is there no need to reflect social tensions and distortions in management research? While case study research has, per definition, to investigate phenomena in its natural environment, it is hard to understand why this design has widely been ignored in management and organization research. As a result, testing theory in case study research has to demonstrate that an extended theory exists; a critical case or an anomaly can challenge the theory; theoretical replication and rival explanations will be means to contradict or confirm the theory; and societal circumstances and external forces explain the anomaly.

Compared to theory-building (new concepts/constructs and relationships out of data) and theory development (new elements and relationships within a tentative theory), testing theory challenges extended theory by empirical investigations into failures and anomalies that the current theory cannot explain.

5 Conclusion

Case studies provide a better understanding of phenomena regarding concrete context-dependent knowledge (Andersen and Kragh 2010 ; Flyvbjerg 2006 : 224), but as literature reviews indicate, there is still confusion regarding the adequate utilization of case study methodology (Welch et al. 2011 ). This can be interpreted in a way that authors and even reviewers are not always aware of the methodological fit in case study research. Case study research is mainly narrowed to its “explorative” function, neglecting the scope of possibilities that case study research provides. The claim for more homogeneity of specified rules in case study research misses the important aspect that a method is not a means in itself, but aims at providing improved theories (van Maanen et al. 2007 ). This paper contributes to the fit of case study research designs and the theory continuum regarding the following issues.

5.1 Heterogeneity of case study designs

Although case study research, overall, has similar characteristics, it incorporates various case study research designs that have heterogeneous theoretical goals and use various elements to reach these goals. The analysis revealed that the classical understanding, whereby case study research is adequate for the “exploration” of a theory and quantitative research is adequate for “testing” theory, is oversimplified. Therefore, the theoretical goals of case study research have to be outlined precisely. This study demonstrates that there is variety of case study research designs that have thus far been largely neglected. Case study researchers can utilize the entire spectrum, but have to consider how the phenomenon is related to the theory continuum.

Case study researchers have to demonstrate how they describe new or surprising phenomena, develop new constructs and relationships, add constructs (variables), antecedents, outcomes, moderators, or mediators to a tentative theory, challenge a theory by a critical case, theoretical replication or discarding rival explanations, and reconstruct a theory by tracking failures and anomalies to external circumstances.

5.2 Methodological fit

The rigor of the case study can be enhanced by considering the specific contribution of various case study research designs in each phase of the theory continuum. This paper provides a portfolio of case study research designs that enables researchers and reviewers to evaluate whether the case study arsenal has been adequately located:

At an early phase of the theory continuum, case studies have their strengths in rich descriptions and investigations into new or surprising empirical phenomena and trends. Researchers and readers can benefit from such rich descriptions in understanding and analyzing these phenomena.

Next, on the theory continuum, there is the well-known contribution of case study research in building tentative theory by eliciting constructs or concepts and their relationships out of data.

Third, development of theories is strongly related to literal replication. Strict comparisons, on the one hand, and controlled theoretical advancement, on the other hand, enable the identification of mechanisms, strengthen the notions of causality, and provide generalizable statements.

Fourth, there are specific circumstances under which case study approaches enable one to test theories. This is to confront the theory with a critical case, to test findings of pattern-matching by theoretical replication and discarding rival explanations. Therefore, “Gaps and Holes” provide the opportunity for developing and testing theories through case study design on the theory continuum.

Finally, testing and contradicting theory are not the final rejection of a theory, but is the basis for reconstructing theory by means of case study design. Anomalies can be traced to historical sources, social processes, and external forces.

This paper demonstrates that the precise interplay of case study research designs and theory contributions on the theory continuum is a prerequisite for the contribution of case study research to better theories. If case study research design is differentiated from qualitative research, the intended contribution to theory is stated and designs that fit the aimed contribution to theory are outlined and substantiated; this will critically enhance the rigor of case study research.

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Ridder, HG. The theory contribution of case study research designs. Bus Res 10 , 281–305 (2017). https://doi.org/10.1007/s40685-017-0045-z

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Case studies
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A case study is an in-depth study of a singular situation, person or event.

What does this mean?

In most disciplines, studies are required to prove a hypothesis. These studies are usually very large in nature, with the goal of proving a hypothesis. With a case study, a narrow topic is chosen that can prove (or disprove) an idea, question or hypothesis. Often, case studies are used alongside a larger formal study, or are used on their own.

An idea or theory that hasn't been proven but has scientific merit and is worthy of a study to prove whether it is true or false.

Case studies are used in most disciplines that use or require statistical or informational data. For example, a well-known case study in the field of psychology is the case of "Genie", a feral child.

Obviously, researchers cannot lock up a child for a decade, and do research on the results. So, when a child was discovered locked up for 13 years, it was a perfect opportunity to do research and try to discover what the effects was of a child being isolated it's entire life.

What information could be garnered from the "Genie" case study? How could the case study be used to help children (or adults) under care today?

Case studies are also commonly used in the business world. For example, one of the most well-known business case studies is the Tylenol cyanide scandal. A quick refresher, in 1982 seven people died after ingesting Tylenol tablets laced with cyanide.

Almost immediately Tylenol's market share dropped from 37% to 7%. Johnson & Johnson, the parent company had to work quickly to save the product. They reintroduced the product with tamper resistant packaging and a large media campaign.

Johnson & Johnson was successful. The Tylenol brand recovered and regained customer trust.

The Tylenol Scandal case study details everything that happened from beginning to end. It also details each step J&J took when turning the scandal around…both positive and negative steps.

This case study is now used in business, marketing, crisis management and other disciplines to help them solve their own problems. They can look at what J&J did to solve their problems, and use that information to fix their own issues.

Who Uses Case Studies?

What makes a case study so valuable is that is it is real-life situation or problem. Dealing with hypothetical issues can be helpful, but using actual historical information and data is often a much better way to learn and fix an organization's problems.

Case studies are used in most disciplines, as well as education, where they are becoming more prevalent. In fact, some of the best universities, such as Harvard Business School, use the case method to educate its students.

Think about it, what better way to learn about a subject than to study real-life examples of similar situations?

Case studies are used in just about every discipline. For this article, case studies will belong to one of the following five groups.

Arts, Design, Media and Humanities
Business, Hospitality, Law, Sport and Tourism
Interdisciplinary
Education, Social and Environmental Sciences
Science, Technology, Engineering and Mathematics

Case studies are understandably useful for others to learn from, and an effective case study can help people, businesses, and organizations for years to come. However, what exactly goes into a case study, and how is one developed?

Why Develop A Case Study?

People have several reasons for wanting to develop a case study. For example, a technology company might want to learn why certain members of the population buy certain products. Or a psychologist might want to understand what is the best type of therapy for veterans with PTSD. To accomplish this, both would want to develop a case study.

Let's use our psychologist as an example.

A psychologist wants to begin offering specialized treatment for veterans suffering from PTSD. She currently has many veterans as patients, and she has determined that some therapeutic methods are more effective than others. She wants to use the information she is gaining to develop a track record for which methods are most effective. To do this, she will develop a case study.

The psychologist will use data and information from her current patients (using strict privacy rules), as well as professional resources, to develop her case study. This case study could accomplish many things.

1. Pilot Research – If the psychologist wants to do large-scale research, starting with a few case studies is a great way to go. If the case studies show any patterns or trends, that information can be used to determine the best way to do advanced research.

2. Develop New Theories or Ideas – The psychologist may have her own ideas going into the study. Perhaps she believes that a combination of talk and group therapy is the best treatment for veterans with PTSD. Or maybe through her case study, she realizes that group therapy is often effective alone. If she develops a new theory, she can test it with additional research.

3. Change Existing Theories or Ideas – In psychology, ideas and treatments often change with time or new information or research. While conducting the case study, the psychologist might discover that older ideas are not as effective as newer treatments. If the psychologist feels current professional protocol is not as effective as newer treatments, a case study could be developed to challenge those ideas.

Intrinsic Case Study

A study on a topic that is unique in itself. An example of this would be the study of Genie, the feral child.

Instrumental Case Study

A study on a more general phenomenon or similarity. An example of this would be a study to determine what therapies are most effective for war veterans with PTSD.

Types Of Case Studies

There are generally five different types of case studies, and the subjects that they address. These are:

Person – This type of study focuses on one particular individual. This case study would use several types of research to determine an outcome.

Group – This type of study focuses on a group of people. This could be a family, a group or friends, or even coworkers.

Location – This type of study focuses on a place, and how and why people use the place.

Organization/Company – This type of study focuses on a business or an organization. This could include the people who work for the company, or an event that occurred at the organization.

Event – This type of study focuses on an event, whether cultural or societal, and how it affects those that are affected by it.

What kind of case study is the "Genie" study?

What kind of case study is the "Tylenol Scandal" study?

What Is The Process For Developing A Case Study?

While case studies are smaller than larger research-based studies, their development still requires a strict and detailed systematic plan. There are several steps required to complete a full study. The basic plan is as follows:

1. Define The Task, Question or Topic

What is the topic of the case study? What question is the case study supposed to answer?

The first step is to determine what the case study will be about. This is when a researcher will develop their hypothesis.

This is also when research should be done to determine whether any case studies have been written on this topic in the past. This research can be difficult, since many small case studies exist. However, with the advent of the Internet, finding older studies is easier than it was in the past.

2. Do Research, Interviews, Collect Data

The research stage is the longest and most detailed of the case study process.

One of the primary methods used in case studies is an interview. Whether it is one person or several, the interview process is extremely important. Not only must the subject have several interviews, but also other experts in the subject should be interviewed. Their contribution can be invaluable.

When interviewing subjects, questioned should be open-ended so the subject is forced to answer with more than just a "yes" or "no". For example, when interviewing the first responders of "Genie", the researcher shouldn't say:

"When you found Genie, was she afraid of you?"

This question could easily lead to a "yes" or "no" answer. One could easily assume Genie was frightened when found since she had no socialization skills whatsoever. Instead, the researcher should ask questions like:

"When you first found Genie, what was her disposition?"

"When you removed Genie from her home, how did she react to the sunlight and outdoors"?

"When you gave Genie a cookie in the ambulance, how did she react?"

3. Make Recommendations and Form Conclusions

What did the study prove? After gathering all of the data, what conclusions can be made?

Once the researcher has compiled all of the research, it is time to formulate the data and form a thesis. A thesis is a statement that will tell the reader what to expect from the case study. It is a single sentence that usually is within the first paragraph of the report. The thesis must make a claim that can be disputed by others.

The thesis differs from the hypothesis in that the thesis is the statement that is proven true with the case study. The hypothesis is the question or idea that the researcher had going into the study. It is possible the hypothesis and thesis are the same. However, it is also possible that once all the research has been completed, the thesis changes from the initial hypothesis.

4. Write The Report

Writing the report is the final step, but it includes several steps. A case study is a research study that requires a cover page, references, and all of the acquired data and information compiled in a readable and cohesive report.

While a case study might use scientific facts and information, a case study should not read as a scientific research journal or report. It should be easy to read and understand, and should follow the narrative determined in the first step.

Remember, the case study must analyze a case or situation in a clear and concise way, but should also be readable by people not familiar with scientific methods. The study should have four main sections, the introduction , the background of the study and why it was developed, the presentation of findings , and the conclusion .

The introduction should set the stage for the case study, and state the thesis for the report. The intro must clearly articulate what the study's intention is, as well as how you plan on explaining and answering the thesis. Again, remember that a case study is not a formal scientific research report that will only be read by scientists. The case study must be able to be read and understood by the layperson, and should read almost as a story, with a clear narrative.

The background should detail what information brought the researcher to pose his hypothesis. It should clearly explain the subject or subjects, as well as their background information. And lastly, the background must give the reader a full understanding of the issue at hand, and what process will be taken with the study. Photos and videos are always helpful when applicable.

The presentation of findings should clearly explain how the topic was researched, and summarize what the results are. Data should be summarized as simply as possible so that it is understandable by people without a scientific background. The researcher should describe what was learned from the interviews, and how the results answered the questions asked in the introduction.

The final section of the study is the conclusion . The purpose of the study isn't necessarily to solve the problem, only to offer possible solutions. The final summary should be an end to the story. Remember, the case study is about asking and answering questions. The conclusion should answer the question posed by the researcher, but also leave the reader with questions of his own. The researcher wants the reader to think about the questions posed in the study, and be free to come to their own conclusions as well.

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Introduction to Hypothesis Testing in R

Testing of hypothesis in r, p-value: an alternative way of hypothesis testing:, t-test: hypothesis testing of population mean when population standard deviation is unknown:, two samples tests: hypothesis testing for the difference between two population means, hypothesis testing for equality of population variances, let’s look at some case studies:, references:, hypothesis testing in r- introduction examples and case study.

– By Dr. Masood H. Siddiqui, Professor & Dean (Research) at Jaipuria Institute of Management, Lucknow

The premise of Data Analytics is based on the philosophy of the “ Data-Driven Decision Making ” that univocally states that decision-making based on data has less probability of error than those based on subjective judgement and gut-feeling. So, we require data to make decisions and to answer the business/functional questions. Data may be collected from each and every unit/person, connected with the problem-situation (totality related to the situation). This is known as Census or Complete Enumeration and the ‘totality’ is known as Population . Obv.iously, this will generally give the most optimum results with maximum correctness but this may not be always possible. Actually, it is rare to have access to information from all the members connected with the situation. So, due to practical considerations, we take up a representative subset from the population, known as Sample . A sample is a representative in the sense that it is expected to exhibit the properties of the population, from where it has been drawn.

So, we have evidence (data) from the sample and we need to decide for the population on the basis of that data from the sample i.e. inferring about the population on the basis of a sample. This concept is known as Statistical Inference .

Before going into details, we should be clear about certain terms and concepts that will be useful:

Parameter and Statistic

Parameters are unknown constants that effectively define the population distribution , and in turn, the population , e.g. population mean (µ), population standard deviation (σ), population proportion (P) etc. Statistics are the values characterising the sample i.e. characteristics of the sample. They are actually functions of sample values e. g. sample mean (x̄), sample standard deviation (s), sample proportion (p) etc.

Sampling Distribution

A large number of samples may be drawn from a population. Each sample may provide a value of sample statistic, so there will be a distribution of sample statistic value from all the possible samples i.e. frequency distribution of sample statistic . This is better known as Sampling distribution of the sample statistic . Alternatively, the sample statistic is a random variable , being a function of sample values (which are random variables themselves). The probability distribution of the sample statistic is known as sampling distribution of sample statistic. Just like any other distribution, sampling distribution may partially be described by its mean and standard deviation . The standard deviation of sampling distribution of a sample statistic is better known as the Standard Error of the sample statistic.

Standard Error

It is a measure of the extent of variation among different values of statistics from different possible samples. Higher the standard error, higher is the variation among different possible values of statistics. Hence, less will be the confidence that we may place on the value of the statistic for estimation purposes. Hence, the sample statistic having a lower value of standard error is supposed to be better for estimation of the population parameter.

1(a). A sample of size ‘n’ has been drawn for a normal population N (µ, σ). We are considering sample mean (x̄) as the sample statistic. Then, the sampling distribution of sample statistic x̄ will follow Normal Distribution with mean µ x̄ = µ and standard error σ x̄ = σ/ √ n.

Even if the population is not following the Normal Distribution but for a large sample (n = large), the sampling distribution of x̄ will approach to (approximated by) normal distribution with mean µ x̄ = µ and standard error σ x̄ = σ/ √ n, as per the Central Limit Theorem .

(b). A sample of size ‘n’ has been drawn for a normal population N (µ, σ), but population standard deviation σ is unknown, so in this case σ will be estimated by sample standard deviation(s). Then, sampling distribution of sample statistic x̄ will follow the student’s t distribution (with degree of freedom = n-1) having mean µ x̄ = µ and standard error σ x̄ = s/ √ n.

2. When we consider proportions for categorical data. Sampling distribution of sample proportion p =x/n (where x = Number of success out of a total of n) will follow Normal Distribution with mean µ p = P and standard error σ p = √( PQ/n), (where Q = 1-P). This is under the condition that n is large such that both np and nq should be minimum 5.

Statistical Inference

Statistical Inference encompasses two different but related problems:

1. Knowing about the population-values on the basis of data from the sample. This is known as the problem of Estimation . This is a common problem in business decision-making because of lack of complete information and uncertainty but by using sample information, the estimate will be based on the concept of data based decision making. Here, the concept of probability is used through sampling distribution to deal with the uncertainty. If sample statistics is used to estimate the population parameter , then in that situation that is known as the Estimator; {like sample mean (x̄) to estimate population mean µ, sample proportion (p) to estimate population proportion (P) etc.}. A particular value of the estimator for a given sample is known as Estimate . For example, if we want to estimate average sales of 1000+ outlets of a retail chain and we have taken a sample of 40 outlets and sample mean ( estimator ) x̄ is 40000. Then the estimate will be 40000.

There are two types of estimation:

Point Estimation : Single value/number of the estimator is used to estimate unknown population parameters. The example is given above.
Confidence Interval/Interval Estimation : Interval Estimate gives two values of sample statistic/estimator, forming an interval or range, within which an unknown population is expected to lie. This interval estimate provides confidence with the interval vis-à-vis the population parameter. For example: 95% confidence interval for population mean sale is (35000, 45000) i.e. we are 95% confident that interval estimate will contain the population parameter.

2. Examining the declaration/perception/claim about the population for its correctness on the basis of sample data. This is known as the problem of Significant Testing or Testing of Hypothesis . This belongs to the Confirmatory Data Analysis , as to confirm or otherwise the hypothesis developed in the earlier Exploratory Data Analysis stage.

One Sample Tests

z-test – Hypothesis Testing of Population Mean when Population Standard Deviation is known:

Hypothesis testing in R starts with a claim or perception of the population. Hypothesis may be defined as a claim/ positive declaration/ conjecture about the population parameter. If hypothesis defines the distribution completely, it is known as Simple Hypothesis, otherwise Composite Hypothesis .

Hypothesis may be classified as:

Null Hypothesis (H 0 ): Hypothesis to be tested is known as Null Hypothesis (H 0 ). It is so known because it assumes no relationship or no difference from the hypothesized value of population parameter(s) or to be nullified.

Alternative Hypothesis (H 1 ): The hypothesis opposite/complementary to the Null Hypothesis .

Note: Here, two points are needed to be considered. First, both the hypotheses are to be constructed only for the population parameters. Second, since H 0 is to be tested so it is H 0 only that may be rejected or failed to be rejected (retained).

Hypothesis Testing: Hypothesis testing a rule or statistical process that may be resulted in either rejecting or failing to reject the null hypothesis (H 0 ).

The Five Steps Process of Hypothesis Testing

Here, we take an example of Testing of Mean:

1. Setting up the Hypothesis:

This step is used to define the problem after considering the business situation and deciding the relevant hypotheses H 0 and H 1 , after mentioning the hypotheses in the business language.

We are considering the random variable X = Quarterly sales of the sales executive working in a big FMCG company. Here, we assume that sales follow normal distribution with mean µ (unknown) and standard deviation σ (known) . The value of the population parameter (population mean) to be tested be µ 0 (Hypothesised Value).

Here the hypothesis may be:

H 0 : µ = µ 0 or µ ≤ µ 0 or µ ≥ µ 0 (here, the first one is Simple Hypothesis , rest two variants are composite hypotheses )

H 1 : µ > µ 0 or

H 1 : µ < µ 0 or

H 1 : µ ≠ µ 0

(Here, all three variants are Composite Hypothesis )

2. Defining Test and Test Statistic:

The test is the statistical rule/process of deciding to ‘reject’ or ‘fail to reject’ (retain) the H0. It consists of dividing the sample space (the totality of all the possible outcomes) into two complementary parts. One part, providing the rejection of H 0 , known as Critical Region . The other part, representing the failing to reject H 0 situation , is known as Acceptance Region .

The logic is, since we have evidence only from the sample, we use sample data to decide about the rejection/retaining of the hypothesised value. Sample, in principle, can never be a perfect replica of the population so we do expect that there will be variation in between population and sample values. So the issue is not the difference but actually the magnitude of difference . Suppose, we want to test the claim that the average quarterly sale of the executive is 75k vs sale is below 75k. Here, the hypothesised value for the population mean is µ 0 =75 i.e.

H 0 : µ = 75

H 1 : µ < 75.

Suppose from a sample, we get a value of sample mean x̄=73. Here, the difference is too small to reject the claim under H 0 since the chances (probability) of happening of such a random sample is quite large so we will retain H 0 . Suppose, in some other situation, we get a sample with a sample mean x̄=33. Here, the difference between the sample mean and hypothesised population mean is too large. So the claim under H 0 may be rejected as the chance of having such a sample for this population is quite low.

So, there must be some dividing value (s) that differentiates between the two decisions: rejection (critical region) and retention (acceptance region), this boundary value is known as the critical value .

Type I and Type II Error:

There are two types of situations (H 0 is true or false) which are complementary to each other and two types of complementary decisions (Reject H 0 or Failing to Reject H 0 ). So we have four types of cases:

So, the two possible errors in hypothesis testing can be:

Type I Error = [Reject H 0 when H 0 is true]

Type II Error = [Fails to reject H 0 when H 0 is false].

Type I Error is also known as False Positive and Type II Error is also known as False Negative in the language of Business Analytics.

Since these two are probabilistic events, so we measure them using probabilities:

α = Probability of committing Type I error = P [Reject H 0 / H 0 is true]

β = Probability of committing Type II error = P [Fails to reject H 0 / H 0 is false].

For a good testing procedure, both types of errors should be low (minimise α and β) but simultaneous minimisation of both the errors is not possible because they are interconnected. If we minimize one, the other will increase and vice versa. So, one error is fixed and another is tried to be minimised. Normally α is fixed and we try to minimise β. If Type I error is critical, α is fixed at a low value (allowing β to take relatively high value) otherwise at relatively high value (to minimise β to a low value, Type II error being critical).

Example: In Indian Judicial System we have H 0 : Under trial is innocent. Here, Type I Error = An innocent person is sentenced, while Type II Error = A guilty person is set free. Indian (Anglo Saxon) Judicial System considers type I error to be critical so it will have low α for this case.

Power of the test = 1- β = P [Reject H 0 / H 0 is false].

Higher the power of the test, better it is considered and we look for the Most Powerful Test since power of test can be taken as the probability that the test will detect a deviation from H 0 given that the deviation exists.

One Tailed and Two Tailed Tests of Hypothesis:

H 0 : µ ≤ µ 0

H 1 : µ > µ 0

When x̄ is significantly above the hypothesized population mean µ 0 then H 0 will be rejected and the test used will be right tailed test (upper tailed test) since the critical region (denoting rejection of H 0 will be in the right tail of the normal curve (representing sampling distribution of sample statistic x̄). (The critical region is shown as a shaded portion in the figure).

H 0 : µ ≥ µ 0

H 1 : µ < µ 0

In this case, if x̄ is significantly below the hypothesised population mean µ 0 then H 0 will be rejected and the test used will be the left tailed test (lower tailed test) since the critical region (denoting rejection of H 0 ) will be in the left tail of the normal curve (representing sampling distribution of sample statistic x̄). (The critical region is shown as a shaded portion in the figure).

These two tests are also known as One-tailed tests as there will be a critical region in only one tail of the sampling distribution.

H 0 : µ = µ 0

H 1 : µ ≠ µ 0

When x̄ is significantly different (significantly higher or lower than) from the hypothesised population mean µ 0 , then H 0 will be rejected. In this case, the two tailed test will be applicable because there will be two critical regions (denoting rejection of H 0 ) on both the tails of the normal curve (representing sampling distribution of sample statistic x̄). (The critical regions are shown as shaded portions in the figure).

Hypothesis Testing using Standardized Scale: Here, instead of measuring sample statistic (variable) in the original unit, standardised value is taken (better known as test statistic ). So, the comparison will be between observed value of test statistic (estimated from sample), and critical value of test statistic (obtained from relevant theoretical probability distribution).

Here, since population standard deviation (σ) is known, so the test statistics :

Z= (x- µx̄ x )/σ x̄ = (x- µ 0 )/(σ/√n) follows Standard Normal Distribution N (0, 1).

3.Deciding the Criteria for Rejection or otherwise:

As discussed, hypothesis testing means deciding a rule for rejection/retention of H 0 . Here, the critical region decides rejection of H 0 and there will be a value, known as Critical Value , to define the boundary of the critical region/acceptance region. The size (probability/area) of a critical region is taken as α . Here, α may be known as Significance Level , the level at which hypothesis testing is performed. It is equal to type I error , as discussed earlier.

Suppose, α has been decided as 5%, so the critical value of test statistic (Z) will be +1.645 (for right tail test), -1.645 (for left tail test). For the two tails test, the critical value will be -1.96 and +1.96 (as per the Standard Normal Distribution Z table). The value of α may be chosen as per the criticality of type I and type II. Normally, the value of α is taken as 5% in most of the analytical situations (Fisher, 1956).

4. Taking sample, data collection and estimating the observed value of test statistic:

In this stage, a proper sample of size n is taken and after collecting the data, the values of sample mean (x̄) and the observed value of test statistic Z obs is being estimated, as per the test statistic formula.

5. Taking the Decision to reject or otherwise:

On comparing the observed value of Test statistic with that of the critical value, we may identify whether the observed value lies in the critical region (reject H 0 ) or in the acceptance region (do not reject H 0 ) and decide accordingly.

Right Tailed Test: If Z obs > 1.645 : Reject H 0 at 5% Level of Significance.
Left Tailed Test: If Z obs < -1.645 : Reject H 0 at 5% Level of Significance.
Two Tailed Test: If Z obs > 1.96 or If Z obs < -1.96 : Reject H 0 at 5% Level of Significance.

There is an alternative approach for hypothesis testing, this approach is very much used in all the software packages. It is known as probability value/ prob. value/ p-value. It gives the probability of getting a value of statistic this far or farther from the hypothesised value if H0 is true. This denotes how likely is the result that we have observed. It may be further explained as the probability of observing the test statistic if H 0 is true i.e. what are the chances in support of occurrence of H 0 . If p-value is small, it means there are less chances (rare case) in favour of H 0 occuring, as the difference between a sample value and hypothesised value is significantly large so H 0 may be rejected, otherwise it may be retained.

If p-value < α : Reject H 0

If p-value ≥ α : Fails to Reject H 0

So, it may be mentioned that the level of significance (α) is the maximum threshold for p-value. It should be noted that p-value (two tailed test) = 2* p-value (one tailed test).

Note: Though the application of z-test requires the ‘Normality Assumption’ for the parent population with known standard deviation/ variance but if sample is large (n>30), the normality assumption for the parent population may be relaxed, provided population standard deviation/variance is known (as per Central Limit Theorem).

As we discussed in the previous case, for testing of population mean, we assume that sample has been drawn from the population following normal distribution mean µ and standard deviation σ. In this case test statistic Z = (x- µ 0 )/(σ/√n) ~ Standard Normal Distribution N (0, 1). But in the situations where population s.d. σ is not known (it is a very common situation in all the real life business situations), we estimate population s.d. (σ) by sample s.d. (s).

Hence the corresponding test statistic:

t= (x- µx̄ x )/σ x̄ = (x- µ 0 )/(s/√n) follows Student’s t distribution with (n-1) degrees of freedom. One degree of freedom has been sacrificed for estimating population s.d. (σ) by sample s.d. (s).

Everything else in the testing process remains the same.

t-test is not much affected if assumption of normality is violated provided data is slightly asymmetrical (near to symmetry) and data-set does not contain outliers.

t-distribution:

The Student’s t-distribution, is much similar to the normal distribution. It is a symmetric distribution (bell shaped distribution). In general Student’s t distribution is flatter i.e. having heavier tails. Shape of t distribution changes with degrees of freedom (exact distribution) and becomes approximately close to Normal distribution for large n.

In many business decision making situations, decision makers are interested in comparison of two populations i.e. interested in examining the difference between two population parameters. Example: comparing sales of rural and urban outlets, comparing sales before the advertisement and after advertisement, comparison of salaries in between male and female employees, comparison of salary before and after joining the data science courses etc.

Independent Samples and Dependent (Paired Samples):

Depending on method of collection data for the two samples, samples may be termed as independent or dependent samples. If two samples are drawn independently without any relation (may be from different units/respondents in the two samples), then it is said that samples are drawn independently . If samples are related or paired or having two observations at different points of time on the same unit/respondent, then the samples are said to be dependent or paired . This approach (paired samples) enables us to compare two populations after controlling the extraneous effect on them.

Testing the Difference Between Means: Independent Samples

Two samples z test:.

We have two populations, both following Normal populations as N (µ 1 , σ 1 ) and N (µ 2 , σ 2 ). We want to test the Null Hypothesis:

H 0 : µ 1 – µ 2 = θ or µ 1 – µ 2 ≤ θ or µ 1 – µ 2 ≥ θ

Alternative hypothesis:

H 1 : µ 1 – µ 2 > θ or

H 0 : µ 1 – µ 2 < θ or

H 1 : µ 1 – µ 2 ≠ θ

(where θ may take any value as per the situation or θ =0).

Two samples of size n 1 and n 2 have been taken randomly from the two normal populations respectively and the corresponding sample means are x̄ 1 and x̄ 2 .

Here, we are not interested in individual population parameters (means) but in the difference of population means (µ 1 – µ 2 ). So, the corresponding statistic is = (x̄ 1 – x̄ 2 ).

According, sampling distribution of the statistic (x̄ 1 – x̄ 2 ) will follow Normal distribution with mean µ x̄ = µ 1 – µ 2 and standard error σ x̄ = √ (σ² 1 / n 1 + σ² 2 / n 2 ). So, the corresponding Test Statistics will be:

Other things remaining the same as per the One Sample Tests (as explained earlier).

Two Independent Samples t-Test (when Population Standard Deviations are Unknown):

Here, for testing the difference of two population mean, we assume that samples have been drawn from populations following Normal Distributions, but it is a very common situation that population standard deviations (σ 1 and σ 2 ) are unknown. So they are estimated by sample standard deviations (s 1 and s 2 ) from the respective two samples.

Here, two situations are possible:

(a) Population Standard Deviations are unknown but equal:

In this situation (where σ 1 and σ 2 are unknown but assumed to be equal), sampling distribution of the statistic (x̄ 1 – x̄ 2 ) will follow Student’s t distribution with mean µ x̄ = µ 1 – µ 2 and standard error σ x̄ = √ Sp 2 (1/ n 1 + 1/ n 2 ). Where Sp 2 is the pooled estimate, given by:

Sp 2 = (n 1 -1) S 1 2 +(n 2 -1) S 2 2 /(n 1 +n 2 -2)

So, the corresponding Test Statistics will be:

t = {(x̄ 1 – x̄ 2 ) – (µ 1 – µ 2 )}/{√ Sp 2 (1/n 1 +1/n 2 )}

Here, t statistic will follow t distribution with d.f. (n 1 +n 2 -2).

(b) Population Standard Deviations are unknown but unequal:

In this situation (where σ 1 and σ 2 are unknown and unequal).

Then the sampling distribution of the statistic (x̄ 1 – x̄ 2 ) will follow Student’s t distribution with mean µ x̄ = µ 1 – µ 2 and standard error Se =√ (s² 1 / n 1 + s² 2 / n 2 ).

t = {(x̄ 1 – x̄ 2 ) – (µ 1 – µ 2 )}/{√ (s2 1 /n 1 +s2 2 /n 2 )}

The test statistic will follow Student’s t distribution with degrees of freedom (rounding down to nearest integers):

As discussed in the aforementioned two cases, it is important to figure out whether the two population variances are equal or otherwise. For this purpose, F test can be employed as:

H 0 : σ² 1 = σ² 2 and H 1 : σ² 1 ≠ σ² 2

Two samples of sizes n 1 and n 2 have been drawn from two populations respectively. They provide sample standard deviations s 1 and s 2 . The test statistic is F = s 1 ²/s 2 ²

The test statistic will follow F-distribution with (n 1 -1) df for numerator and (n 2 -1) df for denominator.

Note: There are many other tests that are applied for this purpose.

Paired Sample t-Test (Testing Difference between Means with Dependent Samples):

As discussed earlier, in the situation of Before-After Tests, to examine the impact of any intervention like a training program, health program, any campaign to change status, we have two set of observations (x i and y i ) on the same test unit (respondent or units) before and after the program. Each sample has “n” paired observations. The Samples are said to be dependent or paired.

Here, we consider a random variable: d i = x i – y i .

Accordingly, the sampling distribution of the sample statistic (sample mean of the differentces d i ’s) will follow Student’s t distribution with mean = θ and standard error = sd/ √ n, where sd is the sample standard deviation of d i ’s.

Hence, the corresponding test statistic: t = (d̅- θ)/sd/√n will follow t distribution with (n-1).

As we have observed, paired t-test is actually one sample test since two samples got converted into one sample of differences. If ‘Two Independent Samples t-Test’ and ‘Paired t-test’ are applied on the same data set then two tests will give much different results because in case of Paired t-Test, standard error will be quite low as compared to Two Independent Samples t-Test. The Paired t-Test is applied essentially on one sample while the earlier one is applied on two samples. The result of the difference in standard error is that t-statistic will take larger value in case of ‘Paired t-Test’ in comparison to the ‘Two Independent Samples t-Test and finally p-values get affected accordingly.

t-Test in SPSS:

One sample t-test.

Analyze => Compare Means => One-Sample T-Test to open relevant dialogue box.
Test variable (variable under consideration) in the Test variable(s) box and hypothesised value µ 0 = 75 (for example) in the Test Value box are to be entered.
Press Ok to have the output.

Here, we consider the example of Ventura Sales, and want to examine the perception that average sales in the first quarter is 75 (thousand) vs it is not. So, the Hypotheses:

Null Hypothesis H 0 : µ=75

Alternative Hypothesis H 1 : µ≠75

One-Sample Statistics

Descriptive table showing the sample size n = 60, sample mean x̄=72.02, sample sd s=9.724.

One-Sample Test

One Sample Test Table shows the result of the t-test. Here, test statistic value (from the sample) is t = -2.376 and the corresponding p-value (2 tailed) = 0.021 <0.05. So, H 0 got rejected and it can be said that the claim of average first quarterly sales being 75 (thousand) does not hold.

Two Independent Samples t-Test

Analyze => Compare Means => Independent-Samples T-Test to open the dialogue box.
Enter the Test variable (variable under consideration) in the Test Variable(s) box and variable categorising the groups in the Grouping Variable box.
Define the groups by clicking on Define Groups and enter the relevant numeric-codes into the relevant groups in the Define Groups sub-dialogue box. Press Continue to return back to the main dialogue box.

We continue with the example of Ventura Sales, and want to compare the average first quarter sales with respect to Urban Outlets and Rural Outlets (two independent samples/groups). Here, the claim is that urban outlets are giving lower sales as compared to rural outlets. So, the Hypotheses:

H 0 : µ 1 – µ 2 = 0 or µ 1 = µ 2 (Where, µ 1 = Population Mean Sale of Urban Outlets and µ 2 = Population Mean Sale of Rural Outlets)

H 1 : µ 1 < µ 2

Group Statistics

Descriptive table showing the sample sizes n 1 =37 and n 2 =23, sample means x̄ 1 =67.86 and x̄ 2 =78.70, sample standard deviations s 1 =8.570 and s 2 = 7.600.

The below table is the Independent Sample Test Table, proving all the relevant test statistics and p-values. Here, both the outputs for Equal Variance (assumed) and Unequal Variance (assumed) are presented.

Independent Samples Test

So, we have to figure out whether we should go for ‘equal variance’ case or for ‘unequal variances’ case.

Here, Levene’s Test for Equality of Variances has to be applied for this purpose with the hypotheses: H 0 : σ² 1 = σ² 2 and H 1 : σ² 1 ≠ σ² 2 . The p-value (Sig) = 0.460 >0.05, so we can’t reject (so retained) H 0 . Hence, variances can be assumed to be equal.

So, “Equal Variances assumed” case is to be taken up. Accordingly, the value of t statistic = -4.965 and the p-value (two tailed) = 0.000, so the p-value (one tailed) = 0.000/2 = 0.000 <0.05. Hence, H 0 got rejected and it can be said that urban outlets are giving lower sales in the first quarter. So, the claim stands.

Paired t-Test (Testing Difference between Means with Dependent Samples):

Analyze => Compare Means => Paired-Samples T-Test to open the dialogue box.
Enter the relevant pair of variables (paired samples) in the Paired Variables box.
After entering the paired samples, press Ok to have the output.

We continue with the example of Ventura Sales, and want to compare the average first quarter sales with the second quarter sales. Some sales promotion interventions were executed with an expectation of increasing sales in the second quarter. So, the Hypotheses:

H 0 : µ 1 = µ 2 (Where, µ 1 = Population Mean Sale of Quarter-I and µ 2 = Population Mean Sale of Quarter-II)

H 1 : µ 1 < µ 2 (representing the increase of sales i.e. implying the success of sales interventions)

Paired Samples Statistics

Descriptive table showing the sample size n=60, sample means x̄ 1 =72.02 and x̄ 2 =72.43.

As per the following output table (Paired Samples Test), sample mean of differences d̅ = -0.417 with standard deviation of differences sd = 8.011 and value of t statistic = -0.403. Accordingly, the p-value (two tailed) = 0.688, so the p-value (one tailed) = 0.688/2 = 0.344 > 0.05. So, there have not been sufficient reasons to Reject H 0 i.e. H 0 should be retained. So, the effectiveness (success) of the sales promotion interventions is doubtful i.e. it didn’t result in significant increase in sales, provided all other extraneous factors remain the same.

Paired Samples Test

t-Test Application One Sample

Experience Marketing Services reported that the typical American spends a mean of 144 minutes (2.4 hours) per day accessing the Internet via a mobile device. (Source: The 2014 Digital Marketer, available at ex.pn/1kXJifX.) To test the validity of this statement, you select a sample of 30 friends and family. The result for the time spent per day accessing the Internet via a mobile device (in minutes) are stored in Internet_Mobile_Time.csv file.

Is there evidence that the populations mean time spent per day accessing the Internet via a mobile device is different from 144 minutes? Use the p-value approach and a level of significance of 0.05

What assumption about the population distribution is needed to conduct the test in A?

Solution In R

[1] 1.224674

[1] 0.2305533

[1] “Accepted”

Independent t-test two sample

A hotel manager looks to enhance the initial impressions that hotel guests have when they check-in. Contributing to initial impressions is the time it takes to deliver a guest’s luggage to the room after check-in. A random sample of 20 deliveries on a particular day was selected each from Wing A and Wing B of the hotel. The data collated is given in Luggage.csv file. Analyze the data and determine whether there is a difference in the mean delivery times in the two wings of the hotel. (use alpha = 0.05).

Two Sample t-test data: WingA and WingB t = 5.1615, df = 38, p-value = 4.004e-06 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 1.531895 Inf sample estimates: mean of x mean of y 10.3975 8.1225 > t.test(WingA,WingB) Welch Two Sample t-test

t = 5.1615, df = 37.957, p-value = 8.031e-06 alternative hypothesis: true difference in means is not equal to 0 95 per cent confidence interval: 1.38269 3.16731 sample estimates: mean of x mean of y 10.3975 8.1225

Case Study- Titan Insurance Company

The Titan Insurance Company has just installed a new incentive payment scheme for its lift policy salesforce. It wants to have an early view of the success or failure of the new scheme. Indications are that the sales force is selling more policies, but sales always vary in an unpredictable pattern from month to month and it is not clear that the scheme has made a significant difference.

Life Insurance companies typically measure the monthly output of a salesperson as the total sum assured for the policies sold by that person during the month. For example, suppose salesperson X has, in the month, sold seven policies for which the sums assured are £1000, £2500, £3000, £5000, £10000, £35000. X’s output for the month is the total of these sums assured, £61,500.

Titan’s new scheme is that the sales force receives low regular salaries but are paid large bonuses related to their output (i.e. to the total sum assured of policies sold by them). The scheme is expensive for the company, but they are looking for sales increases which more than compensate. The agreement with the sales force is that if the scheme does not at least break even for the company, it will be abandoned after six months.

The scheme has now been in operation for four months. It has settled down after fluctuations in the first two months due to the changeover.

To test the effectiveness of the scheme, Titan has taken a random sample of 30 salespeople measured their output in the penultimate month before changeover and then measured it in the fourth month after the changeover (they have deliberately chosen months not too close to the changeover). Ta ble 1 shows t he outputs of the salespeople in Table 1

Data preparation

Since the given data are in 000, it will be better to convert them in thousands. Problem 1 Describe the five per cent significance test you would apply to these data to determine whether the new scheme has significantly raised outputs? What conclusion does the test lead to? Solution: It is asked that whether the new scheme has significantly raised the output, it is an example of the one-tailed t-test. Note: Two-tailed test could have been used if it was asked “new scheme has significantly changed the output” Mean of amount assured before the introduction of scheme = 68450 Mean of amount assured after the introduction of scheme = 72000 Difference in mean = 72000 – 68450 = 3550 Let, μ1 = Average sums assured by salesperson BEFORE changeover. μ2 = Average sums assured by salesperson AFTER changeover. H0: μ1 = μ2 ; μ2 – μ1 = 0 HA: μ1 < μ2 ; μ2 – μ1 > 0 ; true difference of means is greater than zero. Since population standard deviation is unknown, paired sample t-test will be used.

Since p-value (=0.06529) is higher than 0.05, we accept (fail to reject) NULL hypothesis. The new scheme has NOT significantly raised outputs .

Problem 2 Suppose it has been calculated that for Titan to break even, the average output must increase by £5000. If this figure is an alternative hypothesis, what is: (a) The probability of a type 1 error? (b) What is the p-value of the hypothesis test if we test for a difference of $5000? (c) Power of the test: Solution: 2.a. The probability of a type 1 error? Solution: Probability of Type I error = significant level = 0.05 or 5% 2.b. What is the p-value of the hypothesis test if we test for a difference of $5000? Solution: Let μ2 = Average sums assured by salesperson AFTER changeover. μ1 = Average sums assured by salesperson BEFORE changeover. μd = μ2 – μ1 H0: μd ≤ 5000 HA: μd > 5000 This is a right tail test.

P-value = 0.6499 2.c. Power of the test. Solution: Let μ2 = Average sums assured by salesperson AFTER changeover. μ1 = Average sums assured by salesperson BEFORE changeover. μd = μ2 – μ1 H0: μd = 4000 HA: μd > 0

H0 will be rejected if test statistics > t_critical. With α = 0.05 and df = 29, critical value for t statistic (or t_critical ) will be 1.699127. Hence, H0 will be rejected for test statistics ≥ 1.699127. Hence, H0 will be rejected if for 𝑥̅ ≥ 4368.176

Graphically,

Probability (type II error) is P(Do not reject H0 | H0 is false) Our NULL hypothesis is TRUE at μd = 0 so that H0: μd = 0 ; HA: μd > 0 Probability of type II error at μd = 5000

= P (Do not reject H0 | H0 is false) = P (Do not reject H0 | μd = 5000) = P (𝑥̅ < 4368.176 | μd = 5000) = P (t < | μd = 5000) = P (t < -0.245766) = 0.4037973

R Code: Now, β=0.5934752, Power of test = 1- β = 1- 0.5934752 = 0.4065248

While performing Hypothesis-Testing, Hypotheses can’t be proved or disproved since we have evidence from sample (s) only. At most, Hypotheses may be rejected or retained.
Use of the term “accept H 0 ” in place of “do not reject” should be avoided even if the test statistic falls in the Acceptance Region or p-value ≥ α. This simply means that the sample does not provide sufficient statistical evidence to reject the H 0 . Since we have tried to nullify (reject) H 0 but we haven’t found sufficient support to do so, we may retain it but it won’t be accepted.
Confidence Interval (Interval Estimation) can also be used for testing of hypotheses. If the hypothesis parameter falls within the confidence interval, we do not reject H 0 . Otherwise, if the hypothesised parameter falls outside the confidence interval i.e. confidence interval does not contain the hypothesized parameter, we reject H 0 .
Downey, A. B. (2014). Think Stat: Exploratory Data Analysis , 2 nd Edition, Sebastopol, CA: O’Reilly Media Inc
Fisher, R. A. (1956). Statistical Methods and Scientific Inference , New York: Hafner Publishing Company.
Hogg, R. V.; McKean, J. W. & Craig, A. T. (2013). Introduction to Mathematical Statistics , 7 th Edition, New Delhi: Pearson India.
IBM SPSS Statistics. (2020). IBM Corporation.
Levin, R. I.; Rubin, D. S; Siddiqui, M. H. & Rastogi, S. (2017). Statistics for Management , 8 th Edition, New Delhi: Pearson India.

If you want to get a detailed understanding of Hypothesis testing, you can take up this hypothesis testing in machine learning course. This course will also provide you with a certificate at the end of the course.

If you want to learn more about R programming and other concepts of Business Analytics or Data Science, sign up for Great Learning ’s PG program in Data Science and Business Analytics.

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Blog Beginner Guides 6 Types of Case Studies to Inspire Your Research and Analysis

6 Types of Case Studies to Inspire Your Research and Analysis

Written by: Ronita Mohan Sep 20, 2021

Case studies have become powerful business tools. But what is a case study? What are the benefits of creating one? Are there limitations to the format?

If you’ve asked yourself these questions, our helpful guide will clear things up. Learn how to use a case study for business. Find out how cases analysis works in psychology and research.

We’ve also got examples of case studies to inspire you.

Haven’t made a case study before? You can easily create a case study with Venngage’s customizable case study templates .

Click to jump ahead:

What is a case study?

6 types of case studies, what is a business case study, what is a case study in research, what is a case study in psychology, what is the case study method, benefits of case studies, limitations of case studies, faqs about case studies.

A case study is a research process aimed at learning about a subject, an event or an organization. Case studies are use in business, the social sciences and healthcare.

A case study may focus on one observation or many. It can also examine a series of events or a single case. An effective how to write a case study analysis tells a story and provides a conclusion.

Healthcare industries write reports on patients and diagnoses. Marketing case study examples , like the one below, highlight the benefits of a business product.

Bold Social Media Business Case Study Template

Now that you know what a case study is, let’s look at the six different types of case studies next.

There are six common types of case reports. Depending on your industry, you might use one of these types.

Descriptive case studies

Explanatory case studies, exploratory case reports, intrinsic case studies, instrumental case studies, collective case reports.

We go into more detail about each type of study in the guide below.

Related: 15+ Professional Case Study Examples [Design Tips + Templates]

When you have an existing hypothesis, you can design a descriptive study. This type of report starts with a description. The aim is to find connections between the subject being studied and a theory.

Once these connections are found, the study can conclude. The results of this type of study will usually suggest how to develop a theory further.

A study like the one below has concrete results. A descriptive report would use the quantitative data as a suggestion for researching the subject deeply.

Lead generation business case study template

When an incident occurs in a field, an explanation is required. An explanatory report investigates the cause of the event. It will include explanations for that cause.

The study will also share details about the impact of the event. In most cases, this report will use evidence to predict future occurrences. The results of explanatory reports are definitive.

Note that there is no room for interpretation here. The results are absolute.

The study below is a good example. It explains how one brand used the services of another. It concludes by showing definitive proof that the collaboration was successful.

Bold Content Marketing Case Study Template

Another example of this study would be in the automotive industry. If a vehicle fails a test, an explanatory study will examine why. The results could show that the failure was because of a particular part.

Related: How to Write a Case Study [+ Design Tips]

An explanatory report is a self-contained document. An exploratory one is only the beginning of an investigation.

Exploratory cases act as the starting point of studies. This is usually conducted as a precursor to large-scale investigations. The research is used to suggest why further investigations are needed.

An exploratory study can also be used to suggest methods for further examination.

For example, the below analysis could have found inconclusive results. In that situation, it would be the basis for an in-depth study.

Teal Social Media Business Case Study Template

Intrinsic studies are more common in the field of psychology. These reports can also be conducted in healthcare or social work.

These types of studies focus on a unique subject, such as a patient. They can sometimes study groups close to the researcher.

The aim of such studies is to understand the subject better. This requires learning their history. The researcher will also examine how they interact with their environment.

For instance, if the case study below was about a unique brand, it could be an intrinsic study.

Vibrant Content Marketing Case Study Template

Once the study is complete, the researcher will have developed a better understanding of a phenomenon. This phenomenon will likely not have been studied or theorized about before.

Examples of intrinsic case analysis can be found across psychology. For example, Jean Piaget’s theories on cognitive development. He established the theory from intrinsic studies into his own children.

Related: What Disney Villains Can Tell Us About Color Psychology [Infographic]

This is another type of study seen in medical and psychology fields. Instrumental reports are created to examine more than just the primary subject.

When research is conducted for an instrumental study, it is to provide the basis for a larger phenomenon. The subject matter is usually the best example of the phenomenon. This is why it is being studied.

Take the example of the fictional brand below.

Purple SAAS Business Case Study Template

Assume it’s examining lead generation strategies. It may want to show that visual marketing is the definitive lead generation tool. The brand can conduct an instrumental case study to examine this phenomenon.

Collective studies are based on instrumental case reports. These types of studies examine multiple reports.

There are a number of reasons why collective reports are created:

To provide evidence for starting a new study
To find pattens between multiple instrumental reports
To find differences in similar types of cases
Gain a deeper understanding of a complex phenomenon
Understand a phenomenon from diverse contexts

A researcher could use multiple reports, like the one below, to build a collective case report.

Social Media Business Case Study template

Related: 10+ Case Study Infographic Templates That Convert

A business or marketing case study aims at showcasing a successful partnership. This can be between a brand and a client. Or the case study can examine a brand’s project.

There is a perception that case studies are used to advertise a brand. But effective reports, like the one below, can show clients how a brand can support them.

Light Simple Business Case Study Template

Hubspot created a case study on a customer that successfully scaled its business. The report outlines the various Hubspot tools used to achieve these results.

Hubspot also added a video with testimonials from the client company’s employees.

So, what is the purpose of a case study for businesses? There is a lot of competition in the corporate world. Companies are run by people. They can be on the fence about which brand to work with.

Business reports stand out aesthetically, as well. They use brand colors and brand fonts . Usually, a combination of the client’s and the brand’s.

With the Venngage My Brand Kit feature, businesses can automatically apply their brand to designs.

A business case study, like the one below, acts as social proof. This helps customers decide between your brand and your competitors.

Modern lead Generation Business Case Study Template

Don’t know how to design a report? You can learn how to write a case study with Venngage’s guide. We also share design tips and examples that will help you convert.

Related: 55+ Annual Report Design Templates, Inspirational Examples & Tips [Updated]

Research is a necessary part of every case study. But specific research fields are required to create studies. These fields include user research, healthcare, education, or social work.

For example, this UX Design report examined the public perception of a client. The brand researched and implemented new visuals to improve it. The study breaks down this research through lessons learned.

What is a case study in research? UX Design case study example

Clinical reports are a necessity in the medical field. These documents are used to share knowledge with other professionals. They also help examine new or unusual diseases or symptoms.

The pandemic has led to a significant increase in research. For example, Spectrum Health studied the value of health systems in the pandemic. They created the study by examining community outreach.

What is a case study in research? Spectrum healthcare example

The pandemic has significantly impacted the field of education. This has led to numerous examinations on remote studying. There have also been studies on how students react to decreased peer communication.

Social work case reports often have a community focus. They can also examine public health responses. In certain regions, social workers study disaster responses.

You now know what case studies in various fields are. In the next step of our guide, we explain the case study method.

In the field of psychology, case studies focus on a particular subject. Psychology case histories also examine human behaviors.

Case reports search for commonalities between humans. They are also used to prescribe further research. Or these studies can elaborate on a solution for a behavioral ailment.

The American Psychology Association has a number of case studies on real-life clients. Note how the reports are more text-heavy than a business case study.

What is a case study in psychology? Behavior therapy example

Famous psychologists such as Sigmund Freud and Anna O popularised the use of case studies in the field. They did so by regularly interviewing subjects. Their detailed observations build the field of psychology.

It is important to note that psychological studies must be conducted by professionals. Psychologists, psychiatrists and therapists should be the researchers in these cases.

Related: What Netflix’s Top 50 Shows Can Teach Us About Font Psychology [Infographic]

The case study method, or case method, is a learning technique where you’re presented with a real-world business challenge and asked how you’d solve it.

After working through it independently and with peers, you learn how the actual scenario unfolded. This approach helps develop problem-solving skills and practical knowledge.

This method often uses various data sources like interviews, observations, and documents to provide comprehensive insights. The below example would have been created after numerous interviews.

Case studies are largely qualitative. They analyze and describe phenomena. While some data is included, a case analysis is not quantitative.

There are a few steps in the case method. You have to start by identifying the subject of your study. Then determine what kind of research is required.

In natural sciences, case studies can take years to complete. Business reports, like this one, don’t take that long. A few weeks of interviews should be enough.

Blue Simple Business Case Study Template

The case method will vary depending on the industry. Reports will also look different once produced.

As you will have seen, business reports are more colorful. The design is also more accessible . Healthcare and psychology reports are more text-heavy.

Designing case reports takes time and energy. So, is it worth taking the time to write them? Here are the benefits of creating case studies.

Collects large amounts of information
Helps formulate hypotheses
Builds the case for further research
Discovers new insights into a subject
Builds brand trust and loyalty
Engages customers through stories

For example, the business study below creates a story around a brand partnership. It makes for engaging reading. The study also shows evidence backing up the information.

Blue Content Marketing Case Study Template

We’ve shared the benefits of why studies are needed. We will also look at the limitations of creating them.

Related: How to Present a Case Study like a Pro (With Examples)

There are a few disadvantages to conducting a case analysis. The limitations will vary according to the industry.

Responses from interviews are subjective
Subjects may tailor responses to the researcher
Studies can’t always be replicated
In certain industries, analyses can take time and be expensive
Risk of generalizing the results among a larger population

These are some of the common weaknesses of creating case reports. If you’re on the fence, look at the competition in your industry.

Other brands or professionals are building reports, like this example. In that case, you may want to do the same.

Coral content marketing case study template

What makes a case study a case study?

A case study has a very particular research methodology. They are an in-depth study of a person or a group of individuals. They can also study a community or an organization. Case reports examine real-world phenomena within a set context.

How long should a case study be?

The length of studies depends on the industry. It also depends on the story you’re telling. Most case studies should be at least 500-1500 words long. But you can increase the length if you have more details to share.

What should you ask in a case study?

The one thing you shouldn’t ask is ‘yes’ or ‘no’ questions. Case studies are qualitative. These questions won’t give you the information you need.

Ask your client about the problems they faced. Ask them about solutions they found. Or what they think is the ideal solution. Leave room to ask them follow-up questions. This will help build out the study.

How to present a case study?

When you’re ready to present a case study, begin by providing a summary of the problem or challenge you were addressing. Follow this with an outline of the solution you implemented, and support this with the results you achieved, backed by relevant data. Incorporate visual aids like slides, graphs, and images to make your case study presentation more engaging and impactful.

Now you know what a case study means, you can begin creating one. These reports are a great tool for analyzing brands. They are also useful in a variety of other fields.

Use a visual communication platform like Venngage to design case studies. With Venngage’s templates, you can design easily. Create branded, engaging reports, all without design experience.

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Combined Diet and Supplementation Therapy Resolves Alopecia Areata in a Paediatric Patient: A Case Study

Cliff j harvey.

Author information
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Cliff J. Harvey [email protected]

Corresponding author.

Accepted 2020 Nov 7; Collection date 2020 Nov.

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.

Alopecia areata (AA) is a common autoimmune condition resulting in spot baldness and, rarely, more extensive hair loss. There is an association between both the incidence and the severity of AA and several micronutrients, including vitamin D and zinc. This case reports an eight-year-old male diagnosed with AA and treated with a diet and supplemental regimen based on unrefined foods, rich in vitamins A and D, zinc, and supplemented with a multi-nutrient, zinc sulfate, and fish oil with vitamin D. Complete remission of AA was achieved within five months.

Keywords: alopecia areata, nutrition, vitamin d, zinc, vitamin a, supplementation

Introduction

Alopecia areata (AA), sometimes known as ‘spot baldness’ is a condition in which hair is lost, typically in patches over some of the body but occasionally becoming more severe and affecting the entire body. The condition affects around 2% of people at some time in their life [ 1 ]. It is believed to be an autoimmune disease with some inheritability, and different immune‐cell lines, including plasmacytoid dendritic cells, natural killer cells, and T cells, along with key molecules, such as interferon‐γ, interleukin‐15, MICA and NKG2D, and CD8 T cells have been identified as contributing to the autoimmune process [ 2 - 3 ]. Genome-wide association studies provide evidence for the involvement of both innate and acquired immunity in the pathogenesis of AA [ 3 ]. There is also evidence that AA is associated with oxidative stress [ 4 ].

Case presentation

An eight-year-old male presented for nutritional and supplemental advice secondary to a diagnosis of alopecia areata. Initial blood tests were within normal ranges for C-reactive protein, fasting glucose, ferritin, liver enzymes, electrolytes, and all complete blood count measures. Coeliac disease was ruled out due to tissue transglutan immunoglobulin A (IgA) < 0.5 U/ml and total IgA 0.4 g/L. Thyroid disease was not suspected, as thyroid peroxidase antibodies were within normal ranges (37 U/ml) and thyroid-stimulating hormone was 2.6 mIU/L.

Further blood tests were requested for vitamin B12 and folate, magnesium, serum zinc, rheumatoid factors, anti-nuclear antibodies, along with a repeat complete blood count. Except for marginally low neutrophils and monocytes, no abnormalities were noted. Serum zinc returned a ‘normal’ range result of 0.68 mcg/ml but this was below the suggested lower threshold of >0.7 mcg/ml for functional outcomes in boys of this age (6-9 yrs.) [ 5 ]. Similarly, while the 25 hydroxyvitamin D (25(OH)D) result of 90 nmol/L was within reference ranges, it has been suggested that the lower threshold for optimum 25(OH)D status is >100 nmol/L [ 6 ].

Clinical course

The patient’s parents were provided with advice to increase zinc and vitamin A and D-rich foods, avoid gluten and dairy where able, and to focus on a diet that prioritizes foods in their natural forms in preference to highly processed ‘packaged’ foods. Also, a supplementation regimen consisting of a multi-nutrient (multi) powder rich in vitamins A and D3, zinc, and secondary antioxidant nutrients (Kids Good Stuff, Nuzest, Potts Point NSW, Australia), a zinc sulfate supplement (zinc drops, Clinicians Ltd., Australia), and fish oil with added vitamin D (fish oil + vitamin D, Melrose, Victoria, Australia) was provided (key nutrient summary in Table 1 ), along with lifestyle advice to get outside for 5-10 min per day without sunblock on. A full list of the multi-nutrient ingredients can be found in Appendix 1.

Table 1. Amounts of supplemental nutrients provided .

RE: retinol equivalent; DHA: docosahexaenoic, EPA: eicosapentaenoic acid

A sample of the dietary advice is provided below.

Vitamin A: Fish oil, liver, oily fish (herring, sardines, salmon, cod), eggs, chicken Also: kumara, pumpkin, carrots, mangos, apricots, broccoli, full-fat yogurt and milk*

Vitamin D: Cod liver oil, liver, fatty fish, full-fat milk and yogurt*

Note: It is imperative to use full-fat foods, as vitamins A and D are fat-soluble.

Zinc: Oysters, beef, pork, chicken, pumpkin seeds, full-fat yogurt*, almonds, fish

Note: Excessive intake of cereal grains might inhibit some zinc absorption.

*We are reducing/avoiding dairy in this phase, but these foods can be reintroduced to test tolerance when symptoms abate.

On presentation, the client had experienced severe hair loss with the involvement of the eyelashes, eyebrows, and mostly spot baldness on the crown of the head (Figure 1 ).

Figure 1. Spot baldness one week after the initial consultation.

After following the prescribed dietary regimen for two months, the patient's hair can be seen to be regrowing in Figure 2 .

Figure 2. Patient hair regrowth at two months.

Five months following commencement of the diet and supplement regimen, the hair on the crown was completely recovered and the patient's mother reported that the eyelashes and eyebrows were growing back (Figure 3 ). Approximately two weeks after commencing the diet and supplementation regimen, the patient exhibited a limited, minor popular rash on the cheeks, which resolved shortly afterwards and by August, there were no signs of any eczema-like skin conditions.

Figure 3. Patient hair regrowth five months following commencement of the diet and supplement regimen.

Patients with AA tend to have lower serum vitamin D, zinc, and folate levels as compared to controls, and evidence also suggests that vitamin A status may help modify the disease [ 7 ].

In particular, vitamin D status appears to be markedly different in patients with AA. Vitamin D levels (serum 25(OH)D) in patients with alopecia have been demonstrated to be significantly lower than in healthy controls (11.84 ± 6.18 vs 23.57 ± 9.03 ng/mL p < 0.001) [ 8 ], and the prevalence of vitamin D deficiency significantly higher [ 9 ]. Disease severity in AA also appears to be inversely correlated to vitamin D status [ 8 , 10 - 11 ]. While there have not been significant genetic differences (gene polymorphisms) shown for the vitamin D receptor (expressed in hair follicles) between alopecia and controls [ 12 ], tissue vitamin D receptor levels in tissue are lower in alopecia versus controls [ 13 ] and this is associated with increased inflammation but not vitamin D levels or severity and pattern of illness [ 14 ].

Serum zinc levels have also been demonstrated to be lower in people with AA as compared to health controls (t = 4.206, p = 0.001) and are associated with the severity of the condition (r = -0.573, p = 0.001) [ 15 ]. Other research has also demonstrated that alopecia patients have significantly lower zinc levels than controls [ 16 - 17 ]. For example, Orecchia and colleagues observed a mean plasma zinc level of 74.2 versus 95.5 μg/100 ml in cases as compared to controls respectively [ 17 ]. And while some studies have shown no significant difference in serum zinc levels between alopecia patients and controls, subgroup analysis revealed lower zinc levels in those with greater disease severity [ 18 ].

While this case has focussed on key nutrients with demonstrable associations with either disease incidence or severity, others such as biotin [ 19 ] have also been implicated and warrant further research.

Therefore, it is likely that nutrient-repletion is a critical and yet often overlooked strategy in the treatment of AA.

Conclusions

Vitamin D and zinc (and vitamin A) are critical to immune function and may provide an adjunct treatment option for AA. Insufficiency of these key micronutrients, whether primary or secondary to genetic polymorphisms, is linked to both the incidence and severity of AA. Normal cycles of relapse and remission common to autoimmune conditions, the placebo effect, or lifestyle factors may have contributed to or been responsible for the remission seen in this case and ongoing observation and follow-up will help to ascertain this. However, it demonstrates that a diet, excluding common autoimmune trigger foods and replete in key micronutrients, holds promise for the treatment of this condition, and research is warranted to investigate this hypothesis further.

Table 2. Nutritional information of Nuzest Kids Good Stuff.

RE: retinol equivalent; TE: tocopherol equivalent

Percent of average recommended daily intake for children ages 4-14

The content published in Cureus is the result of clinical experience and/or research by independent individuals or organizations. Cureus is not responsible for the scientific accuracy or reliability of data or conclusions published herein. All content published within Cureus is intended only for educational, research and reference purposes. Additionally, articles published within Cureus should not be deemed a suitable substitute for the advice of a qualified health care professional. Do not disregard or avoid professional medical advice due to content published within Cureus.

The authors have declared financial relationships, which are detailed in the next section.

Cliff Harvey declare(s) personal fees from Melrose Health. Cliff Harvey has provided consultancy services to Melrose Health. . Cliff Harvey declare(s) personal fees and stock/stock options from Nuzest. Cliff Harvey is a stakeholder in Nuzest and has received consultancy fees and stock options.

Human Ethics

Consent was obtained by all participants in this study

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The example of a dependent samples hypothesis testing may be analyzing the weight of a group before and after a weight loss program or a corn, flake manufacturer want to test whether the average weight of packets being manufactured is equal to a specified value of say,500 gms. In our end to the end case study, we shall take independent samples ...
6 Types of Case Studies to Inspire Your Research and Analysis
A case study is a research process aimed at learning about a subject, an event or an organization. Case studies are use in business, the social sciences and healthcare. A case study may focus on one observation or many. It can also examine a series of events or a single case. An effective how to write a case study analysis tells a story and ...
Combined Diet and Supplementation Therapy Resolves Alopecia Areata in a
Genome-wide association studies provide evidence for the involvement of both innate and acquired immunity in the pathogenesis of AA . There is also evidence that AA is associated with oxidative stress . Case presentation. An eight-year-old male presented for nutritional and supplemental advice secondary to a diagnosis of alopecia areata.