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• Case Study | Definition, Examples & Methods

Case Study | Definition, Examples & Methods

Published on 5 May 2022 by Shona McCombes . Revised on 30 January 2023.

A case study is a detailed study of a specific subject, such as a person, group, place, event, organisation, or phenomenon. Case studies are commonly used in social, educational, clinical, and business research.

A case study research design usually involves qualitative methods , but quantitative methods are sometimes also used. Case studies are good for describing , comparing, evaluating, and understanding different aspects of a research problem .

Table of contents

When to do a case study, step 1: select a case, step 2: build a theoretical framework, step 3: collect your data, step 4: describe and analyse the case.

A case study is an appropriate research design when you want to gain concrete, contextual, in-depth knowledge about a specific real-world subject. It allows you to explore the key characteristics, meanings, and implications of the case.

Case studies are often a good choice in a thesis or dissertation . They keep your project focused and manageable when you don’t have the time or resources to do large-scale research.

You might use just one complex case study where you explore a single subject in depth, or conduct multiple case studies to compare and illuminate different aspects of your research problem.

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Once you have developed your problem statement and research questions , you should be ready to choose the specific case that you want to focus on. A good case study should have the potential to:

• Provide new or unexpected insights into the subject
• Challenge or complicate existing assumptions and theories
• Propose practical courses of action to resolve a problem
• Open up new directions for future research

Unlike quantitative or experimental research, a strong case study does not require a random or representative sample. In fact, case studies often deliberately focus on unusual, neglected, or outlying cases which may shed new light on the research problem.

If you find yourself aiming to simultaneously investigate and solve an issue, consider conducting action research . As its name suggests, action research conducts research and takes action at the same time, and is highly iterative and flexible. 

However, you can also choose a more common or representative case to exemplify a particular category, experience, or phenomenon.

While case studies focus more on concrete details than general theories, they should usually have some connection with theory in the field. This way the case study is not just an isolated description, but is integrated into existing knowledge about the topic. It might aim to:

• Exemplify a theory by showing how it explains the case under investigation
• Expand on a theory by uncovering new concepts and ideas that need to be incorporated
• Challenge a theory by exploring an outlier case that doesn’t fit with established assumptions

To ensure that your analysis of the case has a solid academic grounding, you should conduct a literature review of sources related to the topic and develop a theoretical framework . This means identifying key concepts and theories to guide your analysis and interpretation.

There are many different research methods you can use to collect data on your subject. Case studies tend to focus on qualitative data using methods such as interviews, observations, and analysis of primary and secondary sources (e.g., newspaper articles, photographs, official records). Sometimes a case study will also collect quantitative data .

The aim is to gain as thorough an understanding as possible of the case and its context.

In writing up the case study, you need to bring together all the relevant aspects to give as complete a picture as possible of the subject.

How you report your findings depends on the type of research you are doing. Some case studies are structured like a standard scientific paper or thesis, with separate sections or chapters for the methods , results , and discussion .

Others are written in a more narrative style, aiming to explore the case from various angles and analyse its meanings and implications (for example, by using textual analysis or discourse analysis ).

In all cases, though, make sure to give contextual details about the case, connect it back to the literature and theory, and discuss how it fits into wider patterns or debates.

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Writing a Case Study

What is a case study?

A Case study is: 

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

What are the different types of case studies?

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

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

Who are your case study participants?

What is triangulation ? 

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

How to write a Case Study?

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

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Literature as a Foundation for Research: Case Studies and Examples

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• Writing Articles & Reviews
• November 2, 2023

When conducting research, a solid foundation is essential for ensuring the credibility and depth of your work. One such foundation that has been proven effective time and again is literature. By utilizing literature as a basis for research, scholars can draw upon existing knowledge, build upon established theories, and gain insights from previous studies. In this article, we explore the importance of literature in research through case studies and provide examples of how IT can be effectively incorporated into various disciplines.

The Importance of Literature in Research

Literature plays a crucial role in research as IT provides a comprehensive understanding of the existing body of knowledge on a particular topic. IT offers a platform for scholars to engage in scholarly conversations, critically evaluate previous studies, and identify gaps or areas that require further exploration.

By examining literature, researchers can gain insights into various theories, methodologies, and findings that have been developed over time. This allows them to position their research within the existing scholarly discourse and contribute something novel to the field.

Case Study: Literature Review in a Scientific Research Paper

Let’s consider a case study to highlight how literature can be effectively incorporated into research. Imagine a scientific research paper aiming to investigate the effects of a new drug on a specific disease. Before conducting any experiments or data collection, the researchers must undertake a comprehensive literature review.

In this literature review, the researchers will identify and analyze existing studies related to the disease, previous treatments, and any prior research on the drug. They will evaluate the methodologies used, the results obtained, and any gaps in knowledge. By doing so, the researchers gather relevant information that helps them design their own study, ensuring IT aligns with the current understanding of the disease and the drug’s potential impact.

The literature review also allows the researchers to identify the limitations or challenges faced in previous studies. By taking note of these, they can design their experiments and data collection methods to address those limitations and produce more robust results. This demonstrates the fundamental role literature can play in shaping the research process.

Examples of Literature-Based Research

Various disciplines leverage literature as a foundation for research. Here are a few examples:

1. Social Sciences

In social sciences, literature-based research is often used to conduct critical reviews, explore theoretical frameworks, and identify relevant variables. By analyzing previous studies, researchers can gain insights into social trends, cultural dynamics, and various behavioral patterns.

2. Literature and Humanities

In literary and humanities research, scholars analyze literature works, historical documents, and artistic creations to gain a deeper understanding of cultural movements, intellectual exchanges, and societal developments. By studying these texts and artifacts, researchers can provide critical interpretations and theoretical frameworks to enhance our understanding of the human experience.

3. Education

In education research, literature plays a crucial role in identifying best practices, understanding pedagogy, and evaluating teaching methods. Literature-based research in this field helps educators and policymakers make informed decisions based on the existing body of knowledge.

Literature serves as a foundation for research by offering a deep-rooted and well-established body of knowledge on various subjects. IT enables scholars to position their work within existing frameworks and identify gaps that require further exploration. Literature-based research not only helps build credibility but also strengthens the overall quality of research findings.

Q1: What is a literature review in research?

A1: A literature review is a crucial component of research that involves analyzing and summarizing previous scholarly works related to a specific topic. IT provides an overview of existing knowledge, theories, and methodologies, allowing researchers to position their own work within the broader landscape of the field.

Q2: Why is literature important in research?

A2: Literature serves as the foundation for research by providing a comprehensive understanding of existing knowledge on a particular topic. IT helps researchers identify gaps, develop research questions, and design studies that contribute to the field’s growth.

Q3: How can literature-based research be applied in natural sciences?

A3: In natural sciences, literature-based research is utilized in various ways, including reviewing previous studies, understanding theoretical frameworks, and identifying potential research avenues. IT helps scientists consider existing knowledge and build upon IT to create new hypotheses or develop innovative methods.

Q4: Can literature-based research lead to original contributions?

A4: Absolutely. Literature-based research allows scholars to identify gaps or areas with limited study, enabling them to propose novel research questions or approaches. By building on existing knowledge, researchers can make original contributions to their respective fields.

Q5: How should one approach conducting a literature review?

A5: Conducting a literature review requires a systematic approach. Start by defining your research question and search for relevant academic articles, books, and other sources. Analyze and critically evaluate each source, identifying key themes, theories, and findings. Finally, synthesize the information to present a comprehensive understanding of the topic within the context of your research.

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A Review of the Literature on Case Study Research

This paper presents a review of the literature on case study research and comments on the ongoing debate of the value of case study. A research paradigm and its theoretical framework is described. This review focuses extensively on the positions of

Related Papers

Waleed Alabri

An Examination of Case Studies in Management Research: A Paradigmatic Bridge

Mehedi Masud

The paper maps the value of case study in management research. In particular, it deals with the paradigmatic aspects of case study as a research strategy. In order to analyse the convergence and divergence on different dimensions of the case study research, I focus on three well-known methodology experts, namely Robert Yin, Sharan Merriam and Robert Stake. I argue that case study is a comprehensive research strategy. It has the capacity to embrace paradigm plurality representing both inductive and deductive strategies. Because of its epistemological, ontological and methodological flexibility case study has become one of the established research approaches in management. There is no fixed set of methods for the case study research. This depends on the ontological presuppositions of the researchers. The significance of the ontology becomes apparent depending on the nature of the case and the types of the research questions. As case study research is reflexive, flexible and context-specific, it allows emerging contexts to shape methods. That is why it can act as a bridge across the research paradigms. I then look at the considerable influence that the case study approach has on the management research, i.e., the role for case study in the research process. Because of its overarching role, multi-paradigmatic approach can be adopted under case study research. Case study research is, in practice a varied methodology with paradigmatic pluralism covering an array of research methods and techniques and different levels of analysis.

International Leadership Journal

Michael Neubert

Extension of theory using a multiple-case study design can contribute value to a particular theoretical perspective and further define the boundaries of the original theory. Most organizations today operate in volatile economic and social environments. Qualitative research plays an essential role in the investigation of leadership and management problems, given that they remain complex social enigmas. The multiple case study design is a valuable qualitative research tool in studying the links between the personal, social, behavioral, psychological, organizational, cultural, and environmental factors that guide managerial and leadership development. Multiple-case studies can be used by both novice and experienced qualitative researchers to contribute original qualitative data to extant theory. Multiple-case study research is particularly suitable for responding to "how" and "why" and what Eisenhardt terms as "big picture" research questions that remain unanswered in the extant leadership and management literature.

Dhaulagiri Journal of Sociology and Anthropology

Thakur P R A S A D Bhatta

Case study research though increasingly popular in social sciences for positivist and intrepretivist research, a kind of confusion is prevalent when it is used ignoring its philosophical position. Arguably, the case study research is considered more appropriate for qualitative research because of its foremost strength ˗ the in-depth study of complex issues. This paper, drawing from the literature, discusses the philosophical position of case study research and argues that qualitative case study research is appropriate for theory building. For theory building, this paper follows the inductive approach guided by qualitative research paradigm and argues that it is not appropriate to assess theory building from the perspective of quantitative research. Very similar to other research methods, it is natural that the case study research has certain challenges; however, most of the challenges and misunderstandings overlap causing difficulty to understand the role of case study research. Hence, this paper aims to contribute to the understandings of the challenges and misunderstandings associated with the theory building from case study research. This paper argues that most of the challenges associated with theory building from case study can be addressed employing appropriate research strategies particularly clear understanding of philosophical stance and selection of appropriate case. The misunderstandings, on the other hand, are arisen due to the differences in the researcher's perspectives particularly positivistic thinking of them rather than the shortcomings inherent in the qualitative case study research design.

Florian Kohlbacher

This paper aims at exploring and discus­ sing the possibilities of applying qualitative content analysis as a (text) interpretation method in case study research. First, case study research as a research strategy within qualitative social research is briefly presented. Then, a basic introduction to (qualitative) content analysis as an interpretation method for qualitative interviews and other data material is given.

Assessment of Qualitative

15th NCVER conference

John Guenther

milton malaya

Lesley Bartlett

casestudies journal

Qualitative case-study research has experienced an upsurge in business management fields of inquiry in the recent past. A methodology is selection, justification and sequential arranging of activities, procedures and tasks in a research project. Research methodology can no longer be confined to a set of universally applicable rules, conventions and traditions. A research paradigm is a set of propositions that explains how the world is perceived. There are three basic paradigms: positivist, interpretive and critical. Qualitative " approaches to research " , " strategies of inquiry " and " varieties of methodologies " classified into five " types " or " traditions " namely; biography, phenomenology, grounded theory, ethnography and case study. The major criticism made of qualitative methods is that they are impressionistic and non-verifiable, post-positivists who reject this charge claiming that qualitative data is auditable and therefore dependable. The less structured qualitative methodologies reject many of the positivists " constructions over what constitutes rigour, favouring instead the flexibility, creativity and otherwise inaccessible insights afforded by alternative routes of inquiry that embrace storytelling, recollection, and dialogue. Case study research is not really a " methodology " or a method, rather an approach to research. Case studies can be ethnographic or not and some scholars identified it as a strategy of social inquiry. It is argued that, case studies are more appropriate to investigate causal relationships prevailing both in the business field as well as in wider society in general.

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CC0006 Basics of Report Writing

Structure of a report (case study, literature review or survey).

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The information in the report has to be organised in the best possible way for the reader to understand the issue being investigated, analysis of the findings and recommendations or implications that relate directly to the findings. Given below are the main sections of a standard report. Click on each section heading to learn more about it.

• Tells the reader what the report is about
• Informative, short, catchy

Example - Sea level rise in Singapore : Causes, Impact and Solution

The title page must also include group name, group members and their matriculation numbers.

Content s Page

• Has headings and subheadings that show the reader where the various sections of the report are located
• Written on a separate page
• Includes the page numbers of each section
• Briefly summarises the report, the process of research and final conclusions
• Provides a quick overview of the report and describes the main highlights
• Short, usually not more than 150 words in length
• Mention briefly why you choose this project, what are the implications and what kind of problems it will solve

Usually, the abstract is written last, ie. after writing the other sections and you know the key points to draw out from these sections. Abstracts allow readers who may be interested in the report to decide whether it is relevant to their purposes.

Introduction

• Discusses the background and sets the context
• Introduces the topic, significance of the problem, and the purpose of research
• Gives the scope ie shows what it includes and excludes

In the introduction, write about what motivates your project, what makes it interesting, what questions do you aim to answer by doing your project. The introduction lays the foundation for understanding the research problem and should be written in a way that leads the reader from the general subject area of the topic to the particular topic of research.

Literature Review

• Helps to gain an understanding of the existing research in that topic
• To develop on your own ideas and build your ideas based on the existing knowledge
• Prevents duplication of the research done by others

Search the existing literature for information. Identify the data pertinent to your topic. Review, extract the relevant information for eg how the study was conducted and the findings. Summarise the information. Write what is already known about the topic and what do the sources that you have reviewed say. Identify conflicts in previous studies, open questions, or gaps that may exist. If you are doing

• Case study - look for background information and if any similar case studies have been done before.
• Literature review - find out from literature, what is the background to the questions that you are looking into
• Site visit - use the literature review to read up and prepare good questions before hand.
• Survey - find out if similar surveys have been done before and what did they find?

Keep a record of the source details of any information you want to use in your report so that you can reference them accurately.

Methodology

Methodology is the approach that you take to gather data and arrive at the recommendation(s). Choose a method that is appropriate for the research topic and explain it in detail.

In this section, address the following: a) How the data was collected b) How it was analysed and c) Explain or justify why a particular method was chosen.

Usually, the methodology is written in the past tense and can be in the passive voice. Some examples of the different methods that you can use to gather data are given below. The data collected provides evidence to build your arguments. Collect data, integrate the findings and perspectives from different studies and add your own analysis of its feasibility.

• Explore the literature/news/internet sources to know the topic in depth
• Give a description of how you selected the literature for your project
• Compare the studies, and highlight the findings, gaps or limitations.
• An in-depth, detailed examination of specific cases within a real-world context.
• Enables you to examine the data within a specific context.
• Examine a well defined case to identify the essential factors, process and relationship.
• Write the case description, the context and the process involved.
• Make sense of the evidence in the case(s) to answer the research question
• Gather data from a predefined group of respondents by asking relevant questions
• Can be conducted in person or online
• Why you chose this method (questionnaires, focus group, experimental procedure, etc)
• How you carried out the survey. Include techniques and any equipment you used
• If there were participants in your research, who were they? How did you select them and how may were there?
• How the survey questions address the different aspects of the research question
• Analyse the technology / policy approaches by visiting the required sites
• Make a detailed report on its features and your understanding of it

Results and Analysis

• Present the results of the study. You may consider visualising the results in tables and graphs, graphics etc.
• Analyse the results to obtain answer to the research question.
• Provide an analysis of the technical and financial feasibility, social acceptability etc

Discussion, Limitation(s) and Implication(s)

• Discuss your interpretations of the analysis and the significance of your findings
• Explain any new understanding or insights that emerged as a result of your research
• Consider the different perspectives (social, economic and environmental)in the discussion
• Explain the limitation(s)
• Explain how could what you found be used to make a difference for sustainability

Conclusion and Recommendations

• Summarise the significance and outcome of the study highlighting the key points.
• Come up with alternatives and propose specific actions based on the alternatives
• Describe the result or improvement it would achieve
• Explain how it will be implemented

Recommendations should have an innovative approach and should be feasible. It should make a significant difference in solving the issue under discussion.

• List the sources you have referred to in your writing
• Use the recommended citation style consistently in your report

Appendix (if necessary/any)

Include any material relating to the report and research that does not fit in the body of the report, in the appendix. For example, you may include survey questionnaire and results in the appendix.

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A literature review surveys prior research published in books, scholarly articles, and any other sources relevant to a particular issue, area of research, or theory, and by so doing, provides a description, summary, and critical evaluation of these works in relation to the research problem being investigated. Literature reviews are designed to provide an overview of sources you have used in researching a particular topic and to demonstrate to your readers how your research fits within existing scholarship about the topic.

Fink, Arlene. Conducting Research Literature Reviews: From the Internet to Paper . Fourth edition. Thousand Oaks, CA: SAGE, 2014.

Importance of a Good Literature Review

A literature review may consist of simply a summary of key sources, but in the social sciences, a literature review usually has an organizational pattern and combines both summary and synthesis, often within specific conceptual categories . A summary is a recap of the important information of the source, but a synthesis is a re-organization, or a reshuffling, of that information in a way that informs how you are planning to investigate a research problem. The analytical features of a literature review might:

• Give a new interpretation of old material or combine new with old interpretations,
• Trace the intellectual progression of the field, including major debates,
• Depending on the situation, evaluate the sources and advise the reader on the most pertinent or relevant research, or
• Usually in the conclusion of a literature review, identify where gaps exist in how a problem has been researched to date.

Given this, the purpose of a literature review is to:

• Place each work in the context of its contribution to understanding the research problem being studied.
• Describe the relationship of each work to the others under consideration.
• Identify new ways to interpret prior research.
• Reveal any gaps that exist in the literature.
• Resolve conflicts amongst seemingly contradictory previous studies.
• Identify areas of prior scholarship to prevent duplication of effort.
• Point the way in fulfilling a need for additional research.
• Locate your own research within the context of existing literature [very important].

Fink, Arlene. Conducting Research Literature Reviews: From the Internet to Paper. 2nd ed. Thousand Oaks, CA: Sage, 2005; Hart, Chris. Doing a Literature Review: Releasing the Social Science Research Imagination . Thousand Oaks, CA: Sage Publications, 1998; Jesson, Jill. Doing Your Literature Review: Traditional and Systematic Techniques . Los Angeles, CA: SAGE, 2011; Knopf, Jeffrey W. "Doing a Literature Review." PS: Political Science and Politics 39 (January 2006): 127-132; Ridley, Diana. The Literature Review: A Step-by-Step Guide for Students . 2nd ed. Los Angeles, CA: SAGE, 2012.

Types of Literature Reviews

It is important to think of knowledge in a given field as consisting of three layers. First, there are the primary studies that researchers conduct and publish. Second are the reviews of those studies that summarize and offer new interpretations built from and often extending beyond the primary studies. Third, there are the perceptions, conclusions, opinion, and interpretations that are shared informally among scholars that become part of the body of epistemological traditions within the field.

In composing a literature review, it is important to note that it is often this third layer of knowledge that is cited as "true" even though it often has only a loose relationship to the primary studies and secondary literature reviews. Given this, while literature reviews are designed to provide an overview and synthesis of pertinent sources you have explored, there are a number of approaches you could adopt depending upon the type of analysis underpinning your study.

Argumentative Review This form examines literature selectively in order to support or refute an argument, deeply embedded assumption, or philosophical problem already established in the literature. The purpose is to develop a body of literature that establishes a contrarian viewpoint. Given the value-laden nature of some social science research [e.g., educational reform; immigration control], argumentative approaches to analyzing the literature can be a legitimate and important form of discourse. However, note that they can also introduce problems of bias when they are used to make summary claims of the sort found in systematic reviews [see below].

Integrative Review Considered a form of research that reviews, critiques, and synthesizes representative literature on a topic in an integrated way such that new frameworks and perspectives on the topic are generated. The body of literature includes all studies that address related or identical hypotheses or research problems. A well-done integrative review meets the same standards as primary research in regard to clarity, rigor, and replication. This is the most common form of review in the social sciences.

Historical Review Few things rest in isolation from historical precedent. Historical literature reviews focus on examining research throughout a period of time, often starting with the first time an issue, concept, theory, phenomena emerged in the literature, then tracing its evolution within the scholarship of a discipline. The purpose is to place research in a historical context to show familiarity with state-of-the-art developments and to identify the likely directions for future research.

Methodological Review A review does not always focus on what someone said [findings], but how they came about saying what they say [method of analysis]. Reviewing methods of analysis provides a framework of understanding at different levels [i.e. those of theory, substantive fields, research approaches, and data collection and analysis techniques], how researchers draw upon a wide variety of knowledge ranging from the conceptual level to practical documents for use in fieldwork in the areas of ontological and epistemological consideration, quantitative and qualitative integration, sampling, interviewing, data collection, and data analysis. This approach helps highlight ethical issues which you should be aware of and consider as you go through your own study.

Systematic Review This form consists of an overview of existing evidence pertinent to a clearly formulated research question, which uses pre-specified and standardized methods to identify and critically appraise relevant research, and to collect, report, and analyze data from the studies that are included in the review. The goal is to deliberately document, critically evaluate, and summarize scientifically all of the research about a clearly defined research problem . Typically it focuses on a very specific empirical question, often posed in a cause-and-effect form, such as "To what extent does A contribute to B?" This type of literature review is primarily applied to examining prior research studies in clinical medicine and allied health fields, but it is increasingly being used in the social sciences.

Theoretical Review The purpose of this form is to examine the corpus of theory that has accumulated in regard to an issue, concept, theory, phenomena. The theoretical literature review helps to establish what theories already exist, the relationships between them, to what degree the existing theories have been investigated, and to develop new hypotheses to be tested. Often this form is used to help establish a lack of appropriate theories or reveal that current theories are inadequate for explaining new or emerging research problems. The unit of analysis can focus on a theoretical concept or a whole theory or framework.

NOTE : Most often the literature review will incorporate some combination of types. For example, a review that examines literature supporting or refuting an argument, assumption, or philosophical problem related to the research problem will also need to include writing supported by sources that establish the history of these arguments in the literature.

Baumeister, Roy F. and Mark R. Leary. "Writing Narrative Literature Reviews."  Review of General Psychology 1 (September 1997): 311-320; Mark R. Fink, Arlene. Conducting Research Literature Reviews: From the Internet to Paper . 2nd ed. Thousand Oaks, CA: Sage, 2005; Hart, Chris. Doing a Literature Review: Releasing the Social Science Research Imagination . Thousand Oaks, CA: Sage Publications, 1998; Kennedy, Mary M. "Defining a Literature." Educational Researcher 36 (April 2007): 139-147; Petticrew, Mark and Helen Roberts. Systematic Reviews in the Social Sciences: A Practical Guide . Malden, MA: Blackwell Publishers, 2006; Torracro, Richard. "Writing Integrative Literature Reviews: Guidelines and Examples." Human Resource Development Review 4 (September 2005): 356-367; Rocco, Tonette S. and Maria S. Plakhotnik. "Literature Reviews, Conceptual Frameworks, and Theoretical Frameworks: Terms, Functions, and Distinctions." Human Ressource Development Review 8 (March 2008): 120-130; Sutton, Anthea. Systematic Approaches to a Successful Literature Review . Los Angeles, CA: Sage Publications, 2016.

Structure and Writing Style

I.  Thinking About Your Literature Review

The structure of a literature review should include the following in support of understanding the research problem :

• An overview of the subject, issue, or theory under consideration, along with the objectives of the literature review,
• Division of works under review into themes or categories [e.g. works that support a particular position, those against, and those offering alternative approaches entirely],
• An explanation of how each work is similar to and how it varies from the others,
• Conclusions as to which pieces are best considered in their argument, are most convincing of their opinions, and make the greatest contribution to the understanding and development of their area of research.

The critical evaluation of each work should consider :

• Provenance -- what are the author's credentials? Are the author's arguments supported by evidence [e.g. primary historical material, case studies, narratives, statistics, recent scientific findings]?
• Methodology -- were the techniques used to identify, gather, and analyze the data appropriate to addressing the research problem? Was the sample size appropriate? Were the results effectively interpreted and reported?
• Objectivity -- is the author's perspective even-handed or prejudicial? Is contrary data considered or is certain pertinent information ignored to prove the author's point?
• Persuasiveness -- which of the author's theses are most convincing or least convincing?
• Validity -- are the author's arguments and conclusions convincing? Does the work ultimately contribute in any significant way to an understanding of the subject?

II.  Development of the Literature Review

Four Basic Stages of Writing 1.  Problem formulation -- which topic or field is being examined and what are its component issues? 2.  Literature search -- finding materials relevant to the subject being explored. 3.  Data evaluation -- determining which literature makes a significant contribution to the understanding of the topic. 4.  Analysis and interpretation -- discussing the findings and conclusions of pertinent literature.

Consider the following issues before writing the literature review: Clarify If your assignment is not specific about what form your literature review should take, seek clarification from your professor by asking these questions: 1.  Roughly how many sources would be appropriate to include? 2.  What types of sources should I review (books, journal articles, websites; scholarly versus popular sources)? 3.  Should I summarize, synthesize, or critique sources by discussing a common theme or issue? 4.  Should I evaluate the sources in any way beyond evaluating how they relate to understanding the research problem? 5.  Should I provide subheadings and other background information, such as definitions and/or a history? Find Models Use the exercise of reviewing the literature to examine how authors in your discipline or area of interest have composed their literature review sections. Read them to get a sense of the types of themes you might want to look for in your own research or to identify ways to organize your final review. The bibliography or reference section of sources you've already read, such as required readings in the course syllabus, are also excellent entry points into your own research. Narrow the Topic The narrower your topic, the easier it will be to limit the number of sources you need to read in order to obtain a good survey of relevant resources. Your professor will probably not expect you to read everything that's available about the topic, but you'll make the act of reviewing easier if you first limit scope of the research problem. A good strategy is to begin by searching the USC Libraries Catalog for recent books about the topic and review the table of contents for chapters that focuses on specific issues. You can also review the indexes of books to find references to specific issues that can serve as the focus of your research. For example, a book surveying the history of the Israeli-Palestinian conflict may include a chapter on the role Egypt has played in mediating the conflict, or look in the index for the pages where Egypt is mentioned in the text. Consider Whether Your Sources are Current Some disciplines require that you use information that is as current as possible. This is particularly true in disciplines in medicine and the sciences where research conducted becomes obsolete very quickly as new discoveries are made. However, when writing a review in the social sciences, a survey of the history of the literature may be required. In other words, a complete understanding the research problem requires you to deliberately examine how knowledge and perspectives have changed over time. Sort through other current bibliographies or literature reviews in the field to get a sense of what your discipline expects. You can also use this method to explore what is considered by scholars to be a "hot topic" and what is not.

III.  Ways to Organize Your Literature Review

Chronology of Events If your review follows the chronological method, you could write about the materials according to when they were published. This approach should only be followed if a clear path of research building on previous research can be identified and that these trends follow a clear chronological order of development. For example, a literature review that focuses on continuing research about the emergence of German economic power after the fall of the Soviet Union. By Publication Order your sources by publication chronology, then, only if the order demonstrates a more important trend. For instance, you could order a review of literature on environmental studies of brown fields if the progression revealed, for example, a change in the soil collection practices of the researchers who wrote and/or conducted the studies. Thematic [“conceptual categories”] A thematic literature review is the most common approach to summarizing prior research in the social and behavioral sciences. Thematic reviews are organized around a topic or issue, rather than the progression of time, although the progression of time may still be incorporated into a thematic review. For example, a review of the Internet’s impact on American presidential politics could focus on the development of online political satire. While the study focuses on one topic, the Internet’s impact on American presidential politics, it would still be organized chronologically reflecting technological developments in media. The difference in this example between a "chronological" and a "thematic" approach is what is emphasized the most: themes related to the role of the Internet in presidential politics. Note that more authentic thematic reviews tend to break away from chronological order. A review organized in this manner would shift between time periods within each section according to the point being made. Methodological A methodological approach focuses on the methods utilized by the researcher. For the Internet in American presidential politics project, one methodological approach would be to look at cultural differences between the portrayal of American presidents on American, British, and French websites. Or the review might focus on the fundraising impact of the Internet on a particular political party. A methodological scope will influence either the types of documents in the review or the way in which these documents are discussed.

Other Sections of Your Literature Review Once you've decided on the organizational method for your literature review, the sections you need to include in the paper should be easy to figure out because they arise from your organizational strategy. In other words, a chronological review would have subsections for each vital time period; a thematic review would have subtopics based upon factors that relate to the theme or issue. However, sometimes you may need to add additional sections that are necessary for your study, but do not fit in the organizational strategy of the body. What other sections you include in the body is up to you. However, only include what is necessary for the reader to locate your study within the larger scholarship about the research problem.

Here are examples of other sections, usually in the form of a single paragraph, you may need to include depending on the type of review you write:

• Current Situation : Information necessary to understand the current topic or focus of the literature review.
• Sources Used : Describes the methods and resources [e.g., databases] you used to identify the literature you reviewed.
• History : The chronological progression of the field, the research literature, or an idea that is necessary to understand the literature review, if the body of the literature review is not already a chronology.
• Selection Methods : Criteria you used to select (and perhaps exclude) sources in your literature review. For instance, you might explain that your review includes only peer-reviewed [i.e., scholarly] sources.
• Standards : Description of the way in which you present your information.
• Questions for Further Research : What questions about the field has the review sparked? How will you further your research as a result of the review?

IV.  Writing Your Literature Review

Once you've settled on how to organize your literature review, you're ready to write each section. When writing your review, keep in mind these issues.

Use Evidence A literature review section is, in this sense, just like any other academic research paper. Your interpretation of the available sources must be backed up with evidence [citations] that demonstrates that what you are saying is valid. Be Selective Select only the most important points in each source to highlight in the review. The type of information you choose to mention should relate directly to the research problem, whether it is thematic, methodological, or chronological. Related items that provide additional information, but that are not key to understanding the research problem, can be included in a list of further readings . Use Quotes Sparingly Some short quotes are appropriate if you want to emphasize a point, or if what an author stated cannot be easily paraphrased. Sometimes you may need to quote certain terminology that was coined by the author, is not common knowledge, or taken directly from the study. Do not use extensive quotes as a substitute for using your own words in reviewing the literature. Summarize and Synthesize Remember to summarize and synthesize your sources within each thematic paragraph as well as throughout the review. Recapitulate important features of a research study, but then synthesize it by rephrasing the study's significance and relating it to your own work and the work of others. Keep Your Own Voice While the literature review presents others' ideas, your voice [the writer's] should remain front and center. For example, weave references to other sources into what you are writing but maintain your own voice by starting and ending the paragraph with your own ideas and wording. Use Caution When Paraphrasing When paraphrasing a source that is not your own, be sure to represent the author's information or opinions accurately and in your own words. Even when paraphrasing an author’s work, you still must provide a citation to that work.

V.  Common Mistakes to Avoid

These are the most common mistakes made in reviewing social science research literature.

• Sources in your literature review do not clearly relate to the research problem;
• You do not take sufficient time to define and identify the most relevant sources to use in the literature review related to the research problem;
• Relies exclusively on secondary analytical sources rather than including relevant primary research studies or data;
• Uncritically accepts another researcher's findings and interpretations as valid, rather than examining critically all aspects of the research design and analysis;
• Does not describe the search procedures that were used in identifying the literature to review;
• Reports isolated statistical results rather than synthesizing them in chi-squared or meta-analytic methods; and,
• Only includes research that validates assumptions and does not consider contrary findings and alternative interpretations found in the literature.

Cook, Kathleen E. and Elise Murowchick. “Do Literature Review Skills Transfer from One Course to Another?” Psychology Learning and Teaching 13 (March 2014): 3-11; Fink, Arlene. Conducting Research Literature Reviews: From the Internet to Paper . 2nd ed. Thousand Oaks, CA: Sage, 2005; Hart, Chris. Doing a Literature Review: Releasing the Social Science Research Imagination . Thousand Oaks, CA: Sage Publications, 1998; Jesson, Jill. Doing Your Literature Review: Traditional and Systematic Techniques . London: SAGE, 2011; Literature Review Handout. Online Writing Center. Liberty University; Literature Reviews. The Writing Center. University of North Carolina; Onwuegbuzie, Anthony J. and Rebecca Frels. Seven Steps to a Comprehensive Literature Review: A Multimodal and Cultural Approach . Los Angeles, CA: SAGE, 2016; Ridley, Diana. The Literature Review: A Step-by-Step Guide for Students . 2nd ed. Los Angeles, CA: SAGE, 2012; Randolph, Justus J. “A Guide to Writing the Dissertation Literature Review." Practical Assessment, Research, and Evaluation. vol. 14, June 2009; Sutton, Anthea. Systematic Approaches to a Successful Literature Review . Los Angeles, CA: Sage Publications, 2016; Taylor, Dena. The Literature Review: A Few Tips On Conducting It. University College Writing Centre. University of Toronto; Writing a Literature Review. Academic Skills Centre. University of Canberra.

Writing Tip

Break Out of Your Disciplinary Box!

Thinking interdisciplinarily about a research problem can be a rewarding exercise in applying new ideas, theories, or concepts to an old problem. For example, what might cultural anthropologists say about the continuing conflict in the Middle East? In what ways might geographers view the need for better distribution of social service agencies in large cities than how social workers might study the issue? You don’t want to substitute a thorough review of core research literature in your discipline for studies conducted in other fields of study. However, particularly in the social sciences, thinking about research problems from multiple vectors is a key strategy for finding new solutions to a problem or gaining a new perspective. Consult with a librarian about identifying research databases in other disciplines; almost every field of study has at least one comprehensive database devoted to indexing its research literature.

Frodeman, Robert. The Oxford Handbook of Interdisciplinarity . New York: Oxford University Press, 2010.

Another Writing Tip

Don't Just Review for Content!

While conducting a review of the literature, maximize the time you devote to writing this part of your paper by thinking broadly about what you should be looking for and evaluating. Review not just what scholars are saying, but how are they saying it. Some questions to ask:

• How are they organizing their ideas?
• What methods have they used to study the problem?
• What theories have been used to explain, predict, or understand their research problem?
• What sources have they cited to support their conclusions?
• How have they used non-textual elements [e.g., charts, graphs, figures, etc.] to illustrate key points?

When you begin to write your literature review section, you'll be glad you dug deeper into how the research was designed and constructed because it establishes a means for developing more substantial analysis and interpretation of the research problem.

Hart, Chris. Doing a Literature Review: Releasing the Social Science Research Imagination . Thousand Oaks, CA: Sage Publications, 1 998.

Yet Another Writing Tip

When Do I Know I Can Stop Looking and Move On?

Here are several strategies you can utilize to assess whether you've thoroughly reviewed the literature:

• Look for repeating patterns in the research findings . If the same thing is being said, just by different people, then this likely demonstrates that the research problem has hit a conceptual dead end. At this point consider: Does your study extend current research?  Does it forge a new path? Or, does is merely add more of the same thing being said?
• Look at sources the authors cite to in their work . If you begin to see the same researchers cited again and again, then this is often an indication that no new ideas have been generated to address the research problem.
• Search Google Scholar to identify who has subsequently cited leading scholars already identified in your literature review [see next sub-tab]. This is called citation tracking and there are a number of sources that can help you identify who has cited whom, particularly scholars from outside of your discipline. Here again, if the same authors are being cited again and again, this may indicate no new literature has been written on the topic.

Onwuegbuzie, Anthony J. and Rebecca Frels. Seven Steps to a Comprehensive Literature Review: A Multimodal and Cultural Approach . Los Angeles, CA: Sage, 2016; Sutton, Anthea. Systematic Approaches to a Successful Literature Review . Los Angeles, CA: Sage Publications, 2016.

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1 What Is Literature and Why Do We Study It?

In this book created for my English 211 Literary Analysis introductory course for English literature and creative writing majors at the College of Western Idaho, I’ll introduce several different critical approaches that literary scholars may use to answer these questions.  The critical method we apply to a text can provide us with different perspectives as we learn to interpret a text and appreciate its meaning and beauty.

The existence of literature, however we define it, implies that we study literature. While people have been “studying” literature as long as literature has existed, the formal study of literature as we know it in college English literature courses began in the 1940s with the advent of New Criticism. The New Critics were formalists with a vested interest in defining literature–they were, after all, both creating and teaching about literary works. For them, literary criticism was, in fact, as John Crowe Ransom wrote in his 1942 essay “ Criticism, Inc., ” nothing less than “the business of literature.”

Responding to the concern that the study of literature at the university level was often more concerned with the history and life of the author than with the text itself, Ransom responded, “the students of the future must be permitted to study literature, and not merely about literature. But I think this is what the good students have always wanted to do. The wonder is that they have allowed themselves so long to be denied.”

We’ll learn more about New Criticism in Section Three. For now, let’s return to the two questions I posed earlier.

What is literature?

First, what is literature ? I know your high school teacher told you never to look up things on Wikipedia, but for the purposes of literary studies, Wikipedia can actually be an effective resource. You’ll notice that I link to Wikipedia articles occasionally in this book. Here’s how Wikipedia defines literature :

“ Literature  is any collection of  written  work, but it is also used more narrowly for writings specifically considered to be an  art  form, especially  prose   fiction ,  drama , and  poetry . [1]  In recent centuries, the definition has expanded to include  oral literature , much of which has been transcribed. [2] Literature is a method of recording, preserving, and transmitting knowledge and entertainment, and can also have a social, psychological, spiritual, or political role.”

This definition is well-suited for our purposes here because throughout this course, we will be considering several types of literary texts in a variety of contexts.

I’m a Classicist—a student of Greece and Rome and everything they touched—so I am always interested in words with Latin roots. The Latin root of our modern word literature  is  litera , or “letter.” Literature, then, is inextricably intertwined with the act of writing. But what kind of writing?

Who decides which texts are “literature”?

The second question is at least as important as the first one. If we agree that literature is somehow special and different from ordinary writing, then who decides which writings count as literature? Are English professors the only people who get to decide? What qualifications and training does someone need to determine whether or not a text is literature? What role do you as the reader play in this decision about a text?

Let’s consider a few examples of things that we would all probably classify as literature. I think we can all (probably) agree that the works of William Shakespeare are literature. We can look at Toni Morrison’s outstanding ouvre of work and conclude, along with the Nobel Prize Committee, that books such as Beloved   and  Song of Solomon   are literature. And if you’re taking a creative writing course and have been assigned the short stories of Raymond Carver or the poems of Joy Harjo , you’re probably convinced that these texts are literature too.

In each of these three cases, a different “deciding” mechanism is at play. First, with Shakespeare, there’s history and tradition. These plays that were written 500 years ago are still performed around the world and taught in high school and college English classes today. It seems we have consensus about the tragedies, histories, comedies, and sonnets of the Bard of Avon (or whoever wrote the plays).

In the second case, if you haven’t heard of Toni Morrison (and I am very sorry if you haven’t), you probably have heard of the Nobel Prize. This is one of the most prestigious awards given in literature, and since she’s a winner, we can safely assume that Toni Morrison’s works are literature.

Finally, your creative writing professor is an expert in their field. You know they have an MFA (and worked hard for it), so when they share their favorite short stories or poems with you, you trust that they are sharing works considered to be literature, even if you haven’t heard of Raymond Carver or Joy Harjo before taking their class.

(Aside: What about fanfiction? Is fanfiction literature?)

We may have to save the debate about fan fiction for another day, though I introduced it because there’s some fascinating and even literary award-winning fan fiction out there.

Returning to our question, what role do we as readers play in deciding whether something is literature? Like John Crowe Ransom quoted above, I think that the definition of literature should depend on more than the opinions of literary critics and literature professors.

I also want to note that contrary to some opinions, plenty of so-called genre fiction can also be classified as literature. The Nobel Prize winning author Kazuo Ishiguro has written both science fiction and historical fiction. Iain Banks , the British author of the critically acclaimed novel The Wasp Factory , published popular science fiction novels under the name Iain M. Banks. In other words, genre alone can’t tell us whether something is literature or not.

In this book, I want to give you the tools to decide for yourself. We’ll do this by exploring several different critical approaches that we can take to determine how a text functions and whether it is literature. These lenses can reveal different truths about the text, about our culture, and about ourselves as readers and scholars.

“Turf Wars”: Literary criticism vs. authors

It’s important to keep in mind that literature and literary theory have existed in conversation with each other since Aristotle used Sophocles’s play Oedipus Rex to define tragedy. We’ll look at how critical theory and literature complement and disagree with each other throughout this book. For most of literary history, the conversation was largely a friendly one.

But in the twenty-first century, there’s a rising tension between literature and criticism. In his 2016 book Literature Against Criticism: University English and Contemporary Fiction in Conflict, literary scholar Martin Paul Eve argues that twenty-first century authors have developed

a series of novelistic techniques that, whether deliberate or not on the part of the author, function to outmanoeuvre, contain, and determine academic reading practices. This desire to discipline university English through the manipulation and restriction of possible hermeneutic paths is, I contend, a result firstly of the fact that the metafictional paradigm of the high-postmodern era has pitched critical and creative discourses into a type of productive competition with one another. Such tensions and overlaps (or ‘turf wars’) have only increased in light of the ongoing breakdown of coherent theoretical definitions of ‘literature’ as distinct from ‘criticism’ (15).

One of Eve’s points is that by narrowly and rigidly defining the boundaries of literature, university English professors have inadvertently created a situation where the market increasingly defines what “literature” is, despite the protestations of the academy. In other words, the gatekeeper role that literary criticism once played is no longer as important to authors. For example, (almost) no one would call 50 Shades of Grey literature—but the salacious E.L James novel was the bestselling book of the decade from 2010-2019, with more than 35 million copies sold worldwide.

If anyone with a blog can get a six-figure publishing deal , does it still matter that students know how to recognize and analyze literature? I think so, for a few reasons.

• First, the practice of reading critically helps you to become a better reader and writer, which will help you to succeed not only in college English courses but throughout your academic and professional career.
• Second, analysis is a highly sought after and transferable skill. By learning to analyze literature, you’ll practice the same skills you would use to analyze anything important. “Data analyst” is one of the most sought after job positions in the New Economy—and if you can analyze Shakespeare, you can analyze data. Indeed.com’s list of top 10 transferable skills includes analytical skills , which they define as “the traits and abilities that allow you to observe, research and interpret a subject in order to develop complex ideas and solutions.”
• Finally, and for me personally, most importantly, reading and understanding literature makes life make sense. As we read literature, we expand our sense of what is possible for ourselves and for humanity. In the challenges we collectively face today, understanding the world and our place in it will be important for imagining new futures.

A note about using generative artificial intelligence

As I was working on creating this textbook, ChatGPT exploded into academic consciousness. Excited about the possibilities of this new tool, I immediately began incorporating it into my classroom teaching. In this book, I have used ChatGPT to help me with outlining content in chapters. I also used ChatGPT to create sample essays for each critical lens we will study in the course. These essays are dry and rather soulless, but they do a good job of modeling how to apply a specific theory to a literary text. I chose John Donne’s poem “The Canonization” as the text for these essays so that you can see how the different theories illuminate different aspects of the text.

I encourage students in my courses to use ChatGPT in the following ways:

• To generate ideas about an approach to a text.
• To better understand basic concepts.
• To assist with outlining an essay.
• To check grammar, punctuation, spelling, paragraphing, and other grammar/syntax issues.

If you choose to use Chat GPT, please include a brief acknowledgment statement as an appendix to your paper after your Works Cited page explaining how you have used the tool in your work. Here is an example of how to do this from Monash University’s “ Acknowledging the Use of Generative Artificial Intelligence .”

I acknowledge the use of [insert AI system(s) and link] to [specific use of generative artificial intelligence]. The prompts used include [list of prompts]. The output from these prompts was used to [explain use].

Here is more information about how to cite the use of generative AI like ChatGPT in your work. The information below was adapted from “Acknowledging and Citing Generative AI in Academic Work” by Liza Long (CC BY 4.0).

The Modern Language Association (MLA) uses a template of core elements to create citations for a Works Cited page. MLA  asks students to apply this approach when citing any type of generative AI in their work. They provide the following guidelines:

Cite a generative AI tool whenever you paraphrase, quote, or incorporate into your own work any content (whether text, image, data, or other) that was created by it. Acknowledge all functional uses of the tool (like editing your prose or translating words) in a note, your text, or another suitable location. Take care to vet the secondary sources it cites. (MLA)

Here are some examples of how to use and cite generative AI with MLA style:

Example One: Paraphrasing Text

Let’s say that I am trying to generate ideas for a paper on Charlotte Perkins Gilman’s short story “The Yellow Wallpaper.” I ask ChatGPT to provide me with a summary and identify the story’s main themes. Here’s a  link to the chat . I decide that I will explore the problem of identity and self-expression in my paper.

My Paraphrase of ChatGPT with In-Text Citation

The problem of identity and self expression, especially for nineteenth-century women, is a major theme in “The Yellow Wallpaper” by Charlotte Perkins Gilman (“Summarize the short story”).

Works Cited Entry

“Summarize the short story “The Yellow Wallpaper” by Charlotte Perkins Gilman. Include a breakdown of the main themes” prompt.  ChatGPT.  24 May Version, OpenAI, 20 Jul. 2023,  https://chat.openai.com/share/d1526b95-920c-48fc-a9be-83cd7dfa4be5 

Example Two: Quoting Text

In the same chat, I continue to ask ChatGPT about the theme of identity and self expression. Here’s an example of how I could quote the response in the body of my paper:

When I asked  ChatGPT  to describe the theme of identity and self expression, it noted that the eponymous yellow wallpaper acts as a symbol of the narrator’s self-repression. However, when prompted to share the scholarly sources that formed the basis of this observation,  ChatGPT  responded, “As an AI language model, I don’t have access to my training data, but I was trained on a mixture of licensed data, data created by human trainers, and publicly available data. OpenAI, the organization behind my development, has not publicly disclosed the specifics of the individual datasets used, including whether scholarly sources were specifically used” (“Summarize the short story”).

It’s worth noting here that ChatGPT can “ hallucinate ” fake sources. As a Microsoft training manual notes, these chatbots are “built to be persuasive, not truthful” (Weiss &Metz, 2023). The May 24, 2023 version will no longer respond to direct requests for references; however, I was able to get around this restriction fairly easily by asking for “resources” instead.

When I ask for resources to learn more about “The Yellow Wallpaper,” here is one source it recommends:

“Charlotte Perkins Gilman’s The Yellow Wallpaper: A Symptomatic Reading” by Elaine R. Hedges: This scholarly article delves into the psychological and feminist themes of the story, analyzing the narrator’s experience and the implications of the yellow wallpaper on her mental state. It’s available in the journal “Studies in Short Fiction.” (“Summarize the short story”).

Using Google Scholar, I look up this source to see if it’s real. Unsurprisingly, this source is not a real one, but it does lead me to another (real) source: Kasmer, Lisa. “Charlotte Perkins Gilman’s’ The Yellow Wallpaper’: A Symptomatic Reading.”  Literature and Psychology  36.3 (1990): 1.

Note: ALWAYS check any sources that ChatGPT or other generative AI tools recommend.

For more information about integrating and citing generative artificial intelligence tools such as ChatGPT, please see this section of  Write What Matters.

I acknowledge that ChatGPT does not respect the individual rights of authors and artists and ignores concerns over copyright and intellectual property in its training; additionally, I acknowledge that the system was trained in part through the exploitation of precarious workers in the global south. In this work I specifically used ChatGPT to assist with outlining chapters, providing background information about critical lenses, and creating “model” essays for the critical lenses we will learn about together. I have included links to my chats in an appendix to this book.

Critical theories: A targeted approach to writing about literature

Ultimately, there’s not one “right” way to read a text. In this book. we will explore a variety of critical theories that scholars use to analyze literature. The book is organized around different targets that are associated with the approach introduced in each chapter. In the introduction, for example, our target is literature. In future chapters you’ll explore these targeted analysis techniques:

• Author: Biographical Criticism
• Text: New Criticism
• Reader: Reader Response Criticism
• Gap: Deconstruction (Post-Structuralism)
• Context: New Historicism and Cultural Studies
• Power: Marxist and Postcolonial Criticism
• Mind: Psychological Criticism
• Gender: Feminist, Post Feminist, and Queer Theory
• Nature: Ecocriticism

Each chapter will feature the target image with the central approach in the center. You’ll read a brief introduction about the theory, explore some primary texts (both critical and literary), watch a video, and apply the theory to a primary text. Each one of these theories could be the subject of its own entire course, so keep in mind that our goal in this book is to introduce these theories and give you a basic familiarity with these tools for literary analysis. For more information and practice, I recommend Steven Lynn’s excellent Texts and Contexts: Writing about Literature with Critical Theory , which provides a similar introductory framework.

I am so excited to share these tools with you and see you grow as a literary scholar. As we explore each of these critical worlds, you’ll likely find that some critical theories feel more natural or logical to you than others. I find myself much more comfortable with deconstruction than with psychological criticism, for example. Pay attention to how these theories work for you because this will help you to expand your approaches to texts and prepare you for more advanced courses in literature.

P.S. If you want to know what my favorite book is, I usually tell people it’s Herman Melville’s Moby Dick . And I do love that book! But I really have no idea what my “favorite” book of all time is, let alone what my favorite book was last year. Every new book that I read is a window into another world and a template for me to make sense out of my own experience and better empathize with others. That’s why I love literature. I hope you’ll love this experience too.

writings in prose or verse, especially :  writings having excellence of form or expression and expressing ideas of permanent or universal interest (Merriam Webster)

Critical Worlds Copyright © 2024 by Liza Long is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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• J Orthop Case Rep
• v.6(3); Jul-Aug 2016

How much Literature Review is enough for a Case Report?

Ashok shyam.

1 Indian Orthopaedic Research Group, Thane, India

Literature review is an essential part of any scientific document. It’s the foundation on which the premise of scientific research is built. Every scientific study has to be seen in context of the existing knowledge and literature. However literature is growing at exponential rate today and especially with so many online journals today it’s really difficult to review all literature. This poses unique challenge to authors who wish to submit a case report for Journal of Orthopaedic Case Reports.

First issue is how much important is literature review for a case report. From early days of case reports, literature review is been the most important cornerstone of a case report. Especially since earlier only rare cases were considered as case reports [ 1 ]. So to establish the rarity of the case it was important to thoroughly review the literature. For us at Journal of Orthopaedic Case Report, literature review is one of the most significant part of the case report. Most of the times it is the section which decides on acceptance or rejection of borderline cases. For cases that are rare we recommend our authors to do a thorough review of literature and also prepare a table of literature review which should be added to the manuscript. For cases where is the focus is on a specific clinical learning point, the literature review needs to be more exhaustive. When a clinical point has to be made, the literature review should cover all the alternative plans that are already described in literature or at least similar cases that have used a different plan. Many cases that are published in Journal of Orthopaedic Case Reports are more on clinical strategies that are improvised and applied to clinical cases. In these scenario we wish our authors to provide rationale for their choices with back up from literature. Also a thorough review of all exiting strategies should be added to the review. The intention is to make the reader aware of all existing management options and then understand why particular option was chosen in the particular patient. This will also help effective communication between the authors and reviewers and ultimately the readers.

The second issue is how much literature to review. With so much literature available at times literature review may miss important article which is relevant to the case. At times it happens that too much literature is added to the article making it bulky and in need for repeated editing. To resolve these issues we would recommend authors to do a thorough PubMed and google Scholar review which will include most important of the articles. If the number of articles relevant to your search are exceeding thirty you may apply filters like selecting articles published in last 5 years or selecting articles only from PubMed. Selecting article only on PubMed will help get the most relevant articles in your review but an additional scrutiny of google result will help you not miss out on important articles. Google will most of the times provide a very comprehensive list of articles and it may need some effort on part of authors to find the relevant articles. But combining both search strategies will definitely make the review more complete and relevant. The number of references should be limited to maximum of 30 for journal of orthopaedic case reports. This will again require authors to review select the most relevant articles from the literature search. Try and include the most recent articles and also from the most relevant authors and medical centres. In case a particular authors has written multiple articles on similar topic, one of his most relevant can be included while others can be left. Articles that are most close to your clinical scenario should be preferred over other articles. Also articles that have chosen strategies similar to yours should be preferred. If the number of articles is still much more, try to limit the references in terms of geography and include articles that are relevant in your country or geographical location to make is more comparable. Also patient profiles can be matched in terms of age and gender to provide for a better comparison between your case and the case from literature. As far as possible provide a literature review table with list of articles, authors names, number of patients, interventions, results and complications to provide a complete perspective to reader. Review of complications needs a special mention and it should be a part of every surgical case that is reported.

In the end try and weave a continuous narrative including parts from your case and reference to context from literature and make an interesting story for readers and editors. We all love a good story which is told in a well woven text and has relevant learning points underlined.

Editor-Journal of Orthopaedic Case Reports

Conflict of Interest: Nil

Source of Support: None

• Open access
• Published: 27 June 2011

The case study approach

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

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

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

Peer Review reports

Introduction

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

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

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

What is a case study?

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

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

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

What are case studies used for?

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

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

How are case studies conducted?

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

Defining the case

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

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

Selecting the case(s)

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

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

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

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

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

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

Collecting the data

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

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

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

Analysing, interpreting and reporting case studies

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

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

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

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

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

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

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

Conclusions

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

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Acknowledgements

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

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

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

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DOI : https://doi.org/10.1186/1471-2288-11-100

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Organizing Your Social Sciences Research Paper: Writing a Case Study

• Purpose of Guide
• Design Flaws to Avoid
• Independent and Dependent Variables
• Glossary of Research Terms
• Narrowing a Topic Idea
• Broadening a Topic Idea
• Extending the Timeliness of a Topic Idea
• Academic Writing Style
• Choosing a Title
• Making an Outline
• Paragraph Development
• Executive Summary
• The C.A.R.S. Model
• Background Information
• The Research Problem/Question
• Theoretical Framework
• Citation Tracking
• Content Alert Services
• Evaluating Sources
• Reading Research Effectively
• Primary Sources
• Secondary Sources
• Tiertiary Sources
• What Is Scholarly vs. Popular?
• Qualitative Methods
• Quantitative Methods
• Using Non-Textual Elements
• Limitations of the Study
• Common Grammar Mistakes
• Writing Concisely
• Avoiding Plagiarism
• Footnotes or Endnotes?
• Further Readings
• Annotated Bibliography
• Dealing with Nervousness
• Using Visual Aids
• Grading Someone Else's Paper
• Types of Structured Group Activities
• Group Project Survival Skills
• Multiple Book Review Essay
• Reviewing Collected Essays
• Writing a Case Study
• About Informed Consent
• Writing Field Notes
• Writing a Policy Memo
• Writing a Research Proposal
• Bibliography

The term case study refers to both a method of analysis and a specific research design for examining a problem, both of which are used in most circumstances to generalize across populations. This tab focuses on the latter--how to design and organize a research paper in the social sciences that analyzes a specific case.

A case study research paper examines a person, place, event, 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 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 among more than two 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 this writing guide. Review this page because it may help you identify a subject of analysis that can be investigated using a single 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:

• Does the case represent 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.
• Does the case provide 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.
• Does the case challenge and offer 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 practice. A case may offer you 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 the study a case in order 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.
• Does the case provide 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 in order to better warn drivers of an approaching train, particularly when visibility is hindered by heavy rain, fog, or at night.
• Does the case offer a new direction in future research? A case study can be used as a tool for exploratory research that points to a need for further examination of the research 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 Uganda. A case study of how women contribute to saving water in a particular village 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 throughout rural regions of east Africa. The case could also point to the need for scholars to apply 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 was I studying? Describe the research problem and describe the subject of analysis 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 was 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 research 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 include 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 study 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 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 the context of explaining the relevance of the case in addressing the research problem.

III.  Method

In this section, you explain why you selected a particular subject of analysis to study 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 frames 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; c) what were the consequences of the event.

If your subject of analysis is a person. Explain why you selected this particular individual to be studied and describe what experience he or she has had that provides 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 his/her 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 him or her 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.

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, cultural, economic, political, etc.], 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, why study 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 reveals 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? How might knowing the suppliers of these trucks from overseas 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 be linked to the findings from the literature review. Be sure to cite any prior studies that helped you determine that the case you chose was appropriate for investigating the research 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 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 more common to combine a description of the findings 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 to 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 It is important to 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 for 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.

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 needs for further research.

The function of your paper's conclusion is to: 1)  restate the main argument supported by the findings from the analysis of your case; 2) clearly state 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 for you 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 and your professor's preferences, the concluding paragraph may contain your final reflections on the evidence presented applied 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 on 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 differently 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.

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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Evidence Review of the Adverse Effects of COVID-19 Vaccination and Intramuscular Vaccine Administration

Vaccines are a public health success story, as they have prevented or lessened the effects of many infectious diseases. To address concerns around potential vaccine injuries, the Health Resources and Services Administration (HRSA) administers the Vaccine Injury Compensation Program (VICP) and the Countermeasures Injury Compensation Program (CICP), which provide compensation to those who assert that they were injured by routine vaccines or medical countermeasures, respectively. The National Academies of Sciences, Engineering, and Medicine have contributed to the scientific basis for VICP compensation decisions for decades.

HRSA asked the National Academies to convene an expert committee to review the epidemiological, clinical, and biological evidence about the relationship between COVID-19 vaccines and specific adverse events, as well as intramuscular administration of vaccines and shoulder injuries. This report outlines the committee findings and conclusions.

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• Published: 10 April 2024

A hybrid particle swarm optimization algorithm for solving engineering problem

• Jinwei Qiao 1 , 2 ,
• Guangyuan Wang 1 , 2 ,
• Zhi Yang 1 , 2 ,
• Xiaochuan Luo 3 ,
• Jun Chen 1 , 2 ,
• Kan Li 4 &
• Pengbo Liu 1 , 2  

Scientific Reports volume  14 , Article number:  8357 ( 2024 ) Cite this article

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• Computational science
• Mechanical engineering

To overcome the disadvantages of premature convergence and easy trapping into local optimum solutions, this paper proposes an improved particle swarm optimization algorithm (named NDWPSO algorithm) based on multiple hybrid strategies. Firstly, the elite opposition-based learning method is utilized to initialize the particle position matrix. Secondly, the dynamic inertial weight parameters are given to improve the global search speed in the early iterative phase. Thirdly, a new local optimal jump-out strategy is proposed to overcome the "premature" problem. Finally, the algorithm applies the spiral shrinkage search strategy from the whale optimization algorithm (WOA) and the Differential Evolution (DE) mutation strategy in the later iteration to accelerate the convergence speed. The NDWPSO is further compared with other 8 well-known nature-inspired algorithms (3 PSO variants and 5 other intelligent algorithms) on 23 benchmark test functions and three practical engineering problems. Simulation results prove that the NDWPSO algorithm obtains better results for all 49 sets of data than the other 3 PSO variants. Compared with 5 other intelligent algorithms, the NDWPSO obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( \({f}_{1}-{f}_{13}\) ) with 3 kinds of dimensional spaces (Dim = 30,50,100) and 80% of the best optimal solutions for 10 fixed-multimodal benchmark functions. Also, the best design solutions are obtained by NDWPSO for all 3 classical practical engineering problems.

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Introduction

In the ever-changing society, new optimization problems arise every moment, and they are distributed in various fields, such as automation control 1 , statistical physics 2 , security prevention and temperature prediction 3 , artificial intelligence 4 , and telecommunication technology 5 . Faced with a constant stream of practical engineering optimization problems, traditional solution methods gradually lose their efficiency and convenience, making it more and more expensive to solve the problems. Therefore, researchers have developed many metaheuristic algorithms and successfully applied them to the solution of optimization problems. Among them, Particle swarm optimization (PSO) algorithm 6 is one of the most widely used swarm intelligence algorithms.

However, the basic PSO has a simple operating principle and solves problems with high efficiency and good computational performance, but it suffers from the disadvantages of easily trapping in local optima and premature convergence. To improve the overall performance of the particle swarm algorithm, an improved particle swarm optimization algorithm is proposed by the multiple hybrid strategy in this paper. The improved PSO incorporates the search ideas of other intelligent algorithms (DE, WOA), so the improved algorithm proposed in this paper is named NDWPSO. The main improvement schemes are divided into the following 4 points: Firstly, a strategy of elite opposition-based learning is introduced into the particle population position initialization. A high-quality initialization matrix of population position can improve the convergence speed of the algorithm. Secondly, a dynamic weight methodology is adopted for the acceleration coefficients by combining the iterative map and linearly transformed method. This method utilizes the chaotic nature of the mapping function, the fast convergence capability of the dynamic weighting scheme, and the time-varying property of the acceleration coefficients. Thus, the global search and local search of the algorithm are balanced and the global search speed of the population is improved. Thirdly, a determination mechanism is set up to detect whether the algorithm falls into a local optimum. When the algorithm is “premature”, the population resets 40% of the position information to overcome the local optimum. Finally, the spiral shrinking mechanism combined with the DE/best/2 position mutation is used in the later iteration, which further improves the solution accuracy.

The structure of the paper is given as follows: Sect. “ Particle swarm optimization (PSO) ” describes the principle of the particle swarm algorithm. Section “ Improved particle swarm optimization algorithm ” shows the detailed improvement strategy and a comparison experiment of inertia weight is set up for the proposed NDWPSO. Section “ Experiment and discussion ” includes the experimental and result discussion sections on the performance of the improved algorithm. Section “ Conclusions and future works ” summarizes the main findings of this study.

Literature review

This section reviews some metaheuristic algorithms and other improved PSO algorithms. A simple discussion about recently proposed research studies is given.

Metaheuristic algorithms

A series of metaheuristic algorithms have been proposed in recent years by using various innovative approaches. For instance, Lin et al. 7 proposed a novel artificial bee colony algorithm (ABCLGII) in 2018 and compared ABCLGII with other outstanding ABC variants on 52 frequently used test functions. Abed-alguni et al. 8 proposed an exploratory cuckoo search (ECS) algorithm in 2021 and carried out several experiments to investigate the performance of ECS by 14 benchmark functions. Brajević 9 presented a novel shuffle-based artificial bee colony (SB-ABC) algorithm for solving integer programming and minimax problems in 2021. The experiments are tested on 7 integer programming problems and 10 minimax problems. In 2022, Khan et al. 10 proposed a non-deterministic meta-heuristic algorithm called Non-linear Activated Beetle Antennae Search (NABAS) for a non-convex tax-aware portfolio selection problem. Brajević et al. 11 proposed a hybridization of the sine cosine algorithm (HSCA) in 2022 to solve 15 complex structural and mechanical engineering design optimization problems. Abed-Alguni et al. 12 proposed an improved Salp Swarm Algorithm (ISSA) in 2022 for single-objective continuous optimization problems. A set of 14 standard benchmark functions was used to evaluate the performance of ISSA. In 2023, Nadimi et al. 13 proposed a binary starling murmuration optimization (BSMO) to select the effective features from different important diseases. In the same year, Nadimi et al. 14 systematically reviewed the last 5 years' developments of WOA and made a critical analysis of those WOA variants. In 2024, Fatahi et al. 15 proposed an Improved Binary Quantum-based Avian Navigation Optimizer Algorithm (IBQANA) for the Feature Subset Selection problem in the medical area. Experimental evaluation on 12 medical datasets demonstrates that IBQANA outperforms 7 established algorithms. Abed-alguni et al. 16 proposed an Improved Binary DJaya Algorithm (IBJA) to solve the Feature Selection problem in 2024. The IBJA’s performance was compared against 4 ML classifiers and 10 efficient optimization algorithms.

Improved PSO algorithms

Many researchers have constantly proposed some improved PSO algorithms to solve engineering problems in different fields. For instance, Yeh 17 proposed an improved particle swarm algorithm, which combines a new self-boundary search and a bivariate update mechanism, to solve the reliability redundancy allocation problem (RRAP) problem. Solomon et al. 18 designed a collaborative multi-group particle swarm algorithm with high parallelism that was used to test the adaptability of Graphics Processing Units (GPUs) in distributed computing environments. Mukhopadhyay and Banerjee 19 proposed a chaotic multi-group particle swarm optimization (CMS-PSO) to estimate the unknown parameters of an autonomous chaotic laser system. Duan et al. 20 designed an improved particle swarm algorithm with nonlinear adjustment of inertia weights to improve the coupling accuracy between laser diodes and single-mode fibers. Sun et al. 21 proposed a particle swarm optimization algorithm combined with non-Gaussian stochastic distribution for the optimal design of wind turbine blades. Based on a multiple swarm scheme, Liu et al. 22 proposed an improved particle swarm optimization algorithm to predict the temperatures of steel billets for the reheating furnace. In 2022, Gad 23 analyzed the existing 2140 papers on Swarm Intelligence between 2017 and 2019 and pointed out that the PSO algorithm still needs further research. In general, the improved methods can be classified into four categories:

Adjusting the distribution of algorithm parameters. Feng et al. 24 used a nonlinear adaptive method on inertia weights to balance local and global search and introduced asynchronously varying acceleration coefficients.

Changing the updating formula of the particle swarm position. Both papers 25 and 26 used chaotic mapping functions to update the inertia weight parameters and combined them with a dynamic weighting strategy to update the particle swarm positions. This improved approach enables the particle swarm algorithm to be equipped with fast convergence of performance.

The initialization of the swarm. Alsaidy and Abbood proposed 27 a hybrid task scheduling algorithm that replaced the random initialization of the meta-heuristic algorithm with the heuristic algorithms MCT-PSO and LJFP-PSO.

Combining with other intelligent algorithms: Liu et al. 28 introduced the differential evolution (DE) algorithm into PSO to increase the particle swarm as diversity and reduce the probability of the population falling into local optimum.

Particle swarm optimization (PSO)

The particle swarm optimization algorithm is a population intelligence algorithm for solving continuous and discrete optimization problems. It originated from the social behavior of individuals in bird and fish flocks 6 . The core of the PSO algorithm is that an individual particle identifies potential solutions by flight in a defined constraint space adjusts its exploration direction to approach the global optimal solution based on the shared information among the group, and finally solves the optimization problem. Each particle \(i\) includes two attributes: velocity vector \({V}_{i}=\left[{v}_{i1},{v}_{i2},{v}_{i3},{...,v}_{ij},{...,v}_{iD},\right]\) and position vector \({X}_{i}=[{x}_{i1},{x}_{i2},{x}_{i3},...,{x}_{ij},...,{x}_{iD}]\) . The velocity vector is used to modify the motion path of the swarm; the position vector represents a potential solution for the optimization problem. Here, \(j=\mathrm{1,2},\dots ,D\) , \(D\) represents the dimension of the constraint space. The equations for updating the velocity and position of the particle swarm are shown in Eqs. ( 1 ) and ( 2 ).

Here \({Pbest}_{i}^{k}\) represents the previous optimal position of the particle \(i\) , and \({Gbest}\) is the optimal position discovered by the whole population. \(i=\mathrm{1,2},\dots ,n\) , \(n\) denotes the size of the particle swarm. \({c}_{1}\) and \({c}_{2}\) are the acceleration constants, which are used to adjust the search step of the particle 29 . \({r}_{1}\) and \({r}_{2}\) are two random uniform values distributed in the range \([\mathrm{0,1}]\) , which are used to improve the randomness of the particle search. \(\omega\) inertia weight parameter, which is used to adjust the scale of the search range of the particle swarm 30 . The basic PSO sets the inertia weight parameter as a time-varying parameter to balance global exploration and local seeking. The updated equation of the inertia weight parameter is given as follows:

where \({\omega }_{max}\) and \({\omega }_{min}\) represent the upper and lower limits of the range of inertia weight parameter. \(k\) and \(Mk\) are the current iteration and maximum iteration.

Improved particle swarm optimization algorithm

According to the no free lunch theory 31 , it is known that no algorithm can solve every practical problem with high quality and efficiency for increasingly complex and diverse optimization problems. In this section, several improvement strategies are proposed to improve the search efficiency and overcome this shortcoming of the basic PSO algorithm.

Improvement strategies

The optimization strategies of the improved PSO algorithm are shown as follows:

The inertia weight parameter is updated by an improved chaotic variables method instead of a linear decreasing strategy. Chaotic mapping performs the whole search at a higher speed and is more resistant to falling into local optimal than the probability-dependent random search 32 . However, the population may result in that particles can easily fly out of the global optimum boundary. To ensure that the population can converge to the global optimum, an improved Iterative mapping is adopted and shown as follows:

Here \({\omega }_{k}\) is the inertia weight parameter in the iteration \(k\) , \(b\) is the control parameter in the range \([\mathrm{0,1}]\) .

The acceleration coefficients are updated by the linear transformation. \({c}_{1}\) and \({c}_{2}\) represent the influential coefficients of the particles by their own and population information, respectively. To improve the search performance of the population, \({c}_{1}\) and \({c}_{2}\) are changed from fixed values to time-varying parameter parameters, that are updated by linear transformation with the number of iterations:

where \({c}_{max}\) and \({c}_{min}\) are the maximum and minimum values of acceleration coefficients, respectively.

The initialization scheme is determined by elite opposition-based learning . The high-quality initial population will accelerate the solution speed of the algorithm and improve the accuracy of the optimal solution. Thus, the elite backward learning strategy 33 is introduced to generate the position matrix of the initial population. Suppose the elite individual of the population is \({X}=[{x}_{1},{x}_{2},{x}_{3},...,{x}_{j},...,{x}_{D}]\) , and the elite opposition-based solution of \(X\) is \({X}_{o}=[{x}_{{\text{o}}1},{x}_{{\text{o}}2},{x}_{{\text{o}}3},...,{x}_{oj},...,{x}_{oD}]\) . The formula for the elite opposition-based solution is as follows:

where \({k}_{r}\) is the random value in the range \((\mathrm{0,1})\) . \({ux}_{oij}\) and \({lx}_{oij}\) are dynamic boundaries of the elite opposition-based solution in \(j\) dimensional variables. The advantage of dynamic boundary is to reduce the exploration space of particles, which is beneficial to the convergence of the algorithm. When the elite opposition-based solution is out of bounds, the out-of-bounds processing is performed. The equation is given as follows:

After calculating the fitness function values of the elite solution and the elite opposition-based solution, respectively, \(n\) high quality solutions were selected to form a new initial population position matrix.

The position updating Eq. ( 2 ) is modified based on the strategy of dynamic weight. To improve the speed of the global search of the population, the strategy of dynamic weight from the artificial bee colony algorithm 34 is introduced to enhance the computational performance. The new position updating equation is shown as follows:

Here \(\rho\) is the random value in the range \((\mathrm{0,1})\) . \(\psi\) represents the acceleration coefficient and \({\omega }{\prime}\) is the dynamic weight coefficient. The updated equations of the above parameters are as follows:

where \(f(i)\) denotes the fitness function value of individual particle \(i\) and u is the average of the population fitness function values in the current iteration. The Eqs. ( 11 , 12 ) are introduced into the position updating equation. And they can attract the particle towards positions of the best-so-far solution in the search space.

New local optimal jump-out strategy is added for escaping from the local optimal. When the value of the fitness function for the population optimal particles does not change in M iterations, the algorithm determines that the population falls into a local optimal. The scheme in which the population jumps out of the local optimum is to reset the position information of the 40% of individuals within the population, in other words, to randomly generate the position vector in the search space. M is set to 5% of the maximum number of iterations.

New spiral update search strategy is added after the local optimal jump-out strategy. Since the whale optimization algorithm (WOA) was good at exploring the local search space 35 , the spiral update search strategy in the WOA 36 is introduced to update the position of the particles after the swarm jumps out of local optimal. The equation for the spiral update is as follows:

Here \(D=\left|{x}_{i}\left(k\right)-Gbest\right|\) denotes the distance between the particle itself and the global optimal solution so far. \(B\) is the constant that defines the shape of the logarithmic spiral. \(l\) is the random value in \([-\mathrm{1,1}]\) . \(l\) represents the distance between the newly generated particle and the global optimal position, \(l=-1\) means the closest distance, while \(l=1\) means the farthest distance, and the meaning of this parameter can be directly observed by Fig.  1 .

Spiral updating position.

The DE/best/2 mutation strategy is introduced to form the mutant particle. 4 individuals in the population are randomly selected that differ from the current particle, then the vector difference between them is rescaled, and the difference vector is combined with the global optimal position to form the mutant particle. The equation for mutation of particle position is shown as follows:

where \({x}^{*}\) is the mutated particle, \(F\) is the scale factor of mutation, \({r}_{1}\) , \({r}_{2}\) , \({r}_{3}\) , \({r}_{4}\) are random integer values in \((0,n]\) and not equal to \(i\) , respectively. Specific particles are selected for mutation with the screening conditions as follows:

where \(Cr\) represents the probability of mutation, \(rand\left(\mathrm{0,1}\right)\) is a random number in \(\left(\mathrm{0,1}\right)\) , and \({i}_{rand}\) is a random integer value in \((0,n]\) .

The improved PSO incorporates the search ideas of other intelligent algorithms (DE, WOA), so the improved algorithm proposed in this paper is named NDWPSO. The pseudo-code for the NDWPSO algorithm is given as follows:

The main procedure of NDWPSO.

Comparing the distribution of inertia weight parameters

There are several improved PSO algorithms (such as CDWPSO 25 , and SDWPSO 26 ) that adopt the dynamic weighted particle position update strategy as their improvement strategy. The updated equations of the CDWPSO and the SDWPSO algorithm for the inertia weight parameters are given as follows:

where \({\text{A}}\) is a value in \((\mathrm{0,1}]\) . \({r}_{max}\) and \({r}_{min}\) are the upper and lower limits of the fluctuation range of the inertia weight parameters, \(k\) is the current number of algorithm iterations, and \(Mk\) denotes the maximum number of iterations.

Considering that the update method of inertia weight parameters by our proposed NDWPSO is comparable to the CDWPSO, and SDWPSO, a comparison experiment for the distribution of inertia weight parameters is set up in this section. The maximum number of iterations in the experiment is \(Mk=500\) . The distributions of CDWPSO, SDWPSO, and NDWPSO inertia weights are shown sequentially in Fig.  2 .

The inertial weight distribution of CDWPSO, SDWPSO, and NDWPSO.

In Fig.  2 , the inertia weight value of CDWPSO is a random value in (0,1]. It may make individual particles fly out of the range in the late iteration of the algorithm. Similarly, the inertia weight value of SDWPSO is a value that tends to zero infinitely, so that the swarm no longer can fly in the search space, making the algorithm extremely easy to fall into the local optimal value. On the other hand, the distribution of the inertia weights of the NDWPSO forms a gentle slope by two curves. Thus, the swarm can faster lock the global optimum range in the early iterations and locate the global optimal more precisely in the late iterations. The reason is that the inertia weight values between two adjacent iterations are inversely proportional to each other. Besides, the time-varying part of the inertial weight within NDWPSO is designed to reduce the chaos characteristic of the parameters. The inertia weight value of NDWPSO avoids the disadvantages of the above two schemes, so its design is more reasonable.

Experiment and discussion

In this section, three experiments are set up to evaluate the performance of NDWPSO: (1) the experiment of 23 classical functions 37 between NDWPSO and three particle swarm algorithms (PSO 6 , CDWPSO 25 , SDWPSO 26 ); (2) the experiment of benchmark test functions between NDWPSO and other intelligent algorithms (Whale Optimization Algorithm (WOA) 36 , Harris Hawk Algorithm (HHO) 38 , Gray Wolf Optimization Algorithm (GWO) 39 , Archimedes Algorithm (AOA) 40 , Equilibrium Optimizer (EO) 41 and Differential Evolution (DE) 42 ); (3) the experiment for solving three real engineering problems (welded beam design 43 , pressure vessel design 44 , and three-bar truss design 38 ). All experiments are run on a computer with Intel i5-11400F GPU, 2.60 GHz, 16 GB RAM, and the code is written with MATLAB R2017b.

The benchmark test functions are 23 classical functions, which consist of indefinite unimodal (F1–F7), indefinite dimensional multimodal functions (F8–F13), and fixed-dimensional multimodal functions (F14–F23). The unimodal benchmark function is used to evaluate the global search performance of different algorithms, while the multimodal benchmark function reflects the ability of the algorithm to escape from the local optimal. The mathematical equations of the benchmark functions are shown and found as Supplementary Tables S1 – S3 online.

Experiments on benchmark functions between NDWPSO, and other PSO variants

The purpose of the experiment is to show the performance advantages of the NDWPSO algorithm. Here, the dimensions and corresponding population sizes of 13 benchmark functions (7 unimodal and 6 multimodal) are set to (30, 40), (50, 70), and (100, 130). The population size of 10 fixed multimodal functions is set to 40. Each algorithm is repeated 30 times independently, and the maximum number of iterations is 200. The performance of the algorithm is measured by the mean and the standard deviation (SD) of the results for different benchmark functions. The parameters of the NDWPSO are set as: \({[{\omega }_{min},\omega }_{max}]=[\mathrm{0.4,0.9}]\) , \(\left[{c}_{max},{c}_{min}\right]=\left[\mathrm{2.5,1.5}\right],{V}_{max}=0.1,b={e}^{-50}, M=0.05\times Mk, B=1,F=0.7, Cr=0.9.\) And, \(A={\omega }_{max}\) for CDWPSO; \({[r}_{max},{r}_{min}]=[\mathrm{4,0}]\) for SDWPSO.

Besides, the experimental data are retained to two decimal places, but some experimental data will increase the number of retained data to pursue more accuracy in comparison. The best results in each group of experiments will be displayed in bold font. The experimental data is set to 0 if the value is below 10 –323 . The experimental parameter settings in this paper are different from the references (PSO 6 , CDWPSO 25 , SDWPSO 26 , so the final experimental data differ from the ones within the reference.

As shown in Tables 1 and 2 , the NDWPSO algorithm obtains better results for all 49 sets of data than other PSO variants, which include not only 13 indefinite-dimensional benchmark functions and 10 fixed-multimodal benchmark functions. Remarkably, the SDWPSO algorithm obtains the same accuracy of calculation as NDWPSO for both unimodal functions f 1 –f 4 and multimodal functions f 9 –f 11 . The solution accuracy of NDWPSO is higher than that of other PSO variants for fixed-multimodal benchmark functions f 14 -f 23 . The conclusion can be drawn that the NDWPSO has excellent global search capability, local search capability, and the capability for escaping the local optimal.

In addition, the convergence curves of the 23 benchmark functions are shown in Figs. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 . The NDWPSO algorithm has a faster convergence speed in the early stage of the search for processing functions f1-f6, f8-f14, f16, f17, and finds the global optimal solution with a smaller number of iterations. In the remaining benchmark function experiments, the NDWPSO algorithm shows no outstanding performance for convergence speed in the early iterations. There are two reasons of no outstanding performance in the early iterations. On one hand, the fixed-multimodal benchmark function has many disturbances and local optimal solutions in the whole search space. on the other hand, the initialization scheme based on elite opposition-based learning is still stochastic, which leads to the initial position far from the global optimal solution. The inertia weight based on chaotic mapping and the strategy of spiral updating can significantly improve the convergence speed and computational accuracy of the algorithm in the late search stage. Finally, the NDWPSO algorithm can find better solutions than other algorithms in the middle and late stages of the search.

Evolution curve of NDWPSO and other PSO algorithms for f1 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f2 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f3 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f4 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f5 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f6 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f7 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f8 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f9 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f10 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f11(Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f12 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f13 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f14, f15, f16.

Evolution curve of NDWPSO and other PSO algorithms for f17, f18, f19.

Evolution curve of NDWPSO and other PSO algorithms for f20, f21, f22.

Evolution curve of NDWPSO and other PSO algorithms for f23.

To evaluate the performance of different PSO algorithms, a statistical test is conducted. Due to the stochastic nature of the meta-heuristics, it is not enough to compare algorithms based on only the mean and standard deviation values. The optimization results cannot be assumed to obey the normal distribution; thus, it is necessary to judge whether the results of the algorithms differ from each other in a statistically significant way. Here, the Wilcoxon non-parametric statistical test 45 is used to obtain a parameter called p -value to verify whether two sets of solutions are different to a statistically significant extent or not. Generally, it is considered that p  ≤ 0.5 can be considered as a statistically significant superiority of the results. The p -values calculated in Wilcoxon’s rank-sum test comparing NDWPSO and other PSO algorithms are listed in Table  3 for all benchmark functions. The p -values in Table  3 additionally present the superiority of the NDWPSO because all of the p -values are much smaller than 0.5.

In general, the NDWPSO has the fastest convergence rate when finding the global optimum from Figs. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 , and thus we can conclude that the NDWPSO is superior to the other PSO variants during the process of optimization.

Comparison experiments between NDWPSO and other intelligent algorithms

Experiments are conducted to compare NDWPSO with several other intelligent algorithms (WOA, HHO, GWO, AOA, EO and DE). The experimental object is 23 benchmark functions, and the experimental parameters of the NDWPSO algorithm are set the same as in Experiment 4.1. The maximum number of iterations of the experiment is increased to 2000 to fully demonstrate the performance of each algorithm. Each algorithm is repeated 30 times individually. The parameters of the relevant intelligent algorithms in the experiments are set as shown in Table 4 . To ensure the fairness of the algorithm comparison, all parameters are concerning the original parameters in the relevant algorithm literature. The experimental results are shown in Tables 5 , 6 , 7 and 8 and Figs. 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 and 36 .

Evolution curve of NDWPSO and other algorithms for f1 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f2 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f3(Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f4 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f5 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f6 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f7 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f8 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f9(Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f10 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f11 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f12 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f13 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f14, f15, f16.

Evolution curve of NDWPSO and other algorithms for f17, f18, f19.

Evolution curve of NDWPSO and other algorithms for f20, f21, f22.

Evolution curve of NDWPSO and other algorithms for f23.

The experimental data of NDWPSO and other intelligent algorithms for handling 30, 50, and 100-dimensional benchmark functions ( \({f}_{1}-{f}_{13}\) ) are recorded in Tables 8 , 9 and 10 , respectively. The comparison data of fixed-multimodal benchmark tests ( \({f}_{14}-{f}_{23}\) ) are recorded in Table 11 . According to the data in Tables 5 , 6 and 7 , the NDWPSO algorithm obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( \({f}_{1}-{f}_{13}\) ) in the search space of three dimensions (Dim = 30, 50, 100), respectively. In Table 8 , the NDWPSO algorithm obtains 80% of the optimal solutions in 10 fixed-multimodal benchmark functions.

The convergence curves of each algorithm are shown in Figs. 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 and 36 . The NDWPSO algorithm demonstrates two convergence behaviors when calculating the benchmark functions in 30, 50, and 100-dimensional search spaces. The first behavior is the fast convergence of NDWPSO with a small number of iterations at the beginning of the search. The reason is that the Iterative-mapping strategy and the position update scheme of dynamic weighting are used in the NDWPSO algorithm. This scheme can quickly target the region in the search space where the global optimum is located, and then precisely lock the optimal solution. When NDWPSO processes the functions \({f}_{1}-{f}_{4}\) , and \({f}_{9}-{f}_{11}\) , the behavior can be reflected in the convergence trend of their corresponding curves. The second behavior is that NDWPSO gradually improves the convergence accuracy and rapidly approaches the global optimal in the middle and late stages of the iteration. The NDWPSO algorithm fails to converge quickly in the early iterations, which is possible to prevent the swarm from falling into a local optimal. The behavior can be demonstrated by the convergence trend of the curves when NDWPSO handles the functions \({f}_{6}\) , \({f}_{12}\) , and \({f}_{13}\) , and it also shows that the NDWPSO algorithm has an excellent ability of local search.

Combining the experimental data with the convergence curves, it is concluded that the NDWPSO algorithm has a faster convergence speed, so the effectiveness and global convergence of the NDWPSO algorithm are more outstanding than other intelligent algorithms.

Experiments on classical engineering problems

Three constrained classical engineering design problems (welded beam design, pressure vessel design 43 , and three-bar truss design 38 ) are used to evaluate the NDWPSO algorithm. The experiments are the NDWPSO algorithm and 5 other intelligent algorithms (WOA 36 , HHO, GWO, AOA, EO 41 ). Each algorithm is provided with the maximum number of iterations and population size ( \({\text{Mk}}=500,\mathrm{ n}=40\) ), and then repeats 30 times, independently. The parameters of the algorithms are set the same as in Table 4 . The experimental results of three engineering design problems are recorded in Tables 9 , 10 and 11 in turn. The result data is the average value of the solved data.

Welded beam design

The target of the welded beam design problem is to find the optimal manufacturing cost for the welded beam with the constraints, as shown in Fig.  37 . The constraints are the thickness of the weld seam ( \({\text{h}}\) ), the length of the clamped bar ( \({\text{l}}\) ), the height of the bar ( \({\text{t}}\) ) and the thickness of the bar ( \({\text{b}}\) ). The mathematical formulation of the optimization problem is given as follows:

Welded beam design.

In Table 9 , the NDWPSO, GWO, and EO algorithms obtain the best optimal cost. Besides, the standard deviation (SD) of t NDWPSO is the lowest, which means it has very good results in solving the welded beam design problem.

Pressure vessel design

Kannan and Kramer 43 proposed the pressure vessel design problem as shown in Fig.  38 to minimize the total cost, including the cost of material, forming, and welding. There are four design optimized objects: the thickness of the shell \({T}_{s}\) ; the thickness of the head \({T}_{h}\) ; the inner radius \({\text{R}}\) ; the length of the cylindrical section without considering the head \({\text{L}}\) . The problem includes the objective function and constraints as follows:

Pressure vessel design.

The results in Table 10 show that the NDWPSO algorithm obtains the lowest optimal cost with the same constraints and has the lowest standard deviation compared with other algorithms, which again proves the good performance of NDWPSO in terms of solution accuracy.

Three-bar truss design

This structural design problem 44 is one of the most widely-used case studies as shown in Fig.  39 . There are two main design parameters: the area of the bar1 and 3 ( \({A}_{1}={A}_{3}\) ) and area of bar 2 ( \({A}_{2}\) ). The objective is to minimize the weight of the truss. This problem is subject to several constraints as well: stress, deflection, and buckling constraints. The problem is formulated as follows:

Three-bar truss design.

From Table 11 , NDWPSO obtains the best design solution in this engineering problem and has the smallest standard deviation of the result data. In summary, the NDWPSO can reveal very competitive results compared to other intelligent algorithms.

Conclusions and future works

An improved algorithm named NDWPSO is proposed to enhance the solving speed and improve the computational accuracy at the same time. The improved NDWPSO algorithm incorporates the search ideas of other intelligent algorithms (DE, WOA). Besides, we also proposed some new hybrid strategies to adjust the distribution of algorithm parameters (such as the inertia weight parameter, the acceleration coefficients, the initialization scheme, the position updating equation, and so on).

23 classical benchmark functions: indefinite unimodal (f1-f7), indefinite multimodal (f8-f13), and fixed-dimensional multimodal(f14-f23) are applied to evaluate the effective line and feasibility of the NDWPSO algorithm. Firstly, NDWPSO is compared with PSO, CDWPSO, and SDWPSO. The simulation results can prove the exploitative, exploratory, and local optima avoidance of NDWPSO. Secondly, the NDWPSO algorithm is compared with 5 other intelligent algorithms (WOA, HHO, GWO, AOA, EO). The NDWPSO algorithm also has better performance than other intelligent algorithms. Finally, 3 classical engineering problems are applied to prove that the NDWPSO algorithm shows superior results compared to other algorithms for the constrained engineering optimization problems.

Although the proposed NDWPSO is superior in many computation aspects, there are still some limitations and further improvements are needed. The NDWPSO performs a limit initialize on each particle by the strategy of “elite opposition-based learning”, it takes more computation time before speed update. Besides, the” local optimal jump-out” strategy also brings some random process. How to reduce the random process and how to improve the limit initialize efficiency are the issues that need to be further discussed. In addition, in future work, researchers will try to apply the NDWPSO algorithm to wider fields to solve more complex and diverse optimization problems.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by Key R&D plan of Shandong Province, China (2021CXGC010207, 2023CXGC01020); First batch of talent research projects of Qilu University of Technology in 2023 (2023RCKY116); Introduction of urgently needed talent projects in Key Supported Regions of Shandong Province; Key Projects of Natural Science Foundation of Shandong Province (ZR2020ME116); the Innovation Ability Improvement Project for Technology-based Small- and Medium-sized Enterprises of Shandong Province (2022TSGC2051, 2023TSGC0024, 2023TSGC0931); National Key R&D Program of China (2019YFB1705002), LiaoNing Revitalization Talents Program (XLYC2002041) and Young Innovative Talents Introduction & Cultivation Program for Colleges and Universities of Shandong Province (Granted by Department of Education of Shandong Province, Sub-Title: Innovative Research Team of High Performance Integrated Device).

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Analyzing water crisis through the water footprint approach; case of Isfahan province, Iran

• Published: 20 April 2024

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• Hossein Mokhtari Hashi   ORCID: orcid.org/0000-0003-0896-5678 1  

This study examines the impact of an increasing water footprint on exacerbating water scarcity and the crisis in Isfahan province, Iran. It highlights the significance of considering the water footprint approach in water resource management. To achieve this goal, a comprehensive analysis of water availability limitations, population growth, the agricultural sector, and the industrial sector was conducted. The methodology employed for this research involved a combination of qualitative and quantitative data collection approaches, including literature review and statistical data analysis. The findings of this study reveal that Isfahan province faces a significant water crisis due to an imbalance between water supply and demand. The limited renewable water resources in the region exacerbate the challenges associated with meeting the water demands of a continuously expanding population and human activities. The conclusions drawn from this research indicate that focusing on transferring water from adjacent basins as a solution for water scarcity, and even transferring more water if it is available in those basins, regardless of the increasing trend of the water footprint in the province, is not only an unsustainable solution, but also exacerbates the unsustainability of the source water transferred adjacent basins. Some recommendations to improve the water footprint approach in Isfahan province for long-term sustainability include raising awareness to reduce household water usage, promoting efficient irrigation and sustainable agricultural practices, implementing regulations, and encouraging the adoption of water-efficient technologies in the industrial sector. Collaborative efforts between the government, stakeholders, and the public, continued research and data monitoring.

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Data availability

Population data

The population data of Isfahan province obtained from Statistical Center of Iran yearbook and Isfahan municipality yearbook in different years, these websites are in Persian and the data is publicly available. Statistical Center of Iran available at: https://www.amar.org.ir/statistical-information .

Isfahan municipality yearbook (population part) is available at: https://plan.isfahan.ir/sites/default/files/statistics_content/23898/files/98-2.pdf .

Agriculture data

The data for agricultural products obtained from Statistical Center of Iran yearbook and Ministry of Agricultural Jihad and Organization of Agriculture Jihad of Isfahan province statistical yearbooks in different years.

Ministry of Agricultural Jihad Statistics available at: https://maj.ir/page-amar/FA/65/form/pId3352 .

Organization of Agriculture Jihad of Isfahan province statistics available at: http://agri-es.ir/Default.aspx?tabid=1927 .

Industrial data .

The data for industrial products obtained from Statistical Center of Iran yearbooks, Mobarakeh Steel Company, Zobahan (Steel) Company, Iranian Mines & Mining Industries Development & Renovation Organization (IMIDRO), National Iranian Steel Company (NISC), Isfahan Regional Electricity Company and Cement Scientific Monthly.

Electricity data .

The data for electricity obtained from Statistical Center of Iran yearbooks and Isfahan Regional Electrical Company, Available at: https://www.erec.co.ir/fa/history.aspx .

All data used in this paper obtained from official sources that are published and open to public access. The data are in Persian.

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Mokhtari Hashi, H. Analyzing water crisis through the water footprint approach; case of Isfahan province, Iran. Environ Dev Sustain (2024). https://doi.org/10.1007/s10668-024-04882-1

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Received : 28 May 2023

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DOI : https://doi.org/10.1007/s10668-024-04882-1

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