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• How to Write a Discussion Section | Tips & Examples

How to Write a Discussion Section | Tips & Examples

Published on August 21, 2022 by Shona McCombes . Revised on July 18, 2023.

The discussion section is where you delve into the meaning, importance, and relevance of your results .

It should focus on explaining and evaluating what you found, showing how it relates to your literature review and paper or dissertation topic , and making an argument in support of your overall conclusion. It should not be a second results section.

There are different ways to write this section, but you can focus your writing around these key elements:

• Summary : A brief recap of your key results
• Interpretations: What do your results mean?
• Implications: Why do your results matter?
• Limitations: What can’t your results tell us?
• Recommendations: Avenues for further studies or analyses

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Table of contents

What not to include in your discussion section, step 1: summarize your key findings, step 2: give your interpretations, step 3: discuss the implications, step 4: acknowledge the limitations, step 5: share your recommendations, discussion section example, other interesting articles, frequently asked questions about discussion sections.

There are a few common mistakes to avoid when writing the discussion section of your paper.

• Don’t introduce new results: You should only discuss the data that you have already reported in your results section .
• Don’t make inflated claims: Avoid overinterpretation and speculation that isn’t directly supported by your data.
• Don’t undermine your research: The discussion of limitations should aim to strengthen your credibility, not emphasize weaknesses or failures.

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Start this section by reiterating your research problem and concisely summarizing your major findings. To speed up the process you can use a summarizer to quickly get an overview of all important findings. Don’t just repeat all the data you have already reported—aim for a clear statement of the overall result that directly answers your main research question . This should be no more than one paragraph.

Many students struggle with the differences between a discussion section and a results section . The crux of the matter is that your results sections should present your results, and your discussion section should subjectively evaluate them. Try not to blend elements of these two sections, in order to keep your paper sharp.

• The results indicate that…
• The study demonstrates a correlation between…
• This analysis supports the theory that…
• The data suggest that…

The meaning of your results may seem obvious to you, but it’s important to spell out their significance for your reader, showing exactly how they answer your research question.

The form of your interpretations will depend on the type of research, but some typical approaches to interpreting the data include:

• Identifying correlations , patterns, and relationships among the data
• Discussing whether the results met your expectations or supported your hypotheses
• Contextualizing your findings within previous research and theory
• Explaining unexpected results and evaluating their significance
• Considering possible alternative explanations and making an argument for your position

You can organize your discussion around key themes, hypotheses, or research questions, following the same structure as your results section. Alternatively, you can also begin by highlighting the most significant or unexpected results.

• In line with the hypothesis…
• Contrary to the hypothesized association…
• The results contradict the claims of Smith (2022) that…
• The results might suggest that x . However, based on the findings of similar studies, a more plausible explanation is y .

As well as giving your own interpretations, make sure to relate your results back to the scholarly work that you surveyed in the literature review . The discussion should show how your findings fit with existing knowledge, what new insights they contribute, and what consequences they have for theory or practice.

Ask yourself these questions:

• Do your results support or challenge existing theories? If they support existing theories, what new information do they contribute? If they challenge existing theories, why do you think that is?
• Are there any practical implications?

Your overall aim is to show the reader exactly what your research has contributed, and why they should care.

• These results build on existing evidence of…
• The results do not fit with the theory that…
• The experiment provides a new insight into the relationship between…
• These results should be taken into account when considering how to…
• The data contribute a clearer understanding of…
• While previous research has focused on  x , these results demonstrate that y .

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Even the best research has its limitations. Acknowledging these is important to demonstrate your credibility. Limitations aren’t about listing your errors, but about providing an accurate picture of what can and cannot be concluded from your study.

Limitations might be due to your overall research design, specific methodological choices , or unanticipated obstacles that emerged during your research process.

Here are a few common possibilities:

• If your sample size was small or limited to a specific group of people, explain how generalizability is limited.
• If you encountered problems when gathering or analyzing data, explain how these influenced the results.
• If there are potential confounding variables that you were unable to control, acknowledge the effect these may have had.

After noting the limitations, you can reiterate why the results are nonetheless valid for the purpose of answering your research question.

• The generalizability of the results is limited by…
• The reliability of these data is impacted by…
• Due to the lack of data on x , the results cannot confirm…
• The methodological choices were constrained by…
• It is beyond the scope of this study to…

Based on the discussion of your results, you can make recommendations for practical implementation or further research. Sometimes, the recommendations are saved for the conclusion .

Suggestions for further research can lead directly from the limitations. Don’t just state that more studies should be done—give concrete ideas for how future work can build on areas that your own research was unable to address.

• Further research is needed to establish…
• Future studies should take into account…
• Avenues for future research include…

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In the discussion , you explore the meaning and relevance of your research results , explaining how they fit with existing research and theory. Discuss:

• Your  interpretations : what do the results tell us?
• The  implications : why do the results matter?
• The  limitation s : what can’t the results tell us?

The results chapter or section simply and objectively reports what you found, without speculating on why you found these results. The discussion interprets the meaning of the results, puts them in context, and explains why they matter.

In qualitative research , results and discussion are sometimes combined. But in quantitative research , it’s considered important to separate the objective results from your interpretation of them.

In a thesis or dissertation, the discussion is an in-depth exploration of the results, going into detail about the meaning of your findings and citing relevant sources to put them in context.

The conclusion is more shorter and more general: it concisely answers your main research question and makes recommendations based on your overall findings.

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• How to Write Discussions and Conclusions

The discussion section contains the results and outcomes of a study. An effective discussion informs readers what can be learned from your experiment and provides context for the results.

What makes an effective discussion?

When you’re ready to write your discussion, you’ve already introduced the purpose of your study and provided an in-depth description of the methodology. The discussion informs readers about the larger implications of your study based on the results. Highlighting these implications while not overstating the findings can be challenging, especially when you’re submitting to a journal that selects articles based on novelty or potential impact. Regardless of what journal you are submitting to, the discussion section always serves the same purpose: concluding what your study results actually mean.

A successful discussion section puts your findings in context. It should include:

• the results of your research,
• a discussion of related research, and
• a comparison between your results and initial hypothesis.

Tip: Not all journals share the same naming conventions.

You can apply the advice in this article to the conclusion, results or discussion sections of your manuscript.

Our Early Career Researcher community tells us that the conclusion is often considered the most difficult aspect of a manuscript to write. To help, this guide provides questions to ask yourself, a basic structure to model your discussion off of and examples from published manuscripts. 

Questions to ask yourself:

• Was my hypothesis correct?
• If my hypothesis is partially correct or entirely different, what can be learned from the results? 
• How do the conclusions reshape or add onto the existing knowledge in the field? What does previous research say about the topic? 
• Why are the results important or relevant to your audience? Do they add further evidence to a scientific consensus or disprove prior studies? 
• How can future research build on these observations? What are the key experiments that must be done? 
• What is the “take-home” message you want your reader to leave with?

How to structure a discussion

Trying to fit a complete discussion into a single paragraph can add unnecessary stress to the writing process. If possible, you’ll want to give yourself two or three paragraphs to give the reader a comprehensive understanding of your study as a whole. Here’s one way to structure an effective discussion:

Writing Tips

While the above sections can help you brainstorm and structure your discussion, there are many common mistakes that writers revert to when having difficulties with their paper. Writing a discussion can be a delicate balance between summarizing your results, providing proper context for your research and avoiding introducing new information. Remember that your paper should be both confident and honest about the results! 

• Read the journal’s guidelines on the discussion and conclusion sections. If possible, learn about the guidelines before writing the discussion to ensure you’re writing to meet their expectations. 
• Begin with a clear statement of the principal findings. This will reinforce the main take-away for the reader and set up the rest of the discussion. 
• Explain why the outcomes of your study are important to the reader. Discuss the implications of your findings realistically based on previous literature, highlighting both the strengths and limitations of the research. 
• State whether the results prove or disprove your hypothesis. If your hypothesis was disproved, what might be the reasons? 
• Introduce new or expanded ways to think about the research question. Indicate what next steps can be taken to further pursue any unresolved questions. 
• If dealing with a contemporary or ongoing problem, such as climate change, discuss possible consequences if the problem is avoided. 
• Be concise. Adding unnecessary detail can distract from the main findings. 

Don’t

• Rewrite your abstract. Statements with “we investigated” or “we studied” generally do not belong in the discussion. 
• Include new arguments or evidence not previously discussed. Necessary information and evidence should be introduced in the main body of the paper. 
• Apologize. Even if your research contains significant limitations, don’t undermine your authority by including statements that doubt your methodology or execution. 
• Shy away from speaking on limitations or negative results. Including limitations and negative results will give readers a complete understanding of the presented research. Potential limitations include sources of potential bias, threats to internal or external validity, barriers to implementing an intervention and other issues inherent to the study design. 
• Overstate the importance of your findings. Making grand statements about how a study will fully resolve large questions can lead readers to doubt the success of the research. 

Snippets of Effective Discussions:

Consumer-based actions to reduce plastic pollution in rivers: A multi-criteria decision analysis approach

Identifying reliable indicators of fitness in polar bears

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Organizing Your Social Sciences Research Paper

• 8. The Discussion
• Purpose of Guide
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• Reading Research Effectively
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The purpose of the discussion section is to interpret and describe the significance of your findings in relation to what was already known about the research problem being investigated and to explain any new understanding or insights that emerged as a result of your research. The discussion will always connect to the introduction by way of the research questions or hypotheses you posed and the literature you reviewed, but the discussion does not simply repeat or rearrange the first parts of your paper; the discussion clearly explains how your study advanced the reader's understanding of the research problem from where you left them at the end of your review of prior research.

Annesley, Thomas M. “The Discussion Section: Your Closing Argument.” Clinical Chemistry 56 (November 2010): 1671-1674; Peacock, Matthew. “Communicative Moves in the Discussion Section of Research Articles.” System 30 (December 2002): 479-497.

Importance of a Good Discussion

The discussion section is often considered the most important part of your research paper because it:

• Most effectively demonstrates your ability as a researcher to think critically about an issue, to develop creative solutions to problems based upon a logical synthesis of the findings, and to formulate a deeper, more profound understanding of the research problem under investigation;
• Presents the underlying meaning of your research, notes possible implications in other areas of study, and explores possible improvements that can be made in order to further develop the concerns of your research;
• Highlights the importance of your study and how it can contribute to understanding the research problem within the field of study;
• Presents how the findings from your study revealed and helped fill gaps in the literature that had not been previously exposed or adequately described; and,
• Engages the reader in thinking critically about issues based on an evidence-based interpretation of findings; it is not governed strictly by objective reporting of information.

Annesley Thomas M. “The Discussion Section: Your Closing Argument.” Clinical Chemistry 56 (November 2010): 1671-1674; Bitchener, John and Helen Basturkmen. “Perceptions of the Difficulties of Postgraduate L2 Thesis Students Writing the Discussion Section.” Journal of English for Academic Purposes 5 (January 2006): 4-18; Kretchmer, Paul. Fourteen Steps to Writing an Effective Discussion Section. San Francisco Edit, 2003-2008.

Structure and Writing Style

I.  General Rules

These are the general rules you should adopt when composing your discussion of the results :

• Do not be verbose or repetitive; be concise and make your points clearly
• Avoid the use of jargon or undefined technical language
• Follow a logical stream of thought; in general, interpret and discuss the significance of your findings in the same sequence you described them in your results section [a notable exception is to begin by highlighting an unexpected result or a finding that can grab the reader's attention]
• Use the present verb tense, especially for established facts; however, refer to specific works or prior studies in the past tense
• If needed, use subheadings to help organize your discussion or to categorize your interpretations into themes

II.  The Content

The content of the discussion section of your paper most often includes :

• Explanation of results : Comment on whether or not the results were expected for each set of findings; go into greater depth to explain findings that were unexpected or especially profound. If appropriate, note any unusual or unanticipated patterns or trends that emerged from your results and explain their meaning in relation to the research problem.
• References to previous research : Either compare your results with the findings from other studies or use the studies to support a claim. This can include re-visiting key sources already cited in your literature review section, or, save them to cite later in the discussion section if they are more important to compare with your results instead of being a part of the general literature review of prior research used to provide context and background information. Note that you can make this decision to highlight specific studies after you have begun writing the discussion section.
• Deduction : A claim for how the results can be applied more generally. For example, describing lessons learned, proposing recommendations that can help improve a situation, or highlighting best practices.
• Hypothesis : A more general claim or possible conclusion arising from the results [which may be proved or disproved in subsequent research]. This can be framed as new research questions that emerged as a consequence of your analysis.

III.  Organization and Structure

Keep the following sequential points in mind as you organize and write the discussion section of your paper:

• Think of your discussion as an inverted pyramid. Organize the discussion from the general to the specific, linking your findings to the literature, then to theory, then to practice [if appropriate].
• Use the same key terms, narrative style, and verb tense [present] that you used when describing the research problem in your introduction.
• Begin by briefly re-stating the research problem you were investigating and answer all of the research questions underpinning the problem that you posed in the introduction.
• Describe the patterns, principles, and relationships shown by each major findings and place them in proper perspective. The sequence of this information is important; first state the answer, then the relevant results, then cite the work of others. If appropriate, refer the reader to a figure or table to help enhance the interpretation of the data [either within the text or as an appendix].
• Regardless of where it's mentioned, a good discussion section includes analysis of any unexpected findings. This part of the discussion should begin with a description of the unanticipated finding, followed by a brief interpretation as to why you believe it appeared and, if necessary, its possible significance in relation to the overall study. If more than one unexpected finding emerged during the study, describe each of them in the order they appeared as you gathered or analyzed the data. As noted, the exception to discussing findings in the same order you described them in the results section would be to begin by highlighting the implications of a particularly unexpected or significant finding that emerged from the study, followed by a discussion of the remaining findings.
• Before concluding the discussion, identify potential limitations and weaknesses if you do not plan to do so in the conclusion of the paper. Comment on their relative importance in relation to your overall interpretation of the results and, if necessary, note how they may affect the validity of your findings. Avoid using an apologetic tone; however, be honest and self-critical [e.g., in retrospect, had you included a particular question in a survey instrument, additional data could have been revealed].
• The discussion section should end with a concise summary of the principal implications of the findings regardless of their significance. Give a brief explanation about why you believe the findings and conclusions of your study are important and how they support broader knowledge or understanding of the research problem. This can be followed by any recommendations for further research. However, do not offer recommendations which could have been easily addressed within the study. This would demonstrate to the reader that you have inadequately examined and interpreted the data.

IV.  Overall Objectives

The objectives of your discussion section should include the following: I.  Reiterate the Research Problem/State the Major Findings

Briefly reiterate the research problem or problems you are investigating and the methods you used to investigate them, then move quickly to describe the major findings of the study. You should write a direct, declarative, and succinct proclamation of the study results, usually in one paragraph.

II.  Explain the Meaning of the Findings and Why They are Important

No one has thought as long and hard about your study as you have. Systematically explain the underlying meaning of your findings and state why you believe they are significant. After reading the discussion section, you want the reader to think critically about the results and why they are important. You don’t want to force the reader to go through the paper multiple times to figure out what it all means. If applicable, begin this part of the section by repeating what you consider to be your most significant or unanticipated finding first, then systematically review each finding. Otherwise, follow the general order you reported the findings presented in the results section.

III.  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 results to those found in other studies, particularly if questions raised from prior studies served as the motivation for your research. 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 study differs from other research about the topic. Note that any significant or unanticipated finding is often because there was no prior research to indicate the finding could occur. If there is prior research to indicate this, you need to explain why it was significant or unanticipated. IV.  Consider Alternative Explanations of the Findings

It is important to remember that the purpose of research in the social sciences is to discover and not to prove . When writing the discussion section, you should carefully consider all possible explanations for the study results, rather than just those that fit your hypothesis or prior assumptions and biases. This is especially important when describing the discovery of significant or unanticipated findings.

V.  Acknowledge the Study’s Limitations

It is far better for you to identify and acknowledge your study’s limitations than to have them pointed out by your professor! Note any unanswered questions or issues your study could not address and describe the generalizability of your results to other situations. If a limitation is applicable to the method chosen to gather information, then describe in detail the problems you encountered and why. VI.  Make Suggestions for Further Research

You may choose to conclude the discussion section by making suggestions for further research [as opposed to offering suggestions in the conclusion of your paper]. Although your study can offer important insights about the research problem, this is where you can address other questions related to the problem that remain unanswered or highlight hidden issues that were revealed as a result of conducting your research. You should frame your suggestions by linking the need for further research to the limitations of your study [e.g., in future studies, the survey instrument should include more questions that ask..."] or linking to critical issues revealed from the data that were not considered initially in your research.

NOTE: Besides the literature review section, the preponderance of references to sources is usually found in the discussion section . A few historical references may be helpful for perspective, but most of the references should be relatively recent and included to aid in the interpretation of your results, to support the significance of a finding, and/or to place a finding within a particular context. If a study that you cited does not support your findings, don't ignore it--clearly explain why your research findings differ from theirs.

V.  Problems to Avoid

• Do not waste time restating your results . Should you need to remind the reader of a finding to be discussed, use "bridge sentences" that relate the result to the interpretation. An example would be: “In the case of determining available housing to single women with children in rural areas of Texas, the findings suggest that access to good schools is important...," then move on to further explaining this finding and its implications.
• As noted, recommendations for further research can be included in either the discussion or conclusion of your paper, but do not repeat your recommendations in the both sections. Think about the overall narrative flow of your paper to determine where best to locate this information. However, if your findings raise a lot of new questions or issues, consider including suggestions for further research in the discussion section.
• Do not introduce new results in the discussion section. Be wary of mistaking the reiteration of a specific finding for an interpretation because it may confuse the reader. The description of findings [results section] and the interpretation of their significance [discussion section] should be distinct parts of your paper. If you choose to combine the results section and the discussion section into a single narrative, you must be clear in how you report the information discovered and your own interpretation of each finding. This approach is not recommended if you lack experience writing college-level research papers.
• Use of the first person pronoun is generally acceptable. Using first person singular pronouns can help emphasize a point or illustrate a contrasting finding. However, keep in mind that too much use of the first person can actually distract the reader from the main points [i.e., I know you're telling me this--just tell me!].

Analyzing vs. Summarizing. Department of English Writing Guide. George Mason University; Discussion. The Structure, Format, Content, and Style of a Journal-Style Scientific Paper. Department of Biology. Bates College; Hess, Dean R. "How to Write an Effective Discussion." Respiratory Care 49 (October 2004); Kretchmer, Paul. Fourteen Steps to Writing to Writing an Effective Discussion Section. San Francisco Edit, 2003-2008; The Lab Report. University College Writing Centre. University of Toronto; Sauaia, A. et al. "The Anatomy of an Article: The Discussion Section: "How Does the Article I Read Today Change What I Will Recommend to my Patients Tomorrow?” The Journal of Trauma and Acute Care Surgery 74 (June 2013): 1599-1602; Research Limitations & Future Research . Lund Research Ltd., 2012; Summary: Using it Wisely. The Writing Center. University of North Carolina; Schafer, Mickey S. Writing the Discussion. Writing in Psychology course syllabus. University of Florida; Yellin, Linda L. A Sociology Writer's Guide . Boston, MA: Allyn and Bacon, 2009.

Writing Tip

Don’t Over-Interpret the Results!

Interpretation is a subjective exercise. As such, you should always approach the selection and interpretation of your findings introspectively and to think critically about the possibility of judgmental biases unintentionally entering into discussions about the significance of your work. With this in mind, be careful that you do not read more into the findings than can be supported by the evidence you have gathered. Remember that the data are the data: nothing more, nothing less.

MacCoun, Robert J. "Biases in the Interpretation and Use of Research Results." Annual Review of Psychology 49 (February 1998): 259-287; Ward, Paulet al, editors. The Oxford Handbook of Expertise . Oxford, UK: Oxford University Press, 2018.

Another Writing Tip

Don't Write Two Results Sections!

One of the most common mistakes that you can make when discussing the results of your study is to present a superficial interpretation of the findings that more or less re-states the results section of your paper. Obviously, you must refer to your results when discussing them, but focus on the interpretation of those results and their significance in relation to the research problem, not the data itself.

Azar, Beth. "Discussing Your Findings."  American Psychological Association gradPSYCH Magazine (January 2006).

Yet Another Writing Tip

Avoid Unwarranted Speculation!

The discussion section should remain focused on the findings of your study. For example, if the purpose of your research was to measure the impact of foreign aid on increasing access to education among disadvantaged children in Bangladesh, it would not be appropriate to speculate about how your findings might apply to populations in other countries without drawing from existing studies to support your claim or if analysis of other countries was not a part of your original research design. If you feel compelled to speculate, do so in the form of describing possible implications or explaining possible impacts. Be certain that you clearly identify your comments as speculation or as a suggestion for where further research is needed. Sometimes your professor will encourage you to expand your discussion of the results in this way, while others don’t care what your opinion is beyond your effort to interpret the data in relation to the research problem.

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Organizing Academic Research Papers: 8. The Discussion

• Purpose of Guide
• Design Flaws to Avoid
• 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
• Background Information
• The Research Problem/Question
• Theoretical Framework
• Citation Tracking
• Content Alert Services
• Evaluating Sources
• Primary Sources
• Secondary Sources
• Tertiary Sources
• What Is Scholarly vs. Popular?
• Qualitative Methods
• Quantitative Methods
• Using Non-Textual Elements
• Limitations of the Study
• Common Grammar Mistakes
• Avoiding Plagiarism
• Footnotes or Endnotes?
• Further Readings
• Annotated Bibliography
• Dealing with Nervousness
• Using Visual Aids
• Grading Someone Else's Paper
• How to Manage Group Projects
• Multiple Book Review Essay
• Reviewing Collected Essays
• About Informed Consent
• Writing Field Notes
• Writing a Policy Memo
• Writing a Research Proposal
• Acknowledgements

The purpose of the discussion is to interpret and describe the significance of your findings in light of what was already known about the research problem being investigated, and to explain any new understanding or fresh insights about the problem after you've taken the findings into consideration. The discussion will always connect to the introduction by way of the research questions or hypotheses you posed and the literature you reviewed, but it does not simply repeat or rearrange the introduction; the discussion should always explain how your study has moved the reader's understanding of the research problem forward from where you left them at the end of the introduction.

Importance of a Good Discussion

This section is often considered the most important part of a research paper because it most effectively demonstrates your ability as a researcher to think critically about an issue, to develop creative solutions to problems based on the findings, and to formulate a deeper, more profound understanding of the research problem you are studying.

The discussion section is where you explore the underlying meaning of your research , its possible implications in other areas of study, and the possible improvements that can be made in order to further develop the concerns of your research.

This is the section where you need to present the importance of your study and how it may be able to contribute to and/or fill existing gaps in the field. If appropriate, the discussion section is also where you state how the findings from your study revealed new gaps in the literature that had not been previously exposed or adequately described.

This part of the paper is not strictly governed by objective reporting of information but, rather, it is where you can engage in creative thinking about issues through evidence-based interpretation of findings. This is where you infuse your results with meaning.

Kretchmer, Paul. Fourteen Steps to Writing to Writing an Effective Discussion Section . San Francisco Edit, 2003-2008.

Structure and Writing Style

I.  General Rules

These are the general rules you should adopt when composing your discussion of the results :

• Do not be verbose or repetitive.
• Be concise and make your points clearly.
• Avoid using jargon.
• Follow a logical stream of thought.
• Use the present verb tense, especially for established facts; however, refer to specific works and references in the past tense.
• If needed, use subheadings to help organize your presentation or to group your interpretations into themes.

II.  The Content

The content of the discussion section of your paper most often includes :

• Explanation of results : comment on whether or not the results were expected and present explanations for the results; go into greater depth when explaining findings that were unexpected or especially profound. If appropriate, note any unusual or unanticipated patterns or trends that emerged from your results and explain their meaning.
• References to previous research : compare your results with the findings from other studies, or use the studies to support a claim. This can include re-visiting key sources already cited in your literature review section, or, save them to cite later in the discussion section if they are more important to compare with your results than being part of the general research you cited to provide context and background information.
• Deduction : a claim for how the results can be applied more generally. For example, describing lessons learned, proposing recommendations that can help improve a situation, or recommending best practices.
• Hypothesis : a more general claim or possible conclusion arising from the results [which may be proved or disproved in subsequent research].

III. Organization and Structure

Keep the following sequential points in mind as you organize and write the discussion section of your paper:

• Think of your discussion as an inverted pyramid. Organize the discussion from the general to the specific, linking your findings to the literature, then to theory, then to practice [if appropriate].
• Use the same key terms, mode of narration, and verb tense [present] that you used when when describing the research problem in the introduction.
• Begin by briefly re-stating the research problem you were investigating and answer all of the research questions underpinning the problem that you posed in the introduction.
• Describe the patterns, principles, and relationships shown by each major findings and place them in proper perspective. The sequencing of providing this information is important; first state the answer, then the relevant results, then cite the work of others. If appropriate, refer the reader to a figure or table to help enhance the interpretation of the data. The order of interpreting each major finding should be in the same order as they were described in your results section.
• A good discussion section includes analysis of any unexpected findings. This paragraph should begin with a description of the unexpected finding, followed by a brief interpretation as to why you believe it appeared and, if necessary, its possible significance in relation to the overall study. If more than one unexpected finding emerged during the study, describe each them in the order they appeared as you gathered the data.
• Before concluding the discussion, identify potential limitations and weaknesses. Comment on their relative importance in relation to your overall interpretation of the results and, if necessary, note how they may affect the validity of the findings. Avoid using an apologetic tone; however, be honest and self-critical.
• The discussion section should end with a concise summary of the principal implications of the findings regardless of statistical significance. Give a brief explanation about why you believe the findings and conclusions of your study are important and how they support broader knowledge or understanding of the research problem. This can be followed by any recommendations for further research. However, do not offer recommendations which could have been easily addressed within the study. This demonstrates to the reader you have inadequately examined and interpreted the data.

IV.  Overall Objectives

The objectives of your discussion section should include the following: I.  Reiterate the Research Problem/State the Major Findings

Briefly reiterate for your readers the research problem or problems you are investigating and the methods you used to investigate them, then move quickly to describe the major findings of the study. You should write a direct, declarative, and succinct proclamation of the study results.

II.  Explain the Meaning of the Findings and Why They are Important

No one has thought as long and hard about your study as you have. Systematically explain the meaning of the findings and why you believe they are important. After reading the discussion section, you want the reader to think about the results [“why hadn’t I thought of that?”]. You don’t want to force the reader to go through the paper multiple times to figure out what it all means. Begin this part of the section by repeating what you consider to be your most important finding first.

III.  Relate the Findings to Similar Studies

No study is so novel or possesses such a restricted focus that it has absolutely no relation to other previously published research. The discussion section should relate your study findings to those of other studies, particularly if questions raised by previous studies served as the motivation for your study, the findings of other studies support your findings [which strengthens the importance of your study results], and/or they point out how your study differs from other similar studies. IV.  Consider Alternative Explanations of the Findings

It is important to remember that the purpose of research is to discover and not to prove . When writing the discussion section, you should carefully consider all possible explanations for the study results, rather than just those that fit your prior assumptions or biases.

V.  Acknowledge the Study’s Limitations

It is far better for you to identify and acknowledge your study’s limitations than to have them pointed out by your professor! Describe the generalizability of your results to other situations, if applicable to the method chosen, then describe in detail problems you encountered in the method(s) you used to gather information. Note any unanswered questions or issues your study did not address, and.... VI.  Make Suggestions for Further Research

Although your study may offer important insights about the research problem, other questions related to the problem likely remain unanswered. Moreover, some unanswered questions may have become more focused because of your study. You should make suggestions for further research in the discussion section.

NOTE: Besides the literature review section, the preponderance of references to sources in your research paper are usually found in the discussion section . A few historical references may be helpful for perspective but most of the references should be relatively recent and included to aid in the interpretation of your results and/or linked to similar studies. If a study that you cited disagrees with your findings, don't ignore it--clearly explain why the study's findings differ from yours.

V.  Problems to Avoid

• Do not waste entire sentences restating your results . Should you need to remind the reader of the finding to be discussed, use "bridge sentences" that relate the result to the interpretation. An example would be: “The lack of available housing to single women with children in rural areas of Texas suggests that...[then move to the interpretation of this finding].”
• Recommendations for further research can be included in either the discussion or conclusion of your paper but do not repeat your recommendations in the both sections.
• Do not introduce new results in the discussion. Be wary of mistaking the reiteration of a specific finding for an interpretation.
• Use of the first person is acceptable, but too much use of the first person may actually distract the reader from the main points.

Analyzing vs. Summarizing. Department of English Writing Guide. George Mason University; Discussion . The Structure, Format, Content, and Style of a Journal-Style Scientific Paper. Department of Biology. Bates College; Hess, Dean R. How to Write an Effective Discussion. Respiratory Care 49 (October 2004); Kretchmer, Paul. Fourteen Steps to Writing to Writing an Effective Discussion Section . San Francisco Edit, 2003-2008; The Lab Report . University College Writing Centre. University of Toronto; Summary: Using it Wisely . The Writing Center. University of North Carolina; Schafer, Mickey S. Writing the Discussion . Writing in Psychology course syllabus. University of Florida; Yellin, Linda L. A Sociology Writer's Guide. Boston, MA: Allyn and Bacon, 2009.

Writing Tip

Don’t Overinterpret the Results!

Interpretation is a subjective exercise. Therefore, be careful that you do not read more into the findings than can be supported by the evidence you've gathered. Remember that the data are the data: nothing more, nothing less.

Another Writing Tip

Don't Write Two Results Sections!

One of the most common mistakes that you can make when discussing the results of your study is to present a superficial interpretation of the findings that more or less re-states the results section of your paper. Obviously, you must refer to your results when discussing them, but focus on the interpretion of those results, not just the data itself.

Azar, Beth. Discussing Your Findings.  American Psychological Association gradPSYCH Magazine (January 2006)

Yet Another Writing Tip

Avoid Unwarranted Speculation!

The discussion section should remain focused on the findings of your study. For example, if you studied the impact of foreign aid on increasing levels of education among the poor in Bangladesh, it's generally not appropriate to speculate about how your findings might apply to populations in other countries without drawing from existing studies to support your claim. If you feel compelled to speculate, be certain that you clearly identify your comments as speculation or as a suggestion for where further research is needed. Sometimes your professor will encourage you to expand the discussion in this way, while others don’t care what your opinion is beyond your efforts to interpret the data.

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Writing a scientific paper.

• Writing a lab report
• INTRODUCTION

Writing a "good" discussion section

"discussion and conclusions checklist" from: how to write a good scientific paper. chris a. mack. spie. 2018., peer review.

• LITERATURE CITED
• Bibliography of guides to scientific writing and presenting
• Presentations
• Lab Report Writing Guides on the Web

This is is usually the hardest section to write. You are trying to bring out the true meaning of your data without being too long. Do not use words to conceal your facts or reasoning. Also do not repeat your results, this is a discussion.

• Present principles, relationships and generalizations shown by the results
• Point out exceptions or lack of correlations. Define why you think this is so.
• Show how your results agree or disagree with previously published works
• Discuss the theoretical implications of your work as well as practical applications
• State your conclusions clearly. Summarize your evidence for each conclusion.
• Discuss the significance of the results
•  Evidence does not explain itself; the results must be presented and then explained.
• Typical stages in the discussion: summarizing the results, discussing whether results are expected or unexpected, comparing these results to previous work, interpreting and explaining the results (often by comparison to a theory or model), and hypothesizing about their generality.
• Discuss any problems or shortcomings encountered during the course of the work.
• Discuss possible alternate explanations for the results.
• Avoid: presenting results that are never discussed; presenting discussion that does not relate to any of the results; presenting results and discussion in chronological order rather than logical order; ignoring results that do not support the conclusions; drawing conclusions from results without logical arguments to back them up. 

CONCLUSIONS

• Provide a very brief summary of the Results and Discussion.
• Emphasize the implications of the findings, explaining how the work is significant and providing the key message(s) the author wishes to convey.
• Provide the most general claims that can be supported by the evidence.
• Provide a future perspective on the work.
• Avoid: repeating the abstract; repeating background information from the Introduction; introducing new evidence or new arguments not found in the Results and Discussion; repeating the arguments made in the Results and Discussion; failing to address all of the research questions set out in the Introduction. 

WHAT HAPPENS AFTER I COMPLETE MY PAPER?

 The peer review process is the quality control step in the publication of ideas.  Papers that are submitted to a journal for publication are sent out to several scientists (peers) who look carefully at the paper to see if it is "good science".  These reviewers then recommend to the editor of a journal whether or not a paper should be published. Most journals have publication guidelines. Ask for them and follow them exactly.    Peer reviewers examine the soundness of the materials and methods section.  Are the materials and methods used written clearly enough for another scientist to reproduce the experiment?  Other areas they look at are: originality of research, significance of research question studied, soundness of the discussion and interpretation, correct spelling and use of technical terms, and length of the article.

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How to Write the Discussion Section of a Research Paper

The discussion section of a research paper analyzes and interprets the findings, provides context, compares them with previous studies, identifies limitations, and suggests future research directions.

Updated on September 15, 2023

Structure your discussion section right, and you’ll be cited more often while doing a greater service to the scientific community. So, what actually goes into the discussion section? And how do you write it?

The discussion section of your research paper is where you let the reader know how your study is positioned in the literature, what to take away from your paper, and how your work helps them. It can also include your conclusions and suggestions for future studies.

First, we’ll define all the parts of your discussion paper, and then look into how to write a strong, effective discussion section for your paper or manuscript.

Discussion section: what is it, what it does

The discussion section comes later in your paper, following the introduction, methods, and results. The discussion sets up your study’s conclusions. Its main goals are to present, interpret, and provide a context for your results.

What is it?

The discussion section provides an analysis and interpretation of the findings, compares them with previous studies, identifies limitations, and suggests future directions for research.

This section combines information from the preceding parts of your paper into a coherent story. By this point, the reader already knows why you did your study (introduction), how you did it (methods), and what happened (results). In the discussion, you’ll help the reader connect the ideas from these sections.

Why is it necessary?

The discussion provides context and interpretations for the results. It also answers the questions posed in the introduction. While the results section describes your findings, the discussion explains what they say. This is also where you can describe the impact or implications of your research.

Adds context for your results

Most research studies aim to answer a question, replicate a finding, or address limitations in the literature. These goals are first described in the introduction. However, in the discussion section, the author can refer back to them to explain how the study's objective was achieved. 

Shows what your results actually mean and real-world implications

The discussion can also describe the effect of your findings on research or practice. How are your results significant for readers, other researchers, or policymakers?

What to include in your discussion (in the correct order)

A complete and effective discussion section should at least touch on the points described below.

Summary of key findings

The discussion should begin with a brief factual summary of the results. Concisely overview the main results you obtained.

Begin with key findings with supporting evidence

Your results section described a list of findings, but what message do they send when you look at them all together?

Your findings were detailed in the results section, so there’s no need to repeat them here, but do provide at least a few highlights. This will help refresh the reader’s memory and help them focus on the big picture.

Read the first paragraph of the discussion section in this article (PDF) for an example of how to start this part of your paper. Notice how the authors break down their results and follow each description sentence with an explanation of why each finding is relevant. 

State clearly and concisely

Following a clear and direct writing style is especially important in the discussion section. After all, this is where you will make some of the most impactful points in your paper. While the results section often contains technical vocabulary, such as statistical terms, the discussion section lets you describe your findings more clearly. 

Interpretation of results

Once you’ve given your reader an overview of your results, you need to interpret those results. In other words, what do your results mean? Discuss the findings’ implications and significance in relation to your research question or hypothesis.

Analyze and interpret your findings

Look into your findings and explore what’s behind them or what may have caused them. If your introduction cited theories or studies that could explain your findings, use these sources as a basis to discuss your results.

For example, look at the second paragraph in the discussion section of this article on waggling honey bees. Here, the authors explore their results based on information from the literature.

Unexpected or contradictory results

Sometimes, your findings are not what you expect. Here’s where you describe this and try to find a reason for it. Could it be because of the method you used? Does it have something to do with the variables analyzed? Comparing your methods with those of other similar studies can help with this task.

Context and comparison with previous work

Refer to related studies to place your research in a larger context and the literature. Compare and contrast your findings with existing literature, highlighting similarities, differences, and/or contradictions.

How your work compares or contrasts with previous work

Studies with similar findings to yours can be cited to show the strength of your findings. Information from these studies can also be used to help explain your results. Differences between your findings and others in the literature can also be discussed here. 

How to divide this section into subsections

If you have more than one objective in your study or many key findings, you can dedicate a separate section to each of these. Here’s an example of this approach. You can see that the discussion section is divided into topics and even has a separate heading for each of them. 

Limitations

Many journals require you to include the limitations of your study in the discussion. Even if they don’t, there are good reasons to mention these in your paper.

Why limitations don’t have a negative connotation

A study’s limitations are points to be improved upon in future research. While some of these may be flaws in your method, many may be due to factors you couldn’t predict.

Examples include time constraints or small sample sizes. Pointing this out will help future researchers avoid or address these issues. This part of the discussion can also include any attempts you have made to reduce the impact of these limitations, as in this study .

How limitations add to a researcher's credibility

Pointing out the limitations of your study demonstrates transparency. It also shows that you know your methods well and can conduct a critical assessment of them.  

Implications and significance

The final paragraph of the discussion section should contain the take-home messages for your study. It can also cite the “strong points” of your study, to contrast with the limitations section.

Restate your hypothesis

Remind the reader what your hypothesis was before you conducted the study. 

How was it proven or disproven?

Identify your main findings and describe how they relate to your hypothesis.

How your results contribute to the literature

Were you able to answer your research question? Or address a gap in the literature?

Future implications of your research

Describe the impact that your results may have on the topic of study. Your results may show, for instance, that there are still limitations in the literature for future studies to address. There may be a need for studies that extend your findings in a specific way. You also may need additional research to corroborate your findings. 

Sample discussion section

This fictitious example covers all the aspects discussed above. Your actual discussion section will probably be much longer, but you can read this to get an idea of everything your discussion should cover.

Our results showed that the presence of cats in a household is associated with higher levels of perceived happiness by its human occupants. These findings support our hypothesis and demonstrate the association between pet ownership and well-being. 

The present findings align with those of Bao and Schreer (2016) and Hardie et al. (2023), who observed greater life satisfaction in pet owners relative to non-owners. Although the present study did not directly evaluate life satisfaction, this factor may explain the association between happiness and cat ownership observed in our sample.

Our findings must be interpreted in light of some limitations, such as the focus on cat ownership only rather than pets as a whole. This may limit the generalizability of our results.

Nevertheless, this study had several strengths. These include its strict exclusion criteria and use of a standardized assessment instrument to investigate the relationships between pets and owners. These attributes bolster the accuracy of our results and reduce the influence of confounding factors, increasing the strength of our conclusions. Future studies may examine the factors that mediate the association between pet ownership and happiness to better comprehend this phenomenon.

This brief discussion begins with a quick summary of the results and hypothesis. The next paragraph cites previous research and compares its findings to those of this study. Information from previous studies is also used to help interpret the findings. After discussing the results of the study, some limitations are pointed out. The paper also explains why these limitations may influence the interpretation of results. Then, final conclusions are drawn based on the study, and directions for future research are suggested.

How to make your discussion flow naturally

If you find writing in scientific English challenging, the discussion and conclusions are often the hardest parts of the paper to write. That’s because you’re not just listing up studies, methods, and outcomes. You’re actually expressing your thoughts and interpretations in words.

• How formal should it be?
• What words should you use, or not use?
• How do you meet strict word limits, or make it longer and more informative?

Always give it your best, but sometimes a helping hand can, well, help. Getting a professional edit can help clarify your work’s importance while improving the English used to explain it. When readers know the value of your work, they’ll cite it. We’ll assign your study to an expert editor knowledgeable in your area of research. Their work will clarify your discussion, helping it to tell your story. Find out more about AJE Editing.

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General Research Paper Guidelines: Discussion

Discussion section.

The overall purpose of a research paper’s discussion section is to evaluate and interpret results, while explaining both the implications and limitations of your findings. Per APA (2020) guidelines, this section requires you to “examine, interpret, and qualify the results and draw inferences and conclusions from them” (p. 89). Discussion sections also require you to detail any new insights, think through areas for future research, highlight the work that still needs to be done to further your topic, and provide a clear conclusion to your research paper. In a good discussion section, you should do the following:

• Clearly connect the discussion of your results to your introduction, including your central argument, thesis, or problem statement.
• Provide readers with a critical thinking through of your results, answering the “so what?” question about each of your findings. In other words, why is this finding important?
• Detail how your research findings might address critical gaps or problems in your field
• Compare your results to similar studies’ findings
• Provide the possibility of alternative interpretations, as your goal as a researcher is to “discover” and “examine” and not to “prove” or “disprove.” Instead of trying to fit your results into your hypothesis, critically engage with alternative interpretations to your results.

For more specific details on your Discussion section, be sure to review Sections 3.8 (pp. 89-90) and 3.16 (pp. 103-104) of your 7 th edition APA manual

*Box content adapted from:

University of Southern California (n.d.). Organizing your social sciences research paper: 8 the discussion . https://libguides.usc.edu/writingguide/discussion

Limitations

Limitations of generalizability or utility of findings, often over which the researcher has no control, should be detailed in your Discussion section. Including limitations for your reader allows you to demonstrate you have thought critically about your given topic, understood relevant literature addressing your topic, and chosen the methodology most appropriate for your research. It also allows you an opportunity to suggest avenues for future research on your topic. An effective limitations section will include the following:

• Detail (a) sources of potential bias, (b) possible imprecision of measures, (c) other limitations or weaknesses of the study, including any methodological or researcher limitations.
• Sample size: In quantitative research, if a sample size is too small, it is more difficult to generalize results.
• Lack of available/reliable data : In some cases, data might not be available or reliable, which will ultimately affect the overall scope of your research. Use this as an opportunity to explain areas for future study.
• Lack of prior research on your study topic: In some cases, you might find that there is very little or no similar research on your study topic, which hinders the credibility and scope of your own research. If this is the case, use this limitation as an opportunity to call for future research. However, make sure you have done a thorough search of the available literature before making this claim.
• Flaws in measurement of data: Hindsight is 20/20, and you might realize after you have completed your research that the data tool you used actually limited the scope or results of your study in some way. Again, acknowledge the weakness and use it as an opportunity to highlight areas for future study.
• Limits of self-reported data: In your research, you are assuming that any participants will be honest and forthcoming with responses or information they provide to you. Simply acknowledging this assumption as a possible limitation is important in your research.
• Access: Most research requires that you have access to people, documents, organizations, etc.. However, for various reasons, access is sometimes limited or denied altogether. If this is the case, you will want to acknowledge access as a limitation to your research.
• Time: Choosing a research focus that is narrow enough in scope to finish in a given time period is important. If such limitations of time prevent you from certain forms of research, access, or study designs, acknowledging this time restraint is important. Acknowledging such limitations is important, as they can point other researchers to areas that require future study.
• Potential Bias: All researchers have some biases, so when reading and revising your draft, pay special attention to the possibilities for bias in your own work. Such bias could be in the form you organized people, places, participants, or events. They might also exist in the method you selected or the interpretation of your results. Acknowledging such bias is an important part of the research process.
• Language Fluency: On occasion, researchers or research participants might have language fluency issues, which could potentially hinder results or how effectively you interpret results. If this is an issue in your research, make sure to acknowledge it in your limitations section.

University of Southern California (n.d.). Organizing your social sciences research paper: Limitations of the study . https://libguides.usc.edu/writingguide/limitations

In many research papers, the conclusion, like the limitations section, is folded into the larger discussion section. If you are unsure whether to include the conclusion as part of your discussion or as a separate section, be sure to defer to the assignment instructions or ask your instructor.

The conclusion is important, as it is specifically designed to highlight your research’s larger importance outside of the specific results of your study. Your conclusion section allows you to reiterate the main findings of your study, highlight their importance, and point out areas for future research. Based on the scope of your paper, your conclusion could be anywhere from one to three paragraphs long. An effective conclusion section should include the following:

• Describe the possibilities for continued research on your topic, including what might be improved, adapted, or added to ensure useful and informed future research.
• Provide a detailed account of the importance of your findings
• Reiterate why your problem is important, detail how your interpretation of results impacts the subfield of study, and what larger issues both within and outside of your field might be affected from such results

University of Southern California (n.d.). Organizing your social sciences research paper: 9. the conclusion . https://libguides.usc.edu/writingguide/conclusion

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Guide to Writing the Results and Discussion Sections of a Scientific Article

A quality research paper has both the qualities of in-depth research and good writing ( Bordage, 2001 ). In addition, a research paper must be clear, concise, and effective when presenting the information in an organized structure with a logical manner ( Sandercock, 2013 ).

In this article, we will take a closer look at the results and discussion section. Composing each of these carefully with sufficient data and well-constructed arguments can help improve your paper overall.

The results section of your research paper contains a description about the main findings of your research, whereas the discussion section interprets the results for readers and provides the significance of the findings. The discussion should not repeat the results.

Let’s dive in a little deeper about how to properly, and clearly organize each part.

How to Organize the Results Section

Since your results follow your methods, you’ll want to provide information about what you discovered from the methods you used, such as your research data. In other words, what were the outcomes of the methods you used?

You may also include information about the measurement of your data, variables, treatments, and statistical analyses.

To start, organize your research data based on how important those are in relation to your research questions. This section should focus on showing major results that support or reject your research hypothesis. Include your least important data as supplemental materials when submitting to the journal.

The next step is to prioritize your research data based on importance – focusing heavily on the information that directly relates to your research questions using the subheadings.

The organization of the subheadings for the results section usually mirrors the methods section. It should follow a logical and chronological order.

Subheading organization

Subheadings within your results section are primarily going to detail major findings within each important experiment. And the first paragraph of your results section should be dedicated to your main findings (findings that answer your overall research question and lead to your conclusion) (Hofmann, 2013).

In the book “Writing in the Biological Sciences,” author Angelika Hofmann recommends you structure your results subsection paragraphs as follows:

• Experimental purpose
• Interpretation

Each subheading may contain a combination of ( Bahadoran, 2019 ; Hofmann, 2013, pg. 62-63):

• Text: to explain about the research data
• Figures: to display the research data and to show trends or relationships, for examples using graphs or gel pictures.
• Tables: to represent a large data and exact value

Decide on the best way to present your data — in the form of text, figures or tables (Hofmann, 2013).

Data or Results?

Sometimes we get confused about how to differentiate between data and results . Data are information (facts or numbers) that you collected from your research ( Bahadoran, 2019 ).

Whereas, results are the texts presenting the meaning of your research data ( Bahadoran, 2019 ).

One mistake that some authors often make is to use text to direct the reader to find a specific table or figure without further explanation. This can confuse readers when they interpret data completely different from what the authors had in mind. So, you should briefly explain your data to make your information clear for the readers.

Common Elements in Figures and Tables

Figures and tables present information about your research data visually. The use of these visual elements is necessary so readers can summarize, compare, and interpret large data at a glance. You can use graphs or figures to compare groups or patterns. Whereas, tables are ideal to present large quantities of data and exact values.

Several components are needed to create your figures and tables. These elements are important to sort your data based on groups (or treatments). It will be easier for the readers to see the similarities and differences among the groups.

When presenting your research data in the form of figures and tables, organize your data based on the steps of the research leading you into a conclusion.

Common elements of the figures (Bahadoran, 2019):

• Figure number
• Figure title
• Figure legend (for example a brief title, experimental/statistical information, or definition of symbols).

Tables in the result section may contain several elements (Bahadoran, 2019):

• Table number
• Table title
• Row headings (for example groups)
• Column headings
• Row subheadings (for example categories or groups)
• Column subheadings (for example categories or variables)
• Footnotes (for example statistical analyses)

Tips to Write the Results Section

• Direct the reader to the research data and explain the meaning of the data.
• Avoid using a repetitive sentence structure to explain a new set of data.
• Write and highlight important findings in your results.
• Use the same order as the subheadings of the methods section.
• Match the results with the research questions from the introduction. Your results should answer your research questions.
• Be sure to mention the figures and tables in the body of your text.
• Make sure there is no mismatch between the table number or the figure number in text and in figure/tables.
• Only present data that support the significance of your study. You can provide additional data in tables and figures as supplementary material.

How to Organize the Discussion Section

It’s not enough to use figures and tables in your results section to convince your readers about the importance of your findings. You need to support your results section by providing more explanation in the discussion section about what you found.

In the discussion section, based on your findings, you defend the answers to your research questions and create arguments to support your conclusions.

Below is a list of questions to guide you when organizing the structure of your discussion section ( Viera et al ., 2018 ):

• What experiments did you conduct and what were the results?
• What do the results mean?
• What were the important results from your study?
• How did the results answer your research questions?
• Did your results support your hypothesis or reject your hypothesis?
• What are the variables or factors that might affect your results?
• What were the strengths and limitations of your study?
• What other published works support your findings?
• What other published works contradict your findings?
• What possible factors might cause your findings different from other findings?
• What is the significance of your research?
• What are new research questions to explore based on your findings?

Organizing the Discussion Section

The structure of the discussion section may be different from one paper to another, but it commonly has a beginning, middle-, and end- to the section.

One way to organize the structure of the discussion section is by dividing it into three parts (Ghasemi, 2019):

• The beginning: The first sentence of the first paragraph should state the importance and the new findings of your research. The first paragraph may also include answers to your research questions mentioned in your introduction section.
• The middle: The middle should contain the interpretations of the results to defend your answers, the strength of the study, the limitations of the study, and an update literature review that validates your findings.
• The end: The end concludes the study and the significance of your research.

Another possible way to organize the discussion section was proposed by Michael Docherty in British Medical Journal: is by using this structure ( Docherty, 1999 ):

• Discussion of important findings
• Comparison of your results with other published works
• Include the strengths and limitations of the study
• Conclusion and possible implications of your study, including the significance of your study – address why and how is it meaningful
• Future research questions based on your findings

Finally, a last option is structuring your discussion this way (Hofmann, 2013, pg. 104):

• First Paragraph: Provide an interpretation based on your key findings. Then support your interpretation with evidence.
• Secondary results
• Limitations
• Unexpected findings
• Comparisons to previous publications
• Last Paragraph: The last paragraph should provide a summarization (conclusion) along with detailing the significance, implications and potential next steps.

Remember, at the heart of the discussion section is presenting an interpretation of your major findings.

Tips to Write the Discussion Section

• Highlight the significance of your findings
• Mention how the study will fill a gap in knowledge.
• Indicate the implication of your research.
• Avoid generalizing, misinterpreting your results, drawing a conclusion with no supportive findings from your results.

Aggarwal, R., & Sahni, P. (2018). The Results Section. In Reporting and Publishing Research in the Biomedical Sciences (pp. 21-38): Springer.

Bahadoran, Z., Mirmiran, P., Zadeh-Vakili, A., Hosseinpanah, F., & Ghasemi, A. (2019). The principles of biomedical scientific writing: Results. International journal of endocrinology and metabolism, 17(2).

Bordage, G. (2001). Reasons reviewers reject and accept manuscripts: the strengths and weaknesses in medical education reports. Academic medicine, 76(9), 889-896.

Cals, J. W., & Kotz, D. (2013). Effective writing and publishing scientific papers, part VI: discussion. Journal of clinical epidemiology, 66(10), 1064.

Docherty, M., & Smith, R. (1999). The case for structuring the discussion of scientific papers: Much the same as that for structuring abstracts. In: British Medical Journal Publishing Group.

Faber, J. (2017). Writing scientific manuscripts: most common mistakes. Dental press journal of orthodontics, 22(5), 113-117.

Fletcher, R. H., & Fletcher, S. W. (2018). The discussion section. In Reporting and Publishing Research in the Biomedical Sciences (pp. 39-48): Springer.

Ghasemi, A., Bahadoran, Z., Mirmiran, P., Hosseinpanah, F., Shiva, N., & Zadeh-Vakili, A. (2019). The Principles of Biomedical Scientific Writing: Discussion. International journal of endocrinology and metabolism, 17(3).

Hofmann, A. H. (2013). Writing in the biological sciences: a comprehensive resource for scientific communication . New York: Oxford University Press.

Kotz, D., & Cals, J. W. (2013). Effective writing and publishing scientific papers, part V: results. Journal of clinical epidemiology, 66(9), 945.

Mack, C. (2014). How to Write a Good Scientific Paper: Structure and Organization. Journal of Micro/ Nanolithography, MEMS, and MOEMS, 13. doi:10.1117/1.JMM.13.4.040101

Moore, A. (2016). What's in a Discussion section? Exploiting 2‐dimensionality in the online world…. Bioessays, 38(12), 1185-1185.

Peat, J., Elliott, E., Baur, L., & Keena, V. (2013). Scientific writing: easy when you know how: John Wiley & Sons.

Sandercock, P. M. L. (2012). How to write and publish a scientific article. Canadian Society of Forensic Science Journal, 45(1), 1-5.

Teo, E. K. (2016). Effective Medical Writing: The Write Way to Get Published. Singapore Medical Journal, 57(9), 523-523. doi:10.11622/smedj.2016156

Van Way III, C. W. (2007). Writing a scientific paper. Nutrition in Clinical Practice, 22(6), 636-640.

Vieira, R. F., Lima, R. C. d., & Mizubuti, E. S. G. (2019). How to write the discussion section of a scientific article. Acta Scientiarum. Agronomy, 41.

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How to Write Effective Discussion and Conclusion Sections

Affiliations.

• 1 Cooper Medical School of Rowan University, Camden, NJ.
• 2 Rothman Institute, Philadelphia, PA.
• PMID: 29979216
• DOI: 10.1097/BSD.0000000000000687

With the exponential increase in research in the field of spine surgery, publishing peer-reviewed articles has become both more desirable and competitive in the past decade. Constructing an impactful manuscript has many important factors, one of which is a well-written Discussion section. A research study can ask a pressing question, have a meticulous methodology and report compelling results; however, without a thoughtful and well-informed analysis of the meaning of the study's findings and their potential influence on the field, the paper will be uninteresting and weak. Thus, formulating an effective Discussion section is crucial to improving the likelihood of the study's publication and its impact.

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How to Write a Discussion Section for a Research Paper

We’ve talked about several useful writing tips that authors should consider while drafting or editing their research papers. In particular, we’ve focused on  figures and legends , as well as the Introduction ,  Methods , and  Results . Now that we’ve addressed the more technical portions of your journal manuscript, let’s turn to the analytical segments of your research article. In this article, we’ll provide tips on how to write a strong Discussion section that best portrays the significance of your research contributions.

What is the Discussion section of a research paper?

In a nutshell,  your Discussion fulfills the promise you made to readers in your Introduction . At the beginning of your paper, you tell us why we should care about your research. You then guide us through a series of intricate images and graphs that capture all the relevant data you collected during your research. We may be dazzled and impressed at first, but none of that matters if you deliver an anti-climactic conclusion in the Discussion section!

Are you feeling pressured? Don’t worry. To be honest, you will edit the Discussion section of your manuscript numerous times. After all, in as little as one to two paragraphs ( Nature ‘s suggestion  based on their 3,000-word main body text limit), you have to explain how your research moves us from point A (issues you raise in the Introduction) to point B (our new understanding of these matters). You must also recommend how we might get to point C (i.e., identify what you think is the next direction for research in this field). That’s a lot to say in two paragraphs!

So, how do you do that? Let’s take a closer look.

What should I include in the Discussion section?

As we stated above, the goal of your Discussion section is to  answer the questions you raise in your Introduction by using the results you collected during your research . The content you include in the Discussions segment should include the following information:

• Remind us why we should be interested in this research project.
• Describe the nature of the knowledge gap you were trying to fill using the results of your study.
• Don’t repeat your Introduction. Instead, focus on why  this  particular study was needed to fill the gap you noticed and why that gap needed filling in the first place.
• Mainly, you want to remind us of how your research will increase our knowledge base and inspire others to conduct further research.
• Clearly tell us what that piece of missing knowledge was.
• Answer each of the questions you asked in your Introduction and explain how your results support those conclusions.
• Make sure to factor in all results relevant to the questions (even if those results were not statistically significant).
• Focus on the significance of the most noteworthy results.
• If conflicting inferences can be drawn from your results, evaluate the merits of all of them.
• Don’t rehash what you said earlier in the Results section. Rather, discuss your findings in the context of answering your hypothesis. Instead of making statements like “[The first result] was this…,” say, “[The first result] suggests [conclusion].”
• Do your conclusions line up with existing literature?
• Discuss whether your findings agree with current knowledge and expectations.
• Keep in mind good persuasive argument skills, such as explaining the strengths of your arguments and highlighting the weaknesses of contrary opinions.
• If you discovered something unexpected, offer reasons. If your conclusions aren’t aligned with current literature, explain.
• Address any limitations of your study and how relevant they are to interpreting your results and validating your findings.
• Make sure to acknowledge any weaknesses in your conclusions and suggest room for further research concerning that aspect of your analysis.
• Make sure your suggestions aren’t ones that should have been conducted during your research! Doing so might raise questions about your initial research design and protocols.
• Similarly, maintain a critical but unapologetic tone. You want to instill confidence in your readers that you have thoroughly examined your results and have objectively assessed them in a way that would benefit the scientific community’s desire to expand our knowledge base.
• Recommend next steps.
• Your suggestions should inspire other researchers to conduct follow-up studies to build upon the knowledge you have shared with them.
• Keep the list short (no more than two).

How to Write the Discussion Section

The above list of what to include in the Discussion section gives an overall idea of what you need to focus on throughout the section. Below are some tips and general suggestions about the technical aspects of writing and organization that you might find useful as you draft or revise the contents we’ve outlined above.

Technical writing elements

• Embrace active voice because it eliminates the awkward phrasing and wordiness that accompanies passive voice.
• Use the present tense, which should also be employed in the Introduction.
• Sprinkle with first person pronouns if needed, but generally, avoid it. We want to focus on your findings.
• Maintain an objective and analytical tone.

Discussion section organization

• Keep the same flow across the Results, Methods, and Discussion sections.
• We develop a rhythm as we read and parallel structures facilitate our comprehension. When you organize information the same way in each of these related parts of your journal manuscript, we can quickly see how a certain result was interpreted and quickly verify the particular methods used to produce that result.
• Notice how using parallel structure will eliminate extra narration in the Discussion part since we can anticipate the flow of your ideas based on what we read in the Results segment. Reducing wordiness is important when you only have a few paragraphs to devote to the Discussion section!
• Within each subpart of a Discussion, the information should flow as follows: (A) conclusion first, (B) relevant results and how they relate to that conclusion and (C) relevant literature.
• End with a concise summary explaining the big-picture impact of your study on our understanding of the subject matter. At the beginning of your Discussion section, you stated why  this  particular study was needed to fill the gap you noticed and why that gap needed filling in the first place. Now, it is time to end with “how your research filled that gap.”

Discussion Part 1: Summarizing Key Findings

Begin the Discussion section by restating your  statement of the problem  and briefly summarizing the major results. Do not simply repeat your findings. Rather, try to create a concise statement of the main results that directly answer the central research question that you stated in the Introduction section . This content should not be longer than one paragraph in length.

Many researchers struggle with understanding the precise differences between a Discussion section and a Results section . The most important thing to remember here is that your Discussion section should subjectively evaluate the findings presented in the Results section, and in relatively the same order. Keep these sections distinct by making sure that you do not repeat the findings without providing an interpretation.

Phrase examples: Summarizing the results

• The findings indicate that …
• These results suggest a correlation between A and B …
• The data present here suggest that …
• An interpretation of the findings reveals a connection between…

Discussion Part 2: Interpreting the Findings

What do the results mean? It may seem obvious to you, but simply looking at the figures in the Results section will not necessarily convey to readers the importance of the findings in answering your research questions.

The exact structure of interpretations depends on the type of research being conducted. Here are some common approaches to interpreting data:

• Identifying correlations and relationships in the findings
• Explaining whether the results confirm or undermine your research hypothesis
• Giving the findings context within the history of similar research studies
• Discussing unexpected results and analyzing their significance to your study or general research
• Offering alternative explanations and arguing for your position

Organize the Discussion section around key arguments, themes, hypotheses, or research questions or problems. Again, make sure to follow the same order as you did in the Results section.

Discussion Part 3: Discussing the Implications

In addition to providing your own interpretations, show how your results fit into the wider scholarly literature you surveyed in the  literature review section. This section is called the implications of the study . Show where and how these results fit into existing knowledge, what additional insights they contribute, and any possible consequences that might arise from this knowledge, both in the specific research topic and in the wider scientific domain.

Questions to ask yourself when dealing with potential implications:

• Do your findings fall in line with existing theories, or do they challenge these theories or findings? What new information do they contribute to the literature, if any? How exactly do these findings impact or conflict with existing theories or models?
• What are the practical implications on actual subjects or demographics?
• What are the methodological implications for similar studies conducted either in the past or future?

Your purpose in giving the implications is to spell out exactly what your study has contributed and why researchers and other readers should be interested.

Phrase examples: Discussing the implications of the research

• These results confirm the existing evidence in X studies…
• The results are not in line with the foregoing theory that…
• This experiment provides new insights into the connection between…
• These findings present a more nuanced understanding of…
• While previous studies have focused on X, these results demonstrate that Y.

Step 4: Acknowledging the limitations

All research has study limitations of one sort or another. Acknowledging limitations in methodology or approach helps strengthen your credibility as a researcher. Study limitations are not simply a list of mistakes made in the study. Rather, limitations help provide a more detailed picture of what can or cannot be concluded from your findings. In essence, they help temper and qualify the study implications you listed previously.

Study limitations can relate to research design, specific methodological or material choices, or unexpected issues that emerged while you conducted the research. Mention only those limitations directly relate to your research questions, and explain what impact these limitations had on how your study was conducted and the validity of any interpretations.

Possible types of study limitations:

• Insufficient sample size for statistical measurements
• Lack of previous research studies on the topic
• Methods/instruments/techniques used to collect the data
• Limited access to data
• Time constraints in properly preparing and executing the study

After discussing the study limitations, you can also stress that your results are still valid. Give some specific reasons why the limitations do not necessarily handicap your study or narrow its scope.

Phrase examples: Limitations sentence beginners

• “There may be some possible limitations in this study.”
• “The findings of this study have to be seen in light of some limitations.”
•  “The first limitation is the…The second limitation concerns the…”
•  “The empirical results reported herein should be considered in the light of some limitations.”
• “This research, however, is subject to several limitations.”
• “The primary limitation to the generalization of these results is…”
• “Nonetheless, these results must be interpreted with caution and a number of limitations should be borne in mind.”

Discussion Part 5: Giving Recommendations for Further Research

Based on your interpretation and discussion of the findings, your recommendations can include practical changes to the study or specific further research to be conducted to clarify the research questions. Recommendations are often listed in a separate Conclusion section , but often this is just the final paragraph of the Discussion section.

Suggestions for further research often stem directly from the limitations outlined. Rather than simply stating that “further research should be conducted,” provide concrete specifics for how future can help answer questions that your research could not.

Phrase examples: Recommendation sentence beginners

• Further research is needed to establish …
• There is abundant space for further progress in analyzing…
• A further study with more focus on X should be done to investigate…
• Further studies of X that account for these variables must be undertaken.

Consider Receiving Professional Language Editing

As you edit or draft your research manuscript, we hope that you implement these guidelines to produce a more effective Discussion section. And after completing your draft, don’t forget to submit your work to a professional proofreading and English editing service like Wordvice, including our manuscript editing service for  paper editing , cover letter editing , SOP editing , and personal statement proofreading services. Language editors not only proofread and correct errors in grammar, punctuation, mechanics, and formatting but also improve terms and revise phrases so they read more naturally. Wordvice is an industry leader in providing high-quality revision for all types of academic documents.

For additional information about how to write a strong research paper, make sure to check out our full  research writing series !

Wordvice Writing Resources

• How to Write a Research Paper Introduction 
• Which Verb Tenses to Use in a Research Paper
• How to Write an Abstract for a Research Paper
• How to Write a Research Paper Title
• Useful Phrases for Academic Writing
• Common Transition Terms in Academic Papers
• Active and Passive Voice in Research Papers
• 100+ Verbs That Will Make Your Research Writing Amazing
• Tips for Paraphrasing in Research Papers

Additional Academic Resources

•   Guide for Authors.  (Elsevier)
•  How to Write the Results Section of a Research Paper.  (Bates College)
•   Structure of a Research Paper.  (University of Minnesota Biomedical Library)
•   How to Choose a Target Journal  (Springer)
•   How to Write Figures and Tables  (UNC Writing Center)

• Research Paper Guides
• Basics of Research Paper Writing

How to Write a Discussion Section: Writing Guide

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• Basics of Essay Writing
• Essay Topics
• Other Essays
• Main Academic Essays
• Research Paper Topics
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• Methodology
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The discussion section of a research paper is where the author analyzes and explains the importance of the study's results. It presents the conclusions drawn from the study, compares them to previous research, and addresses any potential limitations or weaknesses. The discussion section should also suggest areas for future research.

Everything is not that complicated if you know where to find the required information. We’ll tell you everything there is to know about writing your discussion. Our easy guide covers all important bits, including research questions and your research results. Do you know how all enumerated events are connected? Well, you will after reading this guide we’ve prepared for you!

What Is in the Discussion Section of a Research Paper

The discussion section of a research paper can be viewed as something similar to the conclusion of your paper. But not literal, of course. It’s an ultimate section where you can talk about the findings of your study. Think about these questions when writing:

• Did you answer all of the promised research questions?
• Did you mention why your work matters?
• What are your findings, and why should anyone even care?
• Does your study have a literature review?

So, answer your questions, provide proof, and don’t forget about your promises from the introduction. 

How to Write a Discussion Section in 5 Steps

How to write the discussion section of a research paper is something everyone googles eventually. It's just life. But why not make everything easier? In brief, this section we’re talking about must include all following parts:

• Answers for research questions
• Literature review
• Results of the work
• Limitations of one’s study
• Overall conclusion

Indeed, all those parts may confuse anyone. So by looking at our guide, you'll save yourself some hassle.  P.S. All our steps are easy and explained in detail! But if you are looking for the most efficient solution, consider using professional help. Leave your “ write my research paper for me ” order at StudyCrumb and get a customized study tailored to your requirements.

Step 1. Start Strong: Discussion Section of a Research Paper

First and foremost, how to start the discussion section of a research paper? Here’s what you should definitely consider before settling down to start writing:

• All essays or papers must begin strong. All readers will not wait for any writer to get to the point. We advise summarizing the paper's main findings.
• Moreover, you should relate both discussion and literature review to what you have discovered. Mentioning that would be a plus too.
• Make sure that an introduction or start per se is clear and concise. Word count might be needed for school. But any paper should be understandable and not too diluted.

Step 2. Answer the Questions in Your Discussion Section of a Research Paper

Writing the discussion section of a research paper also involves mentioning your questions. Remember that in your introduction, you have promised your readers to answer certain questions. Well, now it’s a perfect time to finally give the awaited answer. You need to explain all possible correlations between your findings, research questions, and literature proposed. You already had hypotheses. So were they correct, or maybe you want to propose certain corrections? Section’s main goal is to avoid open ends. It’s not a story or a fairytale with an intriguing ending. If you have several questions, you must answer them. As simple as that.

Step 3. Relate Your Results in a Discussion Section

Writing a discussion section of a research paper also requires any writer to explain their results. You will undoubtedly include an impactful literature review. However, your readers should not just try and struggle with understanding what are some specific relationships behind previous studies and your results.  Your results should sound something like: “This guy in their paper discovered that apples are green. Nevertheless, I have proven via experimentation and research that apples are actually red.” Please, don’t take these results directly. It’s just an initial hypothesis. But what you should definitely remember is any practical implications of your study. Why does it matter and how can anyone use it? That’s the most crucial question.

Step 4. Describe the Limitations in Your Discussion Section

Discussion section of a research paper isn’t limitless. What does that mean? Essentially, it means that you also have to discuss any limitations of your study. Maybe you had some methodological inconsistencies. Possibly, there are no particular theories or not enough information for you to be entirely confident in one’s conclusions.  You might say that an available source of literature you have studied does not focus on one’s issue. That’s why one’s main limitation is theoretical. However, keep in mind that your limitations must possess a certain degree of relevancy. You can just say that you haven’t found enough books. Your information must be truthful to research.

Step 5. Conclude Your Discussion Section With Recommendations

Your last step when you write a discussion section in a paper is its conclusion, like in any other academic work. Writer’s conclusion must be as strong as their starting point of the overall work. Check out our brief list of things to know about the conclusion in research paper :

• It must present its scientific relevance and importance of your work.
• It should include different implications of your research.
• It should not, however, discuss anything new or things that you have not mentioned before.
• Leave no open questions and carefully complete the work without them.

Discussion Section of a Research Paper Example

All the best example discussion sections of a research paper will be written according to our brief guide. Don’t forget that you need to state your findings and underline the importance of your work. An undoubtedly big part of one’s discussion will definitely be answering and explaining the research questions. In other words, you’ll already have all the knowledge you have so carefully gathered. Our last step for you is to recollect and wrap up your paper. But we’re sure you’ll succeed!

How to Write a Discussion Section: Final Thoughts

Today we have covered how to write a discussion section. That was quite a brief journey, wasn’t it? Just to remind you to focus on these things:

• Importance of your study.
• Summary of the information you have gathered.
• Main findings and conclusions.
• Answers to all research questions without an open end.
• Correlation between literature review and your results.

But, wait, this guide is not the only thing we can do. Looking for how to write an abstract for a research paper  for example? We have such a blog and much more on our platform.

Our academic writing service is just a click away. We are proud to say that our writers are professionals in their fields. Buy a research paper and our experts can provide prompt solutions without compromising the quality.

Discussion Section of a Research Paper: Frequently Asked Questions

1. how long should the discussion section of a research paper be.

Our discussion section of a research paper should not be longer than other sections. So try to keep it short but as informative as possible. It usually contains around 6-7 paragraphs in length. It is enough to briefly summarize all the important data and not to drag it.

2. What's the difference between the discussion and the results?

The difference between discussion and results is very simple and easy to understand. The results only report your main findings. You stated what you have found and how you have done that. In contrast, one’s discussion mentions your findings and explains how they relate to other literature, research questions, and one’s hypothesis. Therefore, it is not only a report but an efficient as well as proper explanation.

3. What's the difference between a discussion and a conclusion?

The difference between discussion and conclusion is also quite easy. Conclusion is a brief summary of all the findings and results. Still, our favorite discussion section interprets and explains your main results. It is an important but more lengthy and wordy part. Besides, it uses extra literature for references.

4. What is the purpose of the discussion section?

The primary purpose of a discussion section is to interpret and describe all your interesting findings. Therefore, you should state what you have learned, whether your hypothesis was correct and how your results can be explained using other sources. If this section is clear to readers, our congratulations as you have succeeded.

Joe Eckel is an expert on Dissertations writing. He makes sure that each student gets precious insights on composing A-grade academic writing.

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The Process of Writing a Research Paper Guide: The Discussion

• Types of Research Designs
• Choosing a Research Topic
• Preparing to Write
• The Abstract
• The Introduction
• The Literature Review
• The Methodology
• The Results
• The Discussion
• The Conclusion
• Proofreading Your Paper
• Citing Sources
• Annotated Bibliography
• Giving an Oral Presentation
• How to Manage Group Projects
• Writing a Book Review
• Writing a Research Proposal
• Acknowledgements

The purpose of the discussion is to interpret and describe the significance of your findings in light of what was already known about the research problem being investigated and to explain any new understanding or insights that emerged as a result of your study of the problem. The discussion will always connect to the introduction by way of the research questions or hypotheses you posed and the literature you reviewed, but the discussion does not simply repeat or rearrange the first parts of your paper; the discussion clearly explain how your study advanced the reader's understanding of the research problem from where you left them at the end of your review of prior research.

Importance of a Good Discussion

The discussion section is often considered the most important part of your research paper because this is where you:

• Most effectively demonstrates your ability as a researcher to think critically about an issue, to develop creative solutions to problems based upon a logical synthesis of the findings, and  to formulate a deeper, more profound understanding of the research problem under investigation,
• Present the underlying meaning of your research, note possible implications in other areas of study, and explore possible improvements that can be made in order to further develop the concerns of your research,
• Highlight the importance of your study and how it may be able to contribute to and/or help fill existing gaps in the field. If appropriate, the discussion section is also where you state how the findings from your study revealed and helped fill gaps in the literature that had not been previously exposed or adequately described, and
• Engage the reader in thinking critically about issues based upon an evidence-based interpretation of findings; it is not governed strictly by objective reporting of information.

Annesley Thomas M. “The Discussion Section: Your Closing Argument.”  Clinical Chemistry  56 (November 2010): 1671-1674; Bitchener, John and Helen Basturkmen. “Perceptions of the Difficulties of Postgraduate L2 Thesis Students Writing the Discussion Section.”  Journal of English for Academic Purposes  5 (January 2006): 4-18; Kretchmer, Paul.  Fourteen Steps to Writing an Effective Discussion Section . San Francisco Edit, 2003-2008.

Structure and Writing Style

I.  General Rules

These are the general rules you should adopt when composing your discussion of the results :

• Do not be verbose or repetitive
• Be concise  and make your points clearly
• Avoid the use of jargon or undefined technical language
• Follow a logical stream of thought; in general, interpret and discuss the significance of your findings in the same sequence you described them in your results section [a notable exception is to begin by highlighting an unexpected result or finding]
• Use the present verb tense, especially for established facts; however, refer to specific works or prior studies in the past tense
• If needed, use subheadings to help organize your discussion or to categorize your interpretations into themes

II.  The Content

The content of the discussion section of your paper most often includes :

• Explanation of results : comment on whether or not the results were expected for each set of results; go into greater depth to explain findings that were unexpected or especially profound. If appropriate, note any unusual or unanticipated patterns or trends that emerged from your results and explain their meaning in relation to the research problem.
• References to previous research : either compare your results with the findings from other studies or use the studies to support a claim. This can include re-visiting key sources already cited in your literature review section, or, save them to cite later in the discussion section if they are more important to compare with your results instead of being a part of the general literature review of research used to provide context and background information. Note that you can make this decision to highlight specific studies after you have begun writing the discussion section.
• Deduction : a claim for how the results can be applied more generally. For example, describing lessons learned, proposing recommendations that can help improve a situation, or highlighting best practices.
• Hypothesis : a more general claim or possible conclusion arising from the results [which may be proved or disproved in subsequent research]. This can be framed as new research questions that emerged as a result of your analysis.

III.  Organization and Structure

Keep the following sequential points in mind as you organize and write the discussion section of your paper:

• Think of your discussion as an inverted pyramid. Organize the discussion from the general to the specific, linking your findings to the literature, then to theory, then to practice [if appropriate].
• Use the same key terms, narrative style, and verb tense [present] that you used when when describing the research problem in your introduction.
• Begin by briefly re-stating the research problem you were investigating and answer all of the research questions underpinning the problem that you posed in the introduction.
• Describe the patterns, principles, and relationships shown by each major findings and place them in proper perspective. The sequence of this information is important; first state the answer, then the relevant results, then cite the work of others. If appropriate, refer the reader to a figure or table to help enhance the interpretation of the data [either within the text or as an appendix].
• Regardless of where it's mentioned, a good discussion section includes analysis of any unexpected findings. This part of the discussion should begin with a description of the unanticipated finding, followed by a brief interpretation as to why you believe it appeared and, if necessary, its possible significance in relation to the overall study. If more than one unexpected finding emerged during the study, describe each of them in the order they appeared as you gathered or analyzed the data. As noted, the exception to discussing findings in the same order you described them in the results section would be to begin by highlighting the implications of a particularly unexpected or significant finding that emerged from the study, followed by a discussion of the remaining findings.
• Before concluding the discussion, identify potential  limitations and weaknesses  if you do not plan to do so in the conclusion of the paper. Comment on their relative importance in relation to your overall interpretation of the results and, if necessary, note how they may affect the validity of your findings. Avoid using an apologetic tone; however, be honest and self-critical [e.g., had you included a particular question in a survey instrument, additional data could have been revealed].
• The discussion section should end with a concise summary of the principal implications of the findings regardless of their significance. Give a brief explanation about why you believe the findings and conclusions of your study are important and how they support broader knowledge or understanding of the research problem. This can be followed by any recommendations for further research. However, do not offer recommendations which could have been easily addressed within the study. This would demonstrate to the reader that you have inadequately examined and interpreted the data.

IV.  Overall Objectives

The objectives of your discussion section should include the following: I.   Reiterate the Research Problem/State the Major Findings

Briefly reiterate the research problem or problems you are investigating and the methods you used to investigate them, then move quickly to describe the major findings of the study. You should write a direct, declarative, and succinct proclamation of the study results, usually in one paragraph.

II.   Explain the Meaning of the Findings and Why They are Important

Consider the likelihood that no one has thought as long and hard about your study as you have. Systematically explain the underlying meaning of your findings and state why you believe they are significant. After reading the discussion section, you want the reader to think critically about the results [“why didn't I think of that?”]. You don’t want to force the reader to go through the paper multiple times to figure out what it all means. If applicable, begin this part of the section by repeating what you consider to be your most significant or unanticipated finding first, then systematically review each finding. Otherwise, follow the general order you reported the findings in the results section.

III.   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 results to those found in other studies, particularly if questions raised from prior studies served as the motivation for your research. 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 study differs from other research about the topic. Note that any significant or unanticipated finding is often because there was no prior research to indicate the finding could occur. If there is prior research to indicate this, you need to explain why it was significant or unanticipated. IV.   Consider Alternative Explanations of the Findings

It is important to remember that the purpose of research in the social sciences is to  discover  and not to  prove . When writing the discussion section, you should carefully consider all possible explanations for the study results, rather than just those that fit your hypothesis or prior assumptions and biases. This is especially important when describing the discovery of significant or unanticipated findings.

V.   Acknowledge the Study’s Limitations

It is far better for you to identify and acknowledge your study’s limitations than to have them pointed out by your professor! Note any unanswered questions or issues your study did not address and describe the generalizability of your results to other situations. If a limitation is applicable to the method chosen to gather information, then describe in detail the problems you encountered and why. VI.   Make Suggestions for Further Research

You may choose to conclude the discussion section by making suggestions for further research [this can be done in the overall conclusion of your paper]. Although your study may offer important insights about the research problem, this is where you can address other questions related to the problem that remain unanswered or highlight previously hidden questions that were revealed as a result of conducting your research. You should frame your suggestions by linking the need for further research to the limitations of your study [e.g., in future studies, the survey instrument should include more questions that ask..."] or linking to critical issues revealed from the data that were not considered initially in your research.

NOTE:  Besides the literature review section, the preponderance of references to sources is usually found in the discussion section . A few historical references may be helpful for perspective, but most of the references should be relatively recent and included to aid in the interpretation of your results or used to link to similar studies. If a study that you cited does not support your findings, don't ignore it--clearly explain why your research findings differ from theirs.

V.  Problems to Avoid

• Do not waste time restating your results . Should you need to remind the reader of a finding to be discussed, use "bridge sentences" that relate the result to the interpretation. An example would be: “In the case of determining available housing to single women with children in rural areas of Texas, the findings suggest that access to good schools is important," then move on to further explaining this finding and its implications.
• Recommendations for further research can be included in either the discussion or conclusion of your paper,  but do not repeat your recommendations in the both sections. Think about the overall narrative flow of your paper to determine where best to locate this information. However, if your findings raise a lot of new questions or issues, consider including suggestions for further research in the discussion section.
• Do not introduce new results in the discussion section.  Be wary of mistaking the reiteration of a specific finding for an interpretation because it may confuse the reader. The description of findings [results] and the interpretation of their significance [discussion] should be distinct sections of your paper. If you choose to combine the results section and the discussion section into a single narrative, you must be clear in how you report the information discovered and your own interpretation of each finding. This approach is not recommended if you lack experience writing college-level research papers.
• Use of the first person pronoun is generally acceptable.  Using first person singular pronouns can help emphasize a point or illustrate a contrasting finding. However, keep in mind that too much use of the first person can actually distract the reader from the main points [i.e., I know you're telling me this; just tell me!].

Analyzing vs. Summarizing . Department of English Writing Guide. George Mason University;  Discussion . The Structure, Format, Content, and Style of a Journal-Style Scientific Paper. Department of Biology. Bates College; Hess, Dean R. "How to Write an Effective Discussion."  Respiratory Care  49 (October 2004); Kretchmer, Paul.  Fourteen Steps to Writing to Writing an Effective Discussion Section . San Francisco Edit, 2003-2008;  The Lab Report . University College Writing Centre. University of Toronto; Sauaia, A. et al. "The Anatomy of an Article: The Discussion Section: "How Does the Article I Read Today Change What I Will Recommend to my Patients Tomorrow?”  The Journal of Trauma and Acute Care Surgery  74 (June 2013): 1599-1602;  Research Limitations & Future Research . Lund Research Ltd., 2012;  Summary: Using it Wisely . The Writing Center. University of North Carolina; Schafer, Mickey S.  Writing the Discussion . Writing in Psychology course syllabus. University of Florida; Yellin, Linda L.  A Sociology Writer's Guide . Boston, MA: Allyn and Bacon, 2009.

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The 6 key parts in a powerful discussion section

• by kayciebutler
• June 18, 2019 November 13, 2020

The discussion can be a sticking point for many manuscript writers because it seems to be a free for all with no easy pattern for composing it – but there are actually 6 key parts that need to be included!

While it is true that each research project is different – meaning that different parts of the discussion will carry more weight for each manuscript – there are still several key parts to any good discussion.

In fact, ensuring that these 6 parts are included in your discussion will make it more interesting for readers, more useful for other scientists, and therefore will  provide an overall more memorable discussion for your paper.

This post will briefly define a discussion section before detailing the 6 main parts that can help your paper achieve the maximum impact.

These 6 parts represent the various angles that you should consider for all research projects when composing the discussion section, ranging from the narrowest point in scope (your research) to the widest in scope (the impact of your research on the future of science). They should help you brainstorm what to include when writing, and the inclusion of all 6 sections will help to ensure your discussion is well rounded.

What is a discussion?

The discussion answers the questions:

What does your research mean?

How does it fit into the context of the field?

Or, in other words,

a discussion critically analyzes and interprets the results of a scientific study, placing the results in the context of published literature and explaining how they affect the field .

Therefore, a discussion cannot only summarize the results of a paper, but must draw in outside literature from the field to inform the reader of how your latest contribution fits into the current knowledge and how it expands on what is currently known.

6 key parts of a discussion

There are 6 parts to a discussion, and each should be given proper consideration when writing. For most manuscripts, there should be at least some of each category in the discussion, with the proportion depending on the individual manuscript.

It is important to

1. summarize the key points of and then 2. analyze your research before 3. relating how your research fits into the field as a whole. You work should also be compared to 4. the gap in the field, including how your research might have moved the edge of current knowledge. Finally, how your research modified our view of 5. what lies beyond the edge of current knowledge and some 6. suggestions for future directions on how to examine those hypotheses are needed.

Importantly, these parts are not necessarily to be included in the specific order listed here – this list is only designed to highlight the key points that should be included in a discussion, moving from the point narrowest in scope (closest to your every day research) to the point widest in scope (furthest from your every day research, closest to your audience).

A good discussion will ebb and flow between the different sections as the results dictate. Some results will need more critical analysis, some will be more important to relate to the field than others, and some will spark more speculation and future directions.

1. Summary of results

This part of the discussion serves to remind the reader of key results, though care must be taken to avoid extensive summaries, keeping this section to a minimum.

Try for a direct, succinct recap that is used only to help readers avoid having to flip back to the results sections. It is often helpful to reiterate key numbers, especially when they will be next compared to literature values.

This part is often not even written in full sentences, and is used as a bridge into a critical analysis of the results:

• “The results XXX and YYY indicate that [critical analysis]…”
• “Because of XXX, we can say that [interpretation]…”

No new results should be brought up in the discussion.

2. Critical analysis of results

This is where you go beyond a general description of the results to tell the reader what your results actually mean and what you learned from them. This analysis should focus more on unexpected, particularly important, or unusual results, analyzing the meaning of these results for the reader.

You analysis should highlight all of the new trends, relationships, and knowledge uncovered by your research, and should list these analyses in the order in which the results section was written.

If there are possible alternative explanations to your results than the ones you have indicated, these should also be listed along with your rationale for excluding them as possibilities.

3. Relate results to the field

This is where you compare your work to previous studies, especially ones that inspired your work or brought up questions that you have addressed. Your work in only one small chunk of a much larger whole, so let the audience know where in that larger whole your work falls and how it integrates.

This is also where papers from the field can be used to support any claims or speculations that you make. These sources can be reused from the introduction or can be new. Additionally, any studies that contradict your conclusions should be discussed along with plausible explanations for why the contradiction might exist.

In this part of the discussion, you will also want to describe any generalizations you can now make about the field now that your research exists.

4. Relate results to the gap in the field

This part is essential for any discussion, and its lack or absence is one of the biggest mistakes I see in discussion writing.

Only by indicating how your work directly addresses a gap in the field can you show the reader the importance of your study and why it deserves publication. This gap can be a large, obvious gap; a tiny hole that needs to be filled; or even as simple as research reinforcing the current edge of knowledge.

This gap in the field that your research sought to address should be described in the introduction to make sense of why your work was needed. This gap should also be briefly reiterated here in the discussion, often with a brief description of your main results, to highlight how your work addressed this gap.

This part should also describe any important lessons that were learned through your research that advance the current edge of knowledge in your field, such as if you are recommending a change to current best practices or to a known pathway or mechanism .

It is important to ensure you address all of the research questions that were brought up in the introduction in this part, or the reader will feel unfulfilled after finishing your discussion.

5. Speculate beyond current knowledge

The world beyond your field of research is vast and full of unknowns.

Your discussion should therefore also indicate how your results can be applied beyond the limits of current knowledge. This can include possible new insights, developing new hypotheses that can be tested in the future, and speculating on possible new research questions that can now be considered because of your research.

Speculation as to how your results fit into an even bigger picture or how they can be applied or related to the field more generally are also allowed, though it is important to ensure these are claims logically supported by your research and the rest of the field. DO NOT make wild claims that your research cannot support.

6. Future directions

Now its time to tell the reader how we might try to get from where we are to where we want to be in the future.

This is where a note should be made of any questions left unanswered by your research, including possible routes for answering these questions if they are known…with the one major caveat that you should never discuss future directions that should be included within the scope of your research! If you find yourself needing to do that, consider adding those experiments to the current study.

Additionally, discuss possible future studies that could address any new hypotheses brought up by your research and any new technology that might need to be developed to do that. Details for future studies that could avoid or address any of your study limitations should also be included.

Finally, don’t forget to bring up possible applications of your work, though again, make sure to stick within the realm of the feasible!

Finally…

…does the last discussion you wrote include some of all six categories?

Will being aware of these 6 key points help you brainstorm for writing future discussion sections?

Future posts are going to break down published discussion sections to look for patterns that can further help you compose your discussion.

Until then, happy writing!

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• v.318(7193); 1999 May 8

The case for structuring the discussion of scientific papers

Structure is the most difficult part of writing, no matter whether you are writing a novel, a play, a poem, a government report, or a scientific paper. If the structure is right then the rest can follow fairly easily, but no amount of clever language can compensate for a weak structure. Structure is important so that readers don’t become lost. They should know where they’ve come from, where they are, and where they are headed. A strong structure also allows readers to know where to look for particular information and makes it more likely that all important information will be included.

Readers of scientific papers in medical journals are used to the IMRaD structure (Introduction, Methods, Results, and Discussion) 1 and either consciously or unconsciously know the function of each section. Readers have also become used to structured abstracts, which have been shown to include more important information than unstructured summaries. 2 , 3 Journals are now introducing specific structures for particular types of papers—such as the CONSORT structure for reporting randomised trials. 4 Now we are proposing that the discussion of scientific reports should be structured—because it is often the weakest part of the paper where careful explanation gives way to polemic. 5

Old fashioned papers often comprised small amounts of new data—perhaps a case report—with extensive discussion. The function of the discussion seemed to be to convince readers of the rightness of the authors’ interpretation of data and speculation. It was not a dispassionate examination of the evidence. Times have changed, and greater emphasis has been placed on methods and results, particularly as methods have become more complicated and scientifically valid. But still we see many papers where the job of the discussion seems to be to “sell” the paper.

Richard Horton, editor of the Lancet , and others have described how authors use rhetoric in the discussion of papers. 6 , 7 Authors may use extensive text without subheadings; expand reports with comment relating more to the generalities than to the specifics of the study; and introduce bias by emphasising the strengths of the study more than its weaknesses, reiterating selected results, and inflating the importance and generalisability of the findings. Commonly authors go beyond the evidence they have gathered and draw unjustified conclusions.

Our proposal for a structured discussion is shown in the box. The discussion should begin with a restatement of the principal finding. Ideally, this should be no more than one sentence. Next should come a comprehensive examination of the strengths and weaknesses of the study, with equal emphasis given to both. Indeed, editors and readers are likely to be most interested in the weaknesses of the study: all medical studies have them. If editors and readers identify weaknesses that are not discussed then their trust in the paper may be shaken: what other weaknesses might there be that neither they nor the authors have identified?

Suggested structure for discussion of scientific papers

• Statement of principal findings
• Strengths and weaknesses of the study
• Strengths and weaknesses in relation to other studies, discussing particularly any differences in results
• Meaning of the study: possible mechanisms and implications for clinicians or policymakers
• Unanswered questions and future research

The next job is to relate the study to what has gone before. The task here is not to show how your study is better than previous studies but rather to compare strengths and weaknesses. Do not hide the weaknesses of your study relative to other studies. Importantly, you should discuss why you might have reached different conclusions from others. But go easy on the speculation. If you don’t know why your results are different from those of others then don’t pretend you do, and you should certainly not assume that your results are right and the others wrong.

Now you should begin the difficult study of discussing what your study might “mean.” What might be the explanation of your findings and what might they mean for clinicians or policymakers? Here you are on dangerous ground, and most editors and readers will appreciate you being cautious, not moving beyond what is often limited evidence. Leave readers to make up their own minds on meaning: they will anyway. You might even emphasise what your evidence does not mean, holding readers back from reaching overdramatic, unjustified conclusions. Finally, you should discuss what questions remain unanswered and what further work is needed. Again editors and readers will enjoy restraint. Indeed, this is the part of the paper where authors often run amok. There is nothing to stop you writing another piece that is all speculation, but don’t corrupt your evidence with speculation.

Other subheadings might sometimes be needed, but we think that our suggested structure should fit most studies. Although some may find uniform structuring difficult and even restrictive, 8 we believe that our proposed structure should reduce overall length; prevent unjustified extrapolation and selective repetition; reduce reporting bias; and improve the overall quality of reporting. Such a supposition could readily be tested. We invite comment from authors and readers of the BMJ , and if reaction is positive then we will introduce structured discussions.

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• Published: 19 June 2024

Detecting hallucinations in large language models using semantic entropy

• Sebastian Farquhar   ORCID: orcid.org/0000-0002-9185-6415 1   na1 ,
• Jannik Kossen 1   na1 ,
• Lorenz Kuhn 1   na1 &
• Yarin Gal   ORCID: orcid.org/0000-0002-2733-2078 1  

Nature volume  630 ,  pages 625–630 ( 2024 ) Cite this article

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Large language model (LLM) systems, such as ChatGPT 1 or Gemini 2 , can show impressive reasoning and question-answering capabilities but often ‘hallucinate’ false outputs and unsubstantiated answers 3 , 4 . Answering unreliably or without the necessary information prevents adoption in diverse fields, with problems including fabrication of legal precedents 5 or untrue facts in news articles 6 and even posing a risk to human life in medical domains such as radiology 7 . Encouraging truthfulness through supervision or reinforcement has been only partially successful 8 . Researchers need a general method for detecting hallucinations in LLMs that works even with new and unseen questions to which humans might not know the answer. Here we develop new methods grounded in statistics, proposing entropy-based uncertainty estimators for LLMs to detect a subset of hallucinations—confabulations—which are arbitrary and incorrect generations. Our method addresses the fact that one idea can be expressed in many ways by computing uncertainty at the level of meaning rather than specific sequences of words. Our method works across datasets and tasks without a priori knowledge of the task, requires no task-specific data and robustly generalizes to new tasks not seen before. By detecting when a prompt is likely to produce a confabulation, our method helps users understand when they must take extra care with LLMs and opens up new possibilities for using LLMs that are otherwise prevented by their unreliability.

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Testing theory of mind in large language models and humans

Human-like intuitive behavior and reasoning biases emerged in large language models but disappeared in ChatGPT

ThoughtSource: A central hub for large language model reasoning data

‘Hallucinations’ are a critical problem 9 for natural language generation systems using large language models (LLMs), such as ChatGPT 1 or Gemini 2 , because users cannot trust that any given output is correct.

Hallucinations are often defined as LLMs generating “content that is nonsensical or unfaithful to the provided source content” 9 , 10 , 11 but they have come to include a vast array of failures of faithfulness and factuality. We focus on a subset of hallucinations which we call ‘confabulations’ 12 for which LLMs fluently make claims that are both wrong and arbitrary—by which we mean that the answer is sensitive to irrelevant details such as random seed. For example, when asked a medical question “What is the target of Sotorasib?” an LLM confabulates by sometimes answering KRASG12 ‘C’ (correct) and other times KRASG12 ‘D’ (incorrect) despite identical instructions. We distinguish this from cases in which a similar ‘symptom’ is caused by the following different mechanisms: when LLMs are consistently wrong as a result of being trained on erroneous data such as common misconceptions 13 ; when the LLM ‘lies’ in pursuit of a reward 14 ; or systematic failures of reasoning or generalization. We believe that combining these distinct mechanisms in the broad category hallucination is unhelpful. Our method makes progress on a portion of the problem of providing scalable oversight 15 by detecting confabulations that people might otherwise find plausible. However, it does not guarantee factuality because it does not help when LLM outputs are systematically bad. Nevertheless, we significantly improve question-answering accuracy for state-of-the-art LLMs, revealing that confabulations are a great source of error at present.

We show how to detect confabulations by developing a quantitative measure of when an input is likely to cause an LLM to generate arbitrary and ungrounded answers. Detecting confabulations allows systems built on LLMs to avoid answering questions likely to cause confabulations, to make users aware of the unreliability of answers to a question or to supplement the LLM with more grounded search or retrieval. This is essential for the critical emerging field of free-form generation in which naive approaches, suited to closed vocabulary and multiple choice, fail. Past work on uncertainty for LLMs has focused on simpler settings, such as classifiers 16 , 17 and regressors 18 , 19 , whereas the most exciting applications of LLMs relate to free-form generations.

The term hallucination in the context of machine learning originally comes from filling in ungrounded details, either as a deliberate strategy 20 or as a reliability problem 4 . The appropriateness of the metaphor has been questioned as promoting undue anthropomorphism 21 . Although we agree that metaphor must be used carefully with LLMs 22 , the widespread adoption of the term hallucination reflects the fact that it points to an important phenomenon. This work represents a step towards making that phenomenon more precise.

To detect confabulations, we use probabilistic tools to define and then measure the ‘semantic’ entropy of the generations of an LLM—an entropy that is computed over meanings of sentences. High entropy corresponds to high uncertainty 23 , 24 , 25 —so semantic entropy is one way to estimate semantic uncertainties. Semantic uncertainty, the broader category of measures we introduce, could be operationalized with other measures of uncertainty, such as mutual information, instead. Entropy in free-form generation is normally hard to measure because answers might mean the same thing (be semantically equivalent) despite being expressed differently (being syntactically or lexically distinct). This causes naive estimates of entropy or other lexical variation scores 26 to be misleadingly high when the same correct answer might be written in many ways without changing its meaning.

By contrast, our semantic entropy moves towards estimating the entropy of the distribution of meanings of free-form answers to questions, insofar as that is possible, rather than the distribution over the ‘tokens’ (words or word-pieces) which LLMs natively represent. This can be seen as a kind of semantic consistency check 27 for random seed variation. An overview of our approach is provided in Fig. 1 and a worked example in Supplementary Table 1 .

a , Naive entropy-based uncertainty measures variation in the exact answers, treating ‘Paris’, ‘It’s Paris’ and ‘France’s capital Paris’ as different. But this is unsuitable for language tasks for which sometimes different answers mean the same things. Our semantic entropy clusters answers which share meanings before computing the entropy. A low semantic entropy shows that the LLM is confident about the meaning. b , Semantic entropy can also detect confabulations in longer passages. We automatically decompose a long generated answer into factoids. For each factoid, an LLM generates questions to which that factoid might have been the answer. The original LLM then samples  M possible answers to these questions. Finally, we compute the semantic entropy over the answers to each specific question, including the original factoid. Confabulations are indicated by high average semantic entropy for questions associated with that factoid. Here, semantic entropy classifies Fact 1 as probably not a confabulation because generations often mean the same thing, despite very different wordings, which a naive entropy would have missed.

Intuitively, our method works by sampling several possible answers to each question and clustering them algorithmically into answers that have similar meanings, which we determine on the basis of whether answers in the same cluster entail each other bidirectionally 28 . That is, if sentence A entails that sentence B is true and vice versa, then we consider them to be in the same semantic cluster. We measure entailment using both general-purpose LLMs and natural language inference (NLI) tools developed specifically for detecting entailment for which we show direct evaluations in Supplementary Tables 2 and 3 and Supplementary Fig. 1 . Textual entailment has previously been shown to correlate with faithfulness 10 in the context of factual consistency 29 as well as being used to measure factuality in abstractive summarization 30 , especially when applied at the right granularity 31 .

Semantic entropy detects confabulations in free-form text generation across a range of language models and domains, without previous domain knowledge. Our evaluations cover question answering in trivia knowledge (TriviaQA 32 ), general knowledge (SQuAD 1.1; ref. 33 ), life sciences (BioASQ 34 ) and open-domain natural questions (NQ-Open 35 ) derived from actual queries to Google Search 36 . In addition, semantic entropy detects confabulations in mathematical word problems (SVAMP 37 ) and in a biography-generation dataset, FactualBio, accompanying this paper.

Our results for TriviaQA, SQuAD, BioASQ, NQ-Open and SVAMP are all evaluated context-free and involve sentence-length answers (96 ± 70 characters, mean ± s.d.) and use LLaMA 2 Chat (7B, 13B and 70B parameters) 38 , Falcon Instruct (7B and 40B) 39 and Mistral Instruct (7B) 40 . In the Supplementary Information , we further consider short-phrase-length answers. Results for FactualBio (442 ± 122 characters) use GPT-4 (ref. 1 ). At the time of writing, GPT-4 (ref. 1 ) did not expose output probabilities 41 or hidden states, although it does now. As a result, we propose a discrete approximation of our estimator for semantic entropy which allows us to run experiments without access to output probabilities, which we use for all GPT-4 results in this paper and which performs similarly well.

Our confabulation detection with semantic entropy is more robust to user inputs from previously unseen domains than methods which aim to ‘learn’ how to detect confabulations from a set of example demonstrations. Our method is unsupervised, meaning that we do not need labelled examples of confabulations. By contrast, supervised methods detect confabulations by learning patterns behind examples of confabulations, assuming that future questions preserve these patterns. But this assumption is often untrue in new situations or with confabulations that human overseers are unable to identify (compare Fig. 17 of ref. 24 ). As a strong supervised baseline, we compare to an embedding regression method inspired by ref. 24 which trains a logistic regression classifier to predict whether the model correctly answered a question on the basis of the final ‘embedding’ (hidden state) of the LLM. We also use the P (True) method 24 which looks at the probability with which an LLM predicts that the next token is ‘True’ when few-shot prompted to compare a main answer with ‘brainstormed’ alternatives.

Confabulations contribute substantially to incorrect answers given by language models. We show that semantic entropy can be used to predict many incorrect model answers and to improve question-answering accuracy by refusing to answer those questions the model is uncertain about. Corresponding to these two uses, we evaluate two main metrics. First, the widely used area under the receiver operating characteristic (AUROC) curve for the binary event that a given answer is incorrect. This measure captures both precision and recall and ranges from 0 to 1, with 1 representing a perfect classifier and 0.5 representing an un-informative classifier. We also show a new measure, the area under the ‘rejection accuracy’ curve (AURAC). This studies the case in which the confabulation detection score is used to refuse to answer the questions judged most likely to cause confabulations. Rejection accuracy is the accuracy of the answers of the model on the remaining questions and the area under this curve is a summary statistic over many thresholds (representative threshold accuracies are provided in Supplementary Material ). The AURAC captures the accuracy improvement which users would experience if semantic entropy was used to filter out questions causing the highest entropy.

Detecting confabulations in QA and math

In Fig. 2 , we show that both semantic entropy and its discrete approximation outperform our best baselines for sentence-length generations. These results are averaged across datasets and provide the actual scores on the held-out evaluation dataset. We report the raw average score across held-out evaluation datasets without standard error because the distributional characteristics are more a property of the models and datasets selected than the method. Consistency of relative results across different datasets is a stronger indicator of variation in this case.

Semantic entropy outperforms leading baselines and naive entropy. AUROC (scored on the y -axes) measures how well methods predict LLM mistakes, which correlate with confabulations. AURAC (likewise scored on the y -axes) measures the performance improvement of a system that refuses to answer questions which are judged likely to cause confabulations. Results are an average over five datasets, with individual metrics provided in the Supplementary Information .

Semantic entropy greatly outperforms the naive estimation of uncertainty using entropy: computing the entropy of the length-normalized joint probability of the token sequences. Naive entropy estimation ignores the fact that token probabilities also express the uncertainty of the model over phrasings that do not change the meaning of an output.

Our methods also outperform the supervised embedding regression method both in- and out-of-distribution. In pale-yellow bars we show that embedding regression performance deteriorates when its training data do not match the deployment distribution—which mirrors the common real-world case in which there is a distribution shift between training and deployment 42 —the plotted value is the average metric for embedding regression trained on one of the four ‘off-distribution’ datasets for that evaluation. This is critical because reliable uncertainty is most important when the data distribution shifts. Semantic entropy also outperforms P (True) which is supervised ‘in-context’; that is, it is adapted to the deployment task with a few training examples provided in the LLM prompt itself. The discrete variant of semantic entropy performs similarly to our standard estimator, despite not requiring exact output probabilities.

Averaged across the 30 combinations of tasks and models we study, semantic entropy achieves the best AUROC value of 0.790 whereas naive entropy (0.691), P (True) (0.698) and the embedding regression baseline (0.687) lag behind it. Semantic entropy performs well consistently, with stable performance (between 0.78 and 0.81 AUROC) across the different model families (LLaMA, Falcon and Mistral) and scales (from 7B to 70B parameters) which we study (we report summary statistics for each dataset and model as before). Although semantic entropy outperforms the baselines across all model sizes, P (True) seems to improve with model size, suggesting that it might become more competitive for very capable honest models in settings that the model understands well (which are, however, not the most important cases to have good uncertainty). We use ten generations to compute entropy, selected using analysis in Supplementary Fig. 2 . Further results for short-phrase generations are described in Supplementary Figs. 7 – 10 .

The results in Fig. 2 offer a lower bound on the effectiveness of semantic entropy at detecting confabulations. These evaluations determine whether semantic entropy and baseline methods can detect when the answers of the model are incorrect (which we validate against human correctness evaluations in Supplementary Table 4 ). In addition to errors from confabulations (arbitrary incorrectness), this also includes other types of mistakes for which semantic entropy is not suited, such as consistent errors learned from the training data. The fact that methods such as embedding regression are able to spot other kinds of errors, not just confabulations, but still are outperformed by semantic entropy, suggests that confabulations are a principal category of errors for actual generations.

Examples of questions and answers from TriviaQA, SQuAD and BioASQ, for LLaMA 2 Chat 70B, are shown in Table 1 . These illustrate how only semantic entropy detects when the meaning is constant but the form varies (the first row of the table) whereas semantic entropy and naive entropy both correctly predict the presence of confabulations when the form and meaning vary together (second row) and predict the absence of confabulations when the form and meaning are both constant across several resampled generations (third row). In the final row, we give an example in which semantic entropy is erroneously high as a result of overly sensitive semantic clustering relative to the reference answer. Our clustering method distinguishes the answers which provide a precise date from those which only provide a year. For some contexts that would have been correct but in this context the distinction between the specific day and the year is probably irrelevant. This highlights the importance of context and judgement in clustering, especially in subtle cases, as well as the shortcomings of evaluating against fixed reference answers which do not capture the open-ended flexibility of conversational deployments of LLMs.

Detecting confabulations in biographies

Semantic entropy is most natural for sentences that express a single proposition but the idea of semantic equivalence is trickier to apply to longer passages which express many propositions which might only agree partially 43 . Nevertheless, we can use semantic entropy to detect confabulations in longer generations, such as entire paragraphs of text. To show this, we develop a dataset of biographical generations from GPT-4 (v.0613) for 21 individuals notable enough to have their own Wikipedia page but without extensive online biographies. From each biography generated by GPT-4, we automatically extract propositional factual claims about the individual (150 factual claims in total), which we manually label as true or false.

Applying semantic entropy to this problem is challenging. Naively, one might simply regenerate each sentence (conditioned on the text so far) and then compute semantic entropy over these regenerations. However, the resampled sentences often target different aspects of the biography: for example, one time describing family and the next time profession. This is analogous to the original problem semantic entropy was designed to resolve: the model is uncertain about the right ordering of facts, not about the facts themselves. To address this, we break down the entire paragraph into factual claims and reconstruct questions which might have been answered by those claims. Only then do we apply semantic entropy (Fig. 1 ) by generating three new answers to each question (selected with analysis in Supplementary Figs. 3 and 4 ) and computing the semantic entropy over those generations plus the original factual claim. We aggregate these by averaging the semantic entropy over all the questions to get an uncertainty score for each proposition, which we use to detect confabulations. Unaggregated results are shown in Supplementary Figs. 5 and 6 .

As GPT-4 did not allow access to the probability of the generation at the time of writing, we use a discrete variant of semantic entropy which makes the further approximation that we can infer a discrete empirical distribution over semantic meaning clusters from only the generations ( Methods ). This allows us to compute semantic entropy using only the black-box outputs of an LLM. However, we were unable to compute the naive entropy baseline, the standard semantic entropy estimator or the embedding regression baseline for GPT-4 without output probabilities and embeddings.

In Fig. 3 we show that the discrete variant of semantic entropy effectively detects confabulations on this dataset. Its AUROC and AURAC are higher than either a simple ‘self-check’ baseline—which just asks the LLM whether the factoid is likely to be true—or a variant of P (True) which has been adapted to work for the paragraph-length setting. Discrete semantic entropy has better rejection accuracy performance until 20% of the questions have been rejected at which point P (True) has a narrow edge. This indicates that the questions predicted to cause confabulations are indeed more likely to be wrong.

The discrete variant of our semantic entropy estimator outperforms baselines both when measured by AUROC and AURAC metrics (scored on the y -axis). The AUROC and AURAC are substantially higher than for both baselines. At above 80% of questions being answered, semantic entropy has the highest accuracy. Only when the top 20% of answers judged most likely to be confabulations are rejected does the answer accuracy on the remainder for the P (True) baseline exceed semantic entropy.

Our probabilistic approach, accounting for semantic equivalence, detects an important class of hallucinations: those that are caused by a lack of LLM knowledge. These are a substantial portion of the failures at present and will continue even as models grow in capabilities because situations and cases that humans cannot reliably supervise will persist. Confabulations are a particularly noteworthy failure mode for question answering but appear in other domains too. Semantic entropy needs no previous domain knowledge and we expect that algorithmic adaptations to other problems will allow similar advances in, for example, abstractive summarization. In addition, extensions to alternative input variations such as rephrasing or counterfactual scenarios would allow a similar method to act as a form of cross-examination 44 for scalable oversight through debate 45 .

The success of semantic entropy at detecting errors suggests that LLMs are even better at “knowing what they don’t know” than was argued by ref. 24 —they just don’t know they know what they don’t know. Our method explicitly does not directly address situations in which LLMs are confidently wrong because they have been trained with objectives that systematically produce dangerous behaviour, cause systematic reasoning errors or are systematically misleading the user. We believe that these represent different underlying mechanisms—despite similar ‘symptoms’—and need to be handled separately.

One exciting aspect of our approach is the way it makes use of classical probabilistic machine learning methods and adapts them to the unique properties of modern LLMs and free-form language generation. We hope to inspire a fruitful exchange of well-studied methods and emerging new problems by highlighting the importance of meaning when addressing language-based machine learning problems.

Semantic entropy as a strategy for overcoming confabulation builds on probabilistic tools for uncertainty estimation. It can be applied directly to any LLM or similar foundation model without requiring any modifications to the architecture. Our ‘discrete’ variant of semantic uncertainty can be applied even when the predicted probabilities for the generations are not available, for example, because access to the internals of the model is limited.

In this section we introduce background on probabilistic methods and uncertainty in machine learning, discuss how it applies to language models and then discuss our contribution, semantic entropy, in detail.

Uncertainty and machine learning

We aim to detect confabulations in LLMs, using the principle that the model will be uncertain about generations for which its output is going to be arbitrary.

One measure of uncertainty is the predictive entropy of the output distribution, which measures the information one has about the output given the input 25 . The predictive entropy (PE) for an input sentence x is the conditional entropy ( H ) of the output random variable Y with realization y given x ,

A low predictive entropy indicates an output distribution which is heavily concentrated whereas a high predictive entropy indicates that many possible outputs are similarly likely.

Aleatoric and epistemic uncertainty

We do not distinguish between aleatoric and epistemic uncertainty in our analysis. Researchers sometimes separate aleatoric uncertainty (uncertainty in the underlying data distribution) from epistemic uncertainty (caused by having only limited information) 46 . Further advances in uncertainty estimation which separate these kinds of uncertainty would enhance the potential for our semantic uncertainty approach by allowing extensions beyond entropy.

Joint probabilities of sequences of tokens

Generative LLMs produce strings of text by selecting tokens in sequence. Each token is a wordpiece that often represents three or four characters (though especially common sequences and important words such as numbers typically get their own token). To compute entropies, we need access to the probabilities the LLM assigns to the generated sequence of tokens. The probability of the entire sequence, s , conditioned on the context, x , is the product of the conditional probabilities of new tokens given past tokens, whose resulting log-probability is \(\log P({\bf{s}}| {\boldsymbol{x}})={\sum }_{i}\log P({s}_{i}| {{\bf{s}}}_{ < i},{\boldsymbol{x}})\) , where s i is the i th output token and s < i denotes the set of previous tokens.

Length normalization

When comparing the log-probabilities of generated sequences, we use ‘length normalization’, that is, we use an arithmetic mean log-probability, \(\frac{1}{N}{\sum }_{i}^{N}\log P({s}_{i}| {{\bf{s}}}_{ < i},{\boldsymbol{x}})\) , instead of the sum. In expectation, longer sequences have lower joint likelihoods because of the conditional independence of the token probabilities 47 . The joint likelihood of a sequence of length N shrinks exponentially in N . Its negative log-probability therefore grows linearly in N , so longer sentences tend to contribute more to entropy. We therefore interpret length-normalizing the log-probabilities when estimating the entropy as asserting that the expected uncertainty of generations is independent of sentence length. Length normalization has some empirical success 48 , including in our own preliminary experiments, but little theoretical justification in the literature.

Principles of semantic uncertainty

If we naively calculate the predictive entropy directly from the probabilities of the generated sequence of tokens, we conflate the uncertainty of the model over the meaning of its answer with the uncertainty over the exact tokens used to express that meaning. For example, even if the model is confident in the meaning of a generation, there are still usually many different ways for phrasing that generation without changing its meaning. For the purposes of detecting confabulations, the uncertainty of the LLM over meanings is more important than the uncertainty over the exact tokens used to express those meanings.

Our semantic uncertainty method therefore seeks to estimate only the uncertainty the LLM has over the meaning of its generation, not the choice of words. To do this, we introduce an algorithm that clusters model generations by meaning and subsequently calculates semantic uncertainty. At a high level this involves three steps:

Generation: sample output sequences of tokens from the predictive distribution of a LLM given a context x .

Clustering: cluster sequences by their meaning using our clustering algorithm based on bidirectional entailment.

Entropy estimation: estimate semantic entropy by summing probabilities of sequences that share a meaning following equation ( 2 ) and compute their entropy.

Generating a set of answers from the model

Given some context x as input to the LLM, we sample M sequences, { s (1) , …,  s ( M ) } and record their token probabilities, { P ( s (1) ∣ x ), …,  P ( s ( M ) ∣ x )}. We sample all our generations from a single model, varying only the random seed used for sampling from the token probabilities. We do not observe the method to be particularly sensitive to details of the sampling scheme. In our implementation, we sample at temperature 1 using nucleus sampling ( P  = 0.9) (ref. 49 ) and top- K sampling ( K  = 50) (ref. 50 ). We also sample a single generation at low temperature (0.1) as an estimate of the ‘best generation’ of the model to the context, which we use to assess the accuracy of the model. (A lower sampling temperature increases the probability of sampling the most likely tokens).

Clustering by semantic equivalence

To estimate semantic entropy we need to cluster generated outputs from the model into groups of outputs that mean the same thing as each other.

This can be described using ‘semantic equivalence’ which is the relation that holds between two sentences when they mean the same thing. We can formalize semantic equivalence mathematically. Let the space of tokens in a language be \({\mathcal{T}}\) . The space of all possible sequences of tokens of length N is then \({{\mathcal{S}}}_{N}\equiv {{\mathcal{T}}}^{N}\) . Note that N can be made arbitrarily large to accommodate whatever size of sentence one can imagine and one of the tokens can be a ‘padding’ token which occurs with certainty for each token after the end-of-sequence token. For some sentence \({\bf{s}}\in {{\mathcal{S}}}_{N}\) , composed of a sequence of tokens, \({s}_{i}\in {\mathcal{T}}\) , there is an associated meaning. Theories of meaning are contested 51 . However, for specific models and deployment contexts many considerations can be set aside. Care should be taken comparing very different models and contexts.

Let us introduce a semantic equivalence relation, E (  ⋅  ,  ⋅  ), which holds for any two sentences that mean the same thing—we will operationalize this presently. Recall that an equivalence relation is any reflexive, symmetric and transitive relation and that any equivalence relation on a set corresponds to a set of equivalence classes. Each semantic equivalence class captures outputs that can be considered to express the same meaning. That is, for the space of semantic equivalence classes \({\mathcal{C}}\) the sentences in the set \(c\in {\mathcal{C}}\) can be regarded in many settings as expressing a similar meaning such that \(\forall {\bf{s}},{{\bf{s}}}^{{\prime} }\in c:E({\bf{s}},{{\bf{s}}}^{{\prime} })\) . So we can build up these classes of semantically equivalent sentences by checking if new sentences share a meaning with any sentences we have already clustered and, if so, adding them into that class.

We operationalize E (  ⋅  ,  ⋅  ) using the idea of bidirectional entailment, which has a long history in linguistics 52 and natural language processing 28 , 53 , 54 . A sequence, s , means the same thing as a second sequence, s ′, only if the sequences entail (that is, logically imply) each other. For example, ‘The capital of France is Paris’ entails ‘Paris is the capital of France’ and vice versa because they mean the same thing. (See later for a discussion of soft equivalence and cases in which bidirectional entailment does not guarantee equivalent meanings).

Importantly, we require that the sequences mean the same thing with respect to the context—key meaning is sometimes contained in the context. For example, ‘Paris’ does not entail ‘The capital of France is Paris’ because ‘Paris’ is not a declarative sentence without context. But in the context of the question ‘What is the capital of France?’, the one-word answer does entail the longer answer.

Detecting entailment has been the object of study of a great deal of research in NLI 55 . We rely on language models to predict entailment, such as DeBERTa-Large-MNLI 56 , which has been trained to predict entailment, or general-purpose LLMs such as GPT-3.5 (ref. 57 ), which can predict entailment given suitable prompts.

We then cluster sentences according to whether they bidirectionally entail each other using the algorithm presented in Extended Data Fig. 1 . Note that, to check if a sequence should be added to an existing cluster, it is sufficient to check if the sequence bidirectionally entails any of the existing sequences in that cluster (we arbitrarily pick the first one), given the transitivity of semantic equivalence. If a sequence does not share meaning with any existing cluster, we assign it its own cluster.

Computing the semantic entropy

Having determined the classes of generated sequences that mean the same thing, we can estimate the likelihood that a sequence generated by the LLM belongs to a given class by computing the sum of the probabilities of all the possible sequences of tokens which can be considered to express the same meaning as

Formally, this treats the output as a random variable whose event-space is the space of all possible meaning-classes, C , a sub- σ -algebra of the standard event-space S . We can then estimate the semantic entropy (SE) as the entropy over the meaning-distribution,

There is a complication which prevents direct computation: we do not have access to every possible meaning-class c . Instead, we can only sample c from the sequence-generating distribution induced by the model. To handle this, we estimate the expectation in equation ( 3 ) using a Rao–Blackwellized Monte Carlo integration over the semantic equivalence classes C ,

where \(P({C}_{i}| {\boldsymbol{x}})=\frac{P({c}_{i}| {\boldsymbol{x}})}{{\sum }_{c}P(c| {\boldsymbol{x}})}\) estimates a categorical distribution over the cluster meanings, that is, ∑ i P ( C i ∣ x ) = 1. Without this normalization step cluster ‘probabilities’ could exceed one because of length normalization, resulting in degeneracies. Equation ( 5 ) is the estimator giving our main method that we refer to as semantic entropy throughout the text.

For scenarios in which the sequence probabilities are not available, we propose a variant of semantic entropy which we call ‘discrete’ semantic entropy. Discrete semantic entropy approximates P ( C i ∣ x ) directly from the number of generations in each cluster, disregarding the token probabilities. That is, we approximate P ( C i ∣ x ) as \({\sum }_{1}^{M}\frac{{I}_{c={C}_{i}}}{M}\) , the proportion of all the sampled answers which belong to that cluster. Effectively, this just assumes that each output that was actually generated was equally probable—estimating the underlying distribution as the categorical empirical distribution. In the limit of M the estimator converges to equation ( 5 ) by the law of large numbers. We find that discrete semantic entropy results in similar performance empirically.

We provide a worked example of the computation of semantic entropy in Supplementary Note  1 .

Semantic entropy is designed to detect confabulations, that is, model outputs with arbitrary meaning. In our experiments, we use semantic uncertainty to predict model accuracy, demonstrating that confabulations make up a notable fraction of model mistakes. We further show that semantic uncertainty can be used to improve model accuracy by refusing to answer questions when semantic uncertainty is high. Last, semantic uncertainty can be used to give users a way to know when model generations are probably unreliable.

We use the datasets BioASQ 34 , SQuAD 33 , TriviaQA 32 , SVAMP 37 and NQ-Open 35 . BioASQ is a life-sciences question-answering dataset based on the annual challenge of the same name. The specific dataset we use is based on the QA dataset from Task B of the 2023 BioASQ challenge (11B). SQuAD is a reading comprehension dataset whose context passages are drawn from Wikipedia and for which the answers to questions can be found in these passages. We use SQuAD 1.1 which excludes the unanswerable questions added in v.2.0 that are deliberately constructed to induce mistakes so they do not in practice cause confabulations to occur. TriviaQA is a trivia question-answering dataset. SVAMP is a word-problem maths dataset containing elementary-school mathematical reasoning tasks. NQ-Open is a dataset of realistic questions aggregated from Google Search which have been chosen to be answerable without reference to a source text. For each dataset, we use 400 train examples and 400 test examples randomly sampled from the original larger dataset. Note that only some of the methods require training, for example semantic entropy does not use the training data. If the datasets themselves are already split into train and test (or validation) samples, we sample our examples from within the corresponding split.

All these datasets are free-form, rather than multiple choice, because this better captures the opportunities created by LLMs to produce free-form sentences as answers. We refer to this default scenario as our ‘sentence-length’ experiments. In Supplementary Note  7 , we also present results for confabulation detection in a ‘short-phrase’ scenario, in which we constrain model answers on these datasets to be as concise as possible.

To make the problems more difficult and induce confabulations, we do not provide the context passages for any of the datasets. When the context passages are provided, the accuracy rate is too high for these datasets for the latest generations of models to meaningfully study confabulations.

For sentence-length generations we use: Falcon 39 Instruct (7B and 40B), LLaMA 2 Chat 38 (7B, 13B and 70B) and Mistral 40 Instruct (7B).

In addition to reporting results for semantic entropy, discrete semantic entropy and naive entropy, we consider two strong baselines.

Embedding regression is a supervised baseline inspired by the P (IK) method 24 . In that paper, the authors fine-tune their proprietary LLM on a dataset of questions to predict whether the model would have been correct. This requires access to a dataset of ground-truth answers to the questions. Rather than fine-tuning the entire LLM in this way, we simply take the final hidden units and train a logistic regression classifier to make the same prediction. By contrast to their method, this is much simpler because it does not require fine-tuning the entire language model, as well as being more reproducible because the solution to the logistic regression optimization problem is not as seed-dependent as the fine-tuning procedure. As expected, this supervised approach performs well in-distribution but fails when the distribution of questions is different from that on which the classifier is trained.

The second baseline we consider is the P (True) method 24 , in which the model first samples M answers (identically to our semantic entropy approach) and then is prompted with the list of all answers generated followed by the highest probability answer and a question whether this answer is “(a) True” or “(b) False”. The confidence score is then taken to be the probability with which the LLM responds with ‘a’ to the multiple-choice question. The performance of this method is boosted with a few-shot prompt, in which up to 20 examples from the training set are randomly chosen, filled in as above, but then provided with the actual ground truth of whether the proposed answer was true or false. In this way, the method can be considered as supervised ‘in-context’ because it makes use of some ground-truth training labels but can be used without retraining the model. Because of context-size constraints, this method cannot fit a full 20 few-shot examples in the context when input questions are long or large numbers of generations are used. As a result, we sometimes have to reduce the number of few-shot examples to suit the context size and we note this in the  Supplementary Material .

Entailment estimator

Any NLI classification system could be used for our bidirectional entailment clustering algorithm. We consider two different kinds of entailment detector.

One option is to use an instruction-tuned LLM such as LLaMA 2, GPT-3.5 (Turbo 1106) or GPT-4 to predict entailment between generations. We use the following prompt:

We are evaluating answers to the question {question} Here are two possible answers: Possible Answer 1: {text1} Possible Answer 2: {text2} Does Possible Answer 1 semantically entail Possible Answer 2? Respond with entailment, contradiction, or neutral.

Alternatively, we consider using a language model trained for entailment prediction, specifically the DeBERTa-large model 56 fine-tuned on the NLI dataset MNLI 58 . This builds on past work towards paraphrase identification based on embedding similarity 59 , 60 and BERT-style models 61 , 62 . We template more simply, checking if DeBERTa predicts entailment between the concatenation of the question and one answer and the concatenation of the question and another answer. Note that DeBERTa-large is a relatively lightweight model with only 1.5B parameters which is much less powerful than most of the LLMs under study.

In Supplementary Note 2 , we carefully evaluate the benefits and drawbacks of these methods for entailment prediction. We settle on using GPT-3.5 with the above prompt, as its entailment predictions agree well with human raters and lead to good confabulation detection performance.

In Supplementary Note  3 , we provide a discussion of the computational cost and choosing the number of generations for reliable clustering.

Prompting templates

We use a simple generation template for all sentence-length answer datasets:

Answer the following question in a single brief but complete sentence. Question: {question} Answer:

Metrics and accuracy measurements

We use three main metrics to evaluate our method: AUROC, rejection accuracy and AURAC. Each of these is grounded in an automated factuality estimation measurement relative to the reference answers provided by the datasets that we use.

AUROC, rejection accuracy and AURAC

First, we use the AUROC curve, which measures the reliability of a classifier accounting for both precision and recall. The AUROC can be interpreted as the probability that a randomly chosen correct answer has been assigned a higher confidence score than a randomly chosen incorrect answer. For a perfect classifier, this is 1.

Second, we compute the ‘rejection accuracy at X %’, which is the question-answering accuracy of the model on the most-confident X % of the inputs as identified by the respective uncertainty method. If an uncertainty method works well, predictions on the confident subset should be more accurate than predictions on the excluded subset and the rejection accuracy should increase as we reject more inputs.

To summarize this statistic we compute the AURAC—the total area enclosed by the accuracies at all cut-off percentages X %. This should increase towards 1 as given uncertainty method becomes more accurate and better at detecting likely-inaccurate responses but it is more sensitive to the overall accuracy of the model than the AUROC metric.

In Supplementary Note  5 , we provide the unaggregated rejection accuracies for sentence-length generations.

Assessing accuracy

For the short-phrase-length generation setting presented in Supplementary Note  7 , we simply assess the accuracy of the generations by checking if the F1 score of the commonly used SQuAD metric exceeds 0.5. There are limitations to such simple scoring rules 63 but this method is widely used in practice and its error is comparatively small on these standard datasets.

For our default scenario, the longer sentence-length generations, this measure fails, as the overlap between the short reference answer and our long model answer is invariably too small. For sentence-length generations, we therefore automatically determine whether an answer to the question is correct or incorrect by using GPT-4 to compare the given answer to the reference answer. We use the template:

We are assessing the quality of answers to the following question: {question} The expected answer is: {reference answer} The proposed answer is: {predicted answer} Within the context of the question, does the proposed answer mean the same as the expected answer? Respond only with yes or no.

We make a small modification for datasets with several reference answers: line two becomes “The following are expected answers to this question:” and the final line asks “does the proposed answer mean the same as any of the expected answers?”.

In Supplementary Note 6 , we check the quality of our automated ground-truth evaluations against human judgement by hand. We find that GPT-4 gives the best results for determining model accuracy and thus use it in all our sentence-length experiments.

In this section we describe the application of semantic entropy to confabulation detection in longer model generations, specifically paragraph-length biographies.

We introduce a biography-generation dataset—FactualBio—available alongside this paper. FactualBio is a collection of biographies of individuals who are notable enough to have Wikipedia pages but not notable enough to have large amounts of detailed coverage, generated by GPT-4 (v.0613). To generate the dataset, we randomly sampled 21 individuals from the WikiBio dataset 64 . For each biography, we generated a list of factual claims contained in each biography using GPT-4, with 150 total factual claims (the total number is only coincidentally a round number). For each of these factual claims, we manually determined whether the claim was correct or incorrect. Out of 150 claims, 45 were incorrect. As before, we apply confabulation detection to detect incorrect model predictions, even though there may be model errors which are not confabulations.

Prompting and generation

Given a paragraph-length piece of LLM-generated text, we apply the following sequence of steps:

Automatically decompose the paragraph into specific factual claims using an LLM (not necessarily the same as the original).

For each factual claim, use an LLM to automatically construct Q questions which might have produced that claim.

For each question, prompt the original LLM to generate M answers.

For each question, compute the semantic entropy of the answers, including the original factual claim.

Average the semantic entropies over the questions to arrive at a score for the original factual claim.

We pursue this slightly indirect way of generating answers because we find that simply resampling each sentence creates variation unrelated to the uncertainty of the model about the factual claim, such as differences in paragraph structure.

We decompose the paragraph into factual claims using the following prompt:

Please list the specific factual propositions included in the answer above. Be complete and do not leave any factual claims out. Provide each claim as a separate sentence in a separate bullet point.

We found that we agreed with the decompositions in all cases in the dataset.

We then generate six questions for each of the facts from the decomposition. We generate these questions by prompting the model twice with the following:

Following this text: {text so far} You see the sentence: {proposition} Generate a list of three questions, that might have generated the sentence in the context of the preceding original text, as well as their answers. Please do not use specific facts that appear in the follow-up sentence when formulating the question. Make the questions and answers diverse. Avoid yes-no questions. The answers should not be a full sentence and as short as possible, e.g. only a name, place, or thing. Use the format “1. {question} – {answer}”.

These questions are not necessarily well-targeted and the difficulty of this step is the main source of errors in the procedure. We generate three questions with each prompt, as this encourages diversity of the questions, each question targeting a different aspect of the fact. However, we observed that the generated questions will sometimes miss obvious aspects of the fact. Executing the above prompt twice (for a total of six questions) can improve coverage. We also ask for brief answers because the current version of GPT-4 tends to give long, convoluted and highly hedged answers unless explicitly told not to.

Then, for each question, we generate three new answers using the following prompt:

We are writing an answer to the question “{user question}”. So far we have written: {text so far} The next sentence should be the answer to the following question: {question} Please answer this question. Do not answer in a full sentence. Answer with as few words as possible, e.g. only a name, place, or thing.

We then compute the semantic entropy over these answers plus the original factual claim. Including the original fact ensures that the estimator remains grounded in the original claim and helps detect situations in which the question has been interpreted completely differently from the original context. We make a small modification to handle the fact that GPT-4 generations often include refusals to answer questions. These refusals were not something we commonly observe in our experiments with LLaMA 2, Falcon or Mistral models. If more than half of the answers include one of the strings ‘not available’, ‘not provided’, ‘unknown’ or ‘unclear’ then we treat the semantic uncertainty as maximal.

We then average the semantic entropies for each question corresponding to the factual claim to get an entropy for this factual claim.

Despite the extra assumptions and complexity, we find that this method greatly outperforms the baselines.

To compute semantic entailment between the original claim and regenerated answers, we rely on the DeBERTa entailment prediction model as we find empirically that DeBERTa predictions result in higher train-set AUROC than other methods. Because DeBERTa has slightly lower recall than GPT-3.5/4, we use a modified set-up for which we say the answers mean the same as each other if at least one of them entails the other and neither is seen to contradict the other—a kind of ‘non-defeating’ bidirectional entailment check rather than true bidirectional entailment. The good performance of DeBERTa in this scenario is not surprising as both factual claims and regenerated answers are relatively short. We refer to Supplementary Notes 2 and 3 for ablations and experiments regarding our choice of entailment estimator for paragraph-length generations.

We implement two baselines. First, we implement a variant of the P (True) method, which is adapted to the new setting. For each factoid, we generate a question with answers in the same way as for semantic entropy. We then use the following prompt:

Question: {question} Here are some brainstormed ideas: {list of regenerated answers} Possible answer: {original answer} Is the possible answer true? Respond with “yes” or “no”.

As we cannot access the probabilities GPT-4 assigns to predicting ‘yes’ and ‘no’ as the next token, we approximate this using Monte Carlo samples. Concretely, we execute the above prompt ten times (at temperature 1) and then take the fraction of answers which was ‘yes’ as our unbiased Monte Carlo estimate of the token probability GPT-4 assigns to ‘yes’.

As a second, simpler, baseline we check if the model thinks the answer is true. We simply ask:

Following this text: {text so far} You see this statement: {proposition} Is it likely that the statement is true? Respond with ‘yes’ or ‘no’.

It is interesting that this method ought to perform very well if we think that the model has good ‘self-knowledge’ (that is, if “models mostly know what they don’t know” 24 ) but in fact semantic entropy is much better at detecting confabulations.

Data availability

The data used for the short-phrase and sentence-length generations are publicly available and the released code details how to access it. We release a public version of the FactualBio dataset as part of the code base for reproducing the paragraph-length experiments.

Code availability

We release all code used to produce the main experiments. The code for short-phrase and sentence-length experiments can be found at github.com/jlko/semantic_uncertainty and https://doi.org/10.5281/zenodo.10964366 (ref. 65 ). The code for paragraph-length experiments can be found at github.com/jlko/long_hallucinations and https://doi.org/10.5281/zenodo.10964366 (ref. 65 ).

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Acknowledgements

We thank G. Irving, K. Perlin, J. Richens, L. Rimell and M. Turpin for their comments or discussion related to this work. We thank K. Handa for his help with the human evaluation of our automated accuracy assessment. We thank F. Bickford Smith and L. Melo for their code review. Y.G. is supported by a Turing AI Fellowship funded by the UK government’s Office for AI, through UK Research and Innovation (grant reference EP/V030302/1), and delivered by the Alan Turing Institute.

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These authors contributed equally: Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn

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Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn & Yarin Gal

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S.F. led the work from conception to completion and proposed using bidirectional entailment to cluster generations as a way of computing entropy in LLMs. He wrote the main text, most of the Methods and Supplementary Information and prepared most of the figures. J.K. improved the mathematical formalization of semantic entropy; led the extension of semantic entropy to sentence- and paragraph-length generations; wrote the code for, and carried out, all the experiments and evaluations; wrote much of the Methods and Supplementary Information and prepared drafts of many figures; and gave critical feedback on the main text. L.K. developed the initial mathematical formalization of semantic entropy; wrote code for, and carried out, the initial experiments around semantic entropy and its variants which demonstrated the promise of the idea and helped narrow down possible research avenues to explore; and gave critical feedback on the main text. Y.G. ideated the project, proposing the idea to differentiate semantic and syntactic diversity as a tool for detecting hallucinations, provided high-level guidance on the research and gave critical feedback on the main text; he runs the research laboratory in which the work was carried out.

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S.F. is currently employed by Google DeepMind and L.K. by OpenAI. For both, this paper was written under their University of Oxford affiliation. The remaining authors declare no competing interests.

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Extended data figures and tables

Extended data fig. 1 algorithm outline for bidirectional entailment clustering..

Given a set of outputs in response to a context, the bidirectional entailment answer returns a set of sets of outputs which have been classified as sharing a meaning.

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Supplementary information.

Supplementary Notes 1–7, Figs. 1–10, Tables 1–4 and references. Includes, worked example for semantic entropy calculation, discussion of limitations and computational cost of entailment clustering, ablation of entailment prediction and clustering methods, discussion of automated accuracy assessment, unaggregated results for sentence-length generations and further results for short-phrase generations.

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Farquhar, S., Kossen, J., Kuhn, L. et al. Detecting hallucinations in large language models using semantic entropy. Nature 630 , 625–630 (2024). https://doi.org/10.1038/s41586-024-07421-0

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ENGL 241.S01: American Literature I

Tuesday and Thursday 12:30-1:45 p.m.

This course provides a broad, historical survey of American literature from the early colonial period to the Civil War. Ranging across historical periods and literary genres—including early accounts of contact and discovery, narratives of captivity and slavery, poetry of revolution, essays on gender equality and stories of industrial exploitation—this class examines how subjects such as colonialism, nationhood, religion, slavery, westward expansion, race, gender and democracy continue to influence how Americans see themselves and their society.

Required Texts

• The Norton Anthology of American Literature: Package 1, Volumes A and B Beginnings to 1865, Ninth Edition. (ISBN 978-0-393-26454-8)

ENGL 283.S01 Introduction to Creative Writing

Steven Wingate

Students will explore the various forms of creative writing (fiction, nonfiction and poetry) not one at a time in a survey format—as if there were decisive walls of separation between then—but as intensely related genres that share much of their creative DNA. Through close reading and work on personal texts, students will address the decisions that writers in any genre must face on voice, rhetorical position, relationship to audience, etc. Students will produce and revise portfolios of original creative work developed from prompts and research. This course fulfills the same SGR #2 requirements ENGL 201; note that the course will involve a research project. Successful completion of ENGL 101 (including by test or dual credit) is a prerequisite.

ENGL 283.S02 Introduction to Creative Writing

Jodilyn Andrews

This course introduces students to the craft of writing, with readings and practice in at least two genres (including fiction, poetry and drama).

ENGL 283.ST1 Introduction to Creative Writing

Amber Jensen, M.A., M.F.A.

This course explores creative writing as a way of encountering the world, research as a component of the creative writing process, elements of craft and their rhetorical effect and drafting, workshop and revision as integral parts of writing polished literary creative work. Student writers will engage in the research practices that inform the writing of literature and in the composing strategies and writing process writers use to create literary texts. Through their reading and writing of fiction, poetry and creative nonfiction, students will learn about craft elements, find examples of those craft elements in published works and apply these elements in their own creative work, developed through weekly writing activities, small group and large group workshop and conferences with the instructor. Work will be submitted, along with a learning reflection and revision plan in each genre and will then be revised and submitted as a final portfolio at the end of the semester to demonstrate continued growth in the creation of polished literary writing.

• 300-400 level

ENGL 424.S01 Language Arts Methods grades 7-12  

Tuesday 6-8:50 p.m.

Danielle Harms

Techniques, materials and resources for teaching English language and literature to middle and secondary school students. Required of students in the English education option.

AIS/ENGL 447.S01: American Indian Literature of the Present 

Thursdays 3-6 p.m.

This course introduces students to contemporary works by authors from various Indigenous nations. Students examine these works to enhance their historical understanding of Indigenous peoples, discover the variety of literary forms used by those who identify as Indigenous writers, and consider the cultural and political significance of these varieties of expression. Topics and questions to be explored include:

• Genre: What makes Indigenous literature indigenous?
• Political and Cultural Sovereignty: Why have an emphasis on tribal specificity and calls for “literary separatism” emerged in recent decades, and what are some of the critical conversations surrounding such particularized perspectives?
• Gender and Sexuality: What are the intersecting concerns of Indigenous Studies and Women, Gender and Sexuality Studies, and how might these research fields inform one another?
• Trans-Indigeneity: What might we learn by comparing works across different Indigenous traditions, and what challenges do such comparisons present?
• Aesthetics: How do Indigenous writers understand the dynamics between tradition and creativity?
• Visual Forms: What questions or concerns do visual representations (television and film) by or about Indigenous peoples present?

Possible Texts

• Akiwenzie-Damm, Kateri and Josie Douglas (eds), Skins: Contemporary Indigenous Writing. IAD Press, 2000. (978-1864650327)
• Erdrich, Louise, The Sentence. Harper, 2021 (978-0062671127)
• Harjo, Joy, Poet Warrior: A Memoir. Norton, 2021 (978-0393248524)
• Harjo, Sterlin and Taika Waititi, Reservation Dogs (selected episodes)
• Talty, Morgan. Night of the Living Rez, 2022, Tin House (978-1953534187)
• Wall Kimmerer, Robin. Braiding Sweet Grass, Milkweed Editions (978-1571313560)
• Wilson, Diane. The Seed Keeper: A Novel. Milkweed Editions (978-1571311375)
• Critical essays by Alexie, Allen, Cohen, Cox, King, Kroeber, Ortiz, Piatote, Ross and Sexton, Smith, Taylor, Teuton, Treuer, Vizenor, and Womack.

ENGL 472.S01: Film Criticism

Tuesdays 2-4:50 p.m.

Jason McEntee

Do you have an appreciation for, and enjoy watching, movies? Do you want to study movies in a genre-oriented format (such as those we typically call the Western, the screwball comedy, the science fiction or the crime/gangster, to name a few)? Do you want to explore the different critical approaches for talking and writing about movies (such as auteur, feminist, genre or reception)?

In this class, you will examine movies through viewing and defining different genres while, at the same time, studying and utilizing different styles of film criticism. You will share your discoveries in both class discussions and short writings. The final project will be a formal written piece of film criticism based on our work throughout the semester. The course satisfies requirements and electives for all English majors and minors, including both the Film Studies and Professional Writing minors. (Note: Viewing of movies outside of class required and may require rental and/or streaming service fees.)

ENGL 476.ST1: Fiction

In this workshop-based creative writing course, students will develop original fiction based on strong attention to the fundamentals of literary storytelling: full-bodied characters, robust story lines, palpable environments and unique voices. We will pay particular attention to process awareness, to the integrity of the sentence, and to authors' commitments to their characters and the places in which their stories unfold. Some workshop experience is helpful, as student peer critique will be an important element of the class.

ENGL 479.01 Capstone: The Gothic

Wednesday 3-5:50 p.m.

With the publication of Horace Walpole’s "The Castle of Otranto " in 1764, the Gothic officially came into being. Dark tales of physical violence and psychological terror, the Gothic incorporates elements such as distressed heroes and heroines pursued by tyrannical villains; gloomy estates with dark corridors, secret passageways and mysterious chambers; haunting dreams, troubling prophecies and disturbing premonitions; abduction, imprisonment and murder; and a varied assortment of corpses, apparitions and “monsters.” In this course, we will trace the development of Gothic literature—and some film—from the eighteenth-century to the present time. As we do so, we will consider how the Gothic engages philosophical beliefs about the beautiful and sublime; shapes psychological understandings of human beings’ encounters with horror, terror, the fantastic and the uncanny; and intervenes in the social and historical contexts in which it was written. We’ll consider, for example, how the Gothic undermines ideals related to domesticity and marriage through representations of domestic abuse, toxicity and gaslighting. In addition, we’ll discuss Gothic texts that center the injustices of slavery and racism. As many Gothic texts suggest, the true horrors of human existence often have less to do with inexplicable supernatural phenomena than with the realities of the world in which we live. 

ENGL 485.S01: Undergraduate Writing Center Learning Assistants 

Flexible Scheduling

Nathan Serfling

Since their beginnings in the 1920s and 30s, writing centers have come to serve numerous functions: as hubs for writing across the curriculum initiatives, sites to develop and deliver workshops and resource centers for faculty as well as students, among other functions. But the primary function of writing centers has necessarily and rightfully remained the tutoring of student writers. This course will immerse you in that function in two parts. During the first four weeks, you will explore writing center praxis—that is, the dialogic interplay of theory and practice related to writing center work. This part of the course will orient you to writing center history, key theoretical tenets and practical aspects of writing center tutoring. Once we have developed and practiced this foundation, you will begin work in the writing center as a tutor, responsible for assisting a wide variety of student clients with numerous writing tasks. Through this work, you will learn to actively engage with student clients in the revision of a text, respond to different student needs and abilities, work with a variety of writing tasks and rhetorical situations, and develop a richer sense of writing as a complex and negotiated social process.

Graduate Courses

Engl 572.s01: film criticism, engl 576.st1 fiction.

In this workshop-based creative writing course, students will develop original fiction based on strong attention to the fundamentals of literary storytelling: full-bodied characters, robust story lines, palpable environments and unique voices. We will pay particular attention to process awareness, to the integrity of the sentence and to authors' commitments to their characters and the places in which their stories unfold. Some workshop experience is helpful, as student peer critique will be an important element of the class.

ENGL 605.S01 Seminar in Teaching Composition

Thursdays 1-3:50 p.m.

This course will provide you with a foundation in the pedagogies and theories (and their attendant histories) of writing instruction, a foundation that will prepare you to teach your own writing courses at SDSU and elsewhere. As you will discover through our course, though, writing instruction does not come with any prescribed set of “best” practices. Rather, writing pedagogies stem from and continue to evolve because of various and largely unsettled conversations about what constitutes effective writing and effective writing instruction. Part of becoming a practicing writing instructor, then, is studying these conversations to develop a sense of what “good writing” and “effective writing instruction” might mean for you in our particular program and how you might adapt that understanding to different programs and contexts.

As we read about, discuss and research writing instruction, we will address a variety of practical and theoretical topics. The practical focus will allow us to attend to topics relevant to your immediate classroom practices: designing a curriculum and various types of assignments, delivering the course content and assessing student work, among others. Our theoretical topics will begin to reveal the underpinnings of these various practical matters, including their historical, rhetorical, social and political contexts. In other words, we will investigate the praxis—the dialogic interaction of practice and theory—of writing pedagogy. As a result, this course aims to prepare you not only as a writing teacher but also as a nascent writing studies/writing pedagogy scholar.

At the end of this course, you should be able to engage effectively in the classroom practices described above and participate in academic conversations about writing pedagogy, both orally and in writing. Assessment of these outcomes will be based primarily on the various writing assignments you submit and to a smaller degree on your participation in class discussions and activities.

ENGL 726.S01: The New Woman, 1880–1900s 

Thursdays 3–5:50 p.m.

Katherine Malone

This course explores the rise of the New Woman at the end of the nineteenth century. The label New Woman referred to independent women who rebelled against social conventions. Often depicted riding bicycles, smoking cigarettes and wearing masculine clothing, these early feminists challenged gender roles and sought broader opportunities for women’s employment and self-determination. We will read provocative fiction and nonfiction by New Women writers and their critics, including authors such as Sarah Grand, Mona Caird, George Egerton, Amy Levy, Ella Hepworth Dixon, Grant Allen and George Gissing. We will analyze these exciting texts through a range of critical lenses and within the historical context of imperialism, scientific and technological innovation, the growth of the periodical press and discourse about race, class and gender. In addition to writing an argumentative seminar paper, students will complete short research assignments and lead discussion.

ENGL 792.ST1 Women in War: Female Authors and Characters in Contemporary War Lit

In this course, we will explore the voices of female authors and characters in contemporary literature of war. Drawing from various literary theories, our readings and discussion will explore the contributions of these voices to the evolving literature of war through archetypal and feminist criticism. We will read a variety of short works (both theoretical and creative) and complete works such as (selections subject to change): "Eyes Right" by Tracy Crow, "Plenty of Time When We Get Home" by Kayla Williams, "You Know When the Men are Gone" by Siobhan Fallon, "Still, Come Home" by Katie Schultz and "The Fine Art of Camouflage" by Lauren Johnson.