how to write the results and discussion section of a research paper

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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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Reporting Research Results in APA Style | Tips & Examples

Published on December 21, 2020 by Pritha Bhandari . Revised on January 17, 2024.

The results section of a quantitative research paper is where you summarize your data and report the findings of any relevant statistical analyses.

The APA manual provides rigorous guidelines for what to report in quantitative research papers in the fields of psychology, education, and other social sciences.

Use these standards to answer your research questions and report your data analyses in a complete and transparent way.

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Table of contents

What goes in your results section, introduce your data, summarize your data, report statistical results, presenting numbers effectively, what doesn’t belong in your results section, frequently asked questions about results in apa.

In APA style, the results section includes preliminary information about the participants and data, descriptive and inferential statistics, and the results of any exploratory analyses.

Include these in your results section:

• Participant flow and recruitment period. Report the number of participants at every stage of the study, as well as the dates when recruitment took place.
• Missing data . Identify the proportion of data that wasn’t included in your final analysis and state the reasons.
• Any adverse events. Make sure to report any unexpected events or side effects (for clinical studies).
• Descriptive statistics . Summarize the primary and secondary outcomes of the study.
• Inferential statistics , including confidence intervals and effect sizes. Address the primary and secondary research questions by reporting the detailed results of your main analyses.
• Results of subgroup or exploratory analyses, if applicable. Place detailed results in supplementary materials.

Write up the results in the past tense because you’re describing the outcomes of a completed research study.

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Before diving into your research findings, first describe the flow of participants at every stage of your study and whether any data were excluded from the final analysis.

Participant flow and recruitment period

It’s necessary to report any attrition, which is the decline in participants at every sequential stage of a study. That’s because an uneven number of participants across groups sometimes threatens internal validity and makes it difficult to compare groups. Be sure to also state all reasons for attrition.

If your study has multiple stages (e.g., pre-test, intervention, and post-test) and groups (e.g., experimental and control groups), a flow chart is the best way to report the number of participants in each group per stage and reasons for attrition.

Also report the dates for when you recruited participants or performed follow-up sessions.

Missing data

Another key issue is the completeness of your dataset. It’s necessary to report both the amount and reasons for data that was missing or excluded.

Data can become unusable due to equipment malfunctions, improper storage, unexpected events, participant ineligibility, and so on. For each case, state the reason why the data were unusable.

Some data points may be removed from the final analysis because they are outliers—but you must be able to justify how you decided what to exclude.

If you applied any techniques for overcoming or compensating for lost data, report those as well.

Adverse events

For clinical studies, report all events with serious consequences or any side effects that occured.

Descriptive statistics summarize your data for the reader. Present descriptive statistics for each primary, secondary, and subgroup analysis.

Don’t provide formulas or citations for commonly used statistics (e.g., standard deviation) – but do provide them for new or rare equations.

Descriptive statistics

The exact descriptive statistics that you report depends on the types of data in your study. Categorical variables can be reported using proportions, while quantitative data can be reported using means and standard deviations . For a large set of numbers, a table is the most effective presentation format.

Include sample sizes (overall and for each group) as well as appropriate measures of central tendency and variability for the outcomes in your results section. For every point estimate , add a clearly labelled measure of variability as well.

Be sure to note how you combined data to come up with variables of interest. For every variable of interest, explain how you operationalized it.

According to APA journal standards, it’s necessary to report all relevant hypothesis tests performed, estimates of effect sizes, and confidence intervals.

When reporting statistical results, you should first address primary research questions before moving onto secondary research questions and any exploratory or subgroup analyses.

Present the results of tests in the order that you performed them—report the outcomes of main tests before post-hoc tests, for example. Don’t leave out any relevant results, even if they don’t support your hypothesis.

Inferential statistics

For each statistical test performed, first restate the hypothesis , then state whether your hypothesis was supported and provide the outcomes that led you to that conclusion.

Report the following for each hypothesis test:

• the test statistic value,
• the degrees of freedom ,
• the exact p- value (unless it is less than 0.001),
• the magnitude and direction of the effect.

When reporting complex data analyses, such as factor analysis or multivariate analysis, present the models estimated in detail, and state the statistical software used. Make sure to report any violations of statistical assumptions or problems with estimation.

Effect sizes and confidence intervals

For each hypothesis test performed, you should present confidence intervals and estimates of effect sizes .

Confidence intervals are useful for showing the variability around point estimates. They should be included whenever you report population parameter estimates.

Effect sizes indicate how impactful the outcomes of a study are. But since they are estimates, it’s recommended that you also provide confidence intervals of effect sizes.

Subgroup or exploratory analyses

Briefly report the results of any other planned or exploratory analyses you performed. These may include subgroup analyses as well.

Subgroup analyses come with a high chance of false positive results, because performing a large number of comparison or correlation tests increases the chances of finding significant results.

If you find significant results in these analyses, make sure to appropriately report them as exploratory (rather than confirmatory) results to avoid overstating their importance.

While these analyses can be reported in less detail in the main text, you can provide the full analyses in supplementary materials.

To effectively present numbers, use a mix of text, tables , and figures where appropriate:

• To present three or fewer numbers, try a sentence ,
• To present between 4 and 20 numbers, try a table ,
• To present more than 20 numbers, try a figure .

Since these are general guidelines, use your own judgment and feedback from others for effective presentation of numbers.

Tables and figures should be numbered and have titles, along with relevant notes. Make sure to present data only once throughout the paper and refer to any tables and figures in the text.

Formatting statistics and numbers

It’s important to follow capitalization , italicization, and abbreviation rules when referring to statistics in your paper. There are specific format guidelines for reporting statistics in APA , as well as general rules about writing numbers .

If you are unsure of how to present specific symbols, look up the detailed APA guidelines or other papers in your field.

It’s important to provide a complete picture of your data analyses and outcomes in a concise way. For that reason, raw data and any interpretations of your results are not included in the results section.

It’s rarely appropriate to include raw data in your results section. Instead, you should always save the raw data securely and make them available and accessible to any other researchers who request them.

Making scientific research available to others is a key part of academic integrity and open science.

Interpretation or discussion of results

This belongs in your discussion section. Your results section is where you objectively report all relevant findings and leave them open for interpretation by readers.

While you should state whether the findings of statistical tests lend support to your hypotheses, refrain from forming conclusions to your research questions in the results section.

Explanation of how statistics tests work

For the sake of concise writing, you can safely assume that readers of your paper have professional knowledge of how statistical inferences work.

In an APA results section , you should generally report the following:

• Participant flow and recruitment period.
• Missing data and any adverse events.
• Descriptive statistics about your samples.
• Inferential statistics , including confidence intervals and effect sizes.
• Results of any subgroup or exploratory analyses, if applicable.

According to the APA guidelines, you should report enough detail on inferential statistics so that your readers understand your analyses.

• the test statistic value
• the degrees of freedom
• the exact p value (unless it is less than 0.001)
• the magnitude and direction of the effect

You should also present confidence intervals and estimates of effect sizes where relevant.

In APA style, statistics can be presented in the main text or as tables or figures . To decide how to present numbers, you can follow APA guidelines:

• To present three or fewer numbers, try a sentence,
• To present between 4 and 20 numbers, try a table,
• To present more than 20 numbers, try a figure.

Results are usually written in the past tense , because they are describing the outcome of completed actions.

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.

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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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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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Home » Research Results Section – Writing Guide and Examples

Research Results Section – Writing Guide and Examples

Table of Contents

Research Results

Research results refer to the findings and conclusions derived from a systematic investigation or study conducted to answer a specific question or hypothesis. These results are typically presented in a written report or paper and can include various forms of data such as numerical data, qualitative data, statistics, charts, graphs, and visual aids.

Results Section in Research

The results section of the research paper presents the findings of the study. It is the part of the paper where the researcher reports the data collected during the study and analyzes it to draw conclusions.

In the results section, the researcher should describe the data that was collected, the statistical analysis performed, and the findings of the study. It is important to be objective and not interpret the data in this section. Instead, the researcher should report the data as accurately and objectively as possible.

Structure of Research Results Section

The structure of the research results section can vary depending on the type of research conducted, but in general, it should contain the following components:

• Introduction: The introduction should provide an overview of the study, its aims, and its research questions. It should also briefly explain the methodology used to conduct the study.
• Data presentation : This section presents the data collected during the study. It may include tables, graphs, or other visual aids to help readers better understand the data. The data presented should be organized in a logical and coherent way, with headings and subheadings used to help guide the reader.
• Data analysis: In this section, the data presented in the previous section are analyzed and interpreted. The statistical tests used to analyze the data should be clearly explained, and the results of the tests should be presented in a way that is easy to understand.
• Discussion of results : This section should provide an interpretation of the results of the study, including a discussion of any unexpected findings. The discussion should also address the study’s research questions and explain how the results contribute to the field of study.
• Limitations: This section should acknowledge any limitations of the study, such as sample size, data collection methods, or other factors that may have influenced the results.
• Conclusions: The conclusions should summarize the main findings of the study and provide a final interpretation of the results. The conclusions should also address the study’s research questions and explain how the results contribute to the field of study.
• Recommendations : This section may provide recommendations for future research based on the study’s findings. It may also suggest practical applications for the study’s results in real-world settings.

Outline of Research Results Section

The following is an outline of the key components typically included in the Results section:

I. Introduction

• A brief overview of the research objectives and hypotheses
• A statement of the research question

II. Descriptive statistics

• Summary statistics (e.g., mean, standard deviation) for each variable analyzed
• Frequencies and percentages for categorical variables

III. Inferential statistics

• Results of statistical analyses, including tests of hypotheses
• Tables or figures to display statistical results

IV. Effect sizes and confidence intervals

• Effect sizes (e.g., Cohen’s d, odds ratio) to quantify the strength of the relationship between variables
• Confidence intervals to estimate the range of plausible values for the effect size

V. Subgroup analyses

• Results of analyses that examined differences between subgroups (e.g., by gender, age, treatment group)

VI. Limitations and assumptions

• Discussion of any limitations of the study and potential sources of bias
• Assumptions made in the statistical analyses

VII. Conclusions

• A summary of the key findings and their implications
• A statement of whether the hypotheses were supported or not
• Suggestions for future research

Example of Research Results Section

An Example of a Research Results Section could be:

• This study sought to examine the relationship between sleep quality and academic performance in college students.
• Hypothesis : College students who report better sleep quality will have higher GPAs than those who report poor sleep quality.
• Methodology : Participants completed a survey about their sleep habits and academic performance.

II. Participants

• Participants were college students (N=200) from a mid-sized public university in the United States.
• The sample was evenly split by gender (50% female, 50% male) and predominantly white (85%).
• Participants were recruited through flyers and online advertisements.

III. Results

• Participants who reported better sleep quality had significantly higher GPAs (M=3.5, SD=0.5) than those who reported poor sleep quality (M=2.9, SD=0.6).
• See Table 1 for a summary of the results.
• Participants who reported consistent sleep schedules had higher GPAs than those with irregular sleep schedules.

IV. Discussion

• The results support the hypothesis that better sleep quality is associated with higher academic performance in college students.
• These findings have implications for college students, as prioritizing sleep could lead to better academic outcomes.
• Limitations of the study include self-reported data and the lack of control for other variables that could impact academic performance.

V. Conclusion

• College students who prioritize sleep may see a positive impact on their academic performance.
• These findings highlight the importance of sleep in academic success.
• Future research could explore interventions to improve sleep quality in college students.

Example of Research Results in Research Paper :

Our study aimed to compare the performance of three different machine learning algorithms (Random Forest, Support Vector Machine, and Neural Network) in predicting customer churn in a telecommunications company. We collected a dataset of 10,000 customer records, with 20 predictor variables and a binary churn outcome variable.

Our analysis revealed that all three algorithms performed well in predicting customer churn, with an overall accuracy of 85%. However, the Random Forest algorithm showed the highest accuracy (88%), followed by the Support Vector Machine (86%) and the Neural Network (84%).

Furthermore, we found that the most important predictor variables for customer churn were monthly charges, contract type, and tenure. Random Forest identified monthly charges as the most important variable, while Support Vector Machine and Neural Network identified contract type as the most important.

Overall, our results suggest that machine learning algorithms can be effective in predicting customer churn in a telecommunications company, and that Random Forest is the most accurate algorithm for this task.

Example 3 :

Title : The Impact of Social Media on Body Image and Self-Esteem

Abstract : This study aimed to investigate the relationship between social media use, body image, and self-esteem among young adults. A total of 200 participants were recruited from a university and completed self-report measures of social media use, body image satisfaction, and self-esteem.

Results: The results showed that social media use was significantly associated with body image dissatisfaction and lower self-esteem. Specifically, participants who reported spending more time on social media platforms had lower levels of body image satisfaction and self-esteem compared to those who reported less social media use. Moreover, the study found that comparing oneself to others on social media was a significant predictor of body image dissatisfaction and lower self-esteem.

Conclusion : These results suggest that social media use can have negative effects on body image satisfaction and self-esteem among young adults. It is important for individuals to be mindful of their social media use and to recognize the potential negative impact it can have on their mental health. Furthermore, interventions aimed at promoting positive body image and self-esteem should take into account the role of social media in shaping these attitudes and behaviors.

Importance of Research Results

Research results are important for several reasons, including:

• Advancing knowledge: Research results can contribute to the advancement of knowledge in a particular field, whether it be in science, technology, medicine, social sciences, or humanities.
• Developing theories: Research results can help to develop or modify existing theories and create new ones.
• Improving practices: Research results can inform and improve practices in various fields, such as education, healthcare, business, and public policy.
• Identifying problems and solutions: Research results can identify problems and provide solutions to complex issues in society, including issues related to health, environment, social justice, and economics.
• Validating claims : Research results can validate or refute claims made by individuals or groups in society, such as politicians, corporations, or activists.
• Providing evidence: Research results can provide evidence to support decision-making, policy-making, and resource allocation in various fields.

How to Write Results in A Research Paper

Here are some general guidelines on how to write results in a research paper:

• Organize the results section: Start by organizing the results section in a logical and coherent manner. Divide the section into subsections if necessary, based on the research questions or hypotheses.
• Present the findings: Present the findings in a clear and concise manner. Use tables, graphs, and figures to illustrate the data and make the presentation more engaging.
• Describe the data: Describe the data in detail, including the sample size, response rate, and any missing data. Provide relevant descriptive statistics such as means, standard deviations, and ranges.
• Interpret the findings: Interpret the findings in light of the research questions or hypotheses. Discuss the implications of the findings and the extent to which they support or contradict existing theories or previous research.
• Discuss the limitations : Discuss the limitations of the study, including any potential sources of bias or confounding factors that may have affected the results.
• Compare the results : Compare the results with those of previous studies or theoretical predictions. Discuss any similarities, differences, or inconsistencies.
• Avoid redundancy: Avoid repeating information that has already been presented in the introduction or methods sections. Instead, focus on presenting new and relevant information.
• Be objective: Be objective in presenting the results, avoiding any personal biases or interpretations.

When to Write Research Results

Here are situations When to Write Research Results”

• After conducting research on the chosen topic and obtaining relevant data, organize the findings in a structured format that accurately represents the information gathered.
• Once the data has been analyzed and interpreted, and conclusions have been drawn, begin the writing process.
• Before starting to write, ensure that the research results adhere to the guidelines and requirements of the intended audience, such as a scientific journal or academic conference.
• Begin by writing an abstract that briefly summarizes the research question, methodology, findings, and conclusions.
• Follow the abstract with an introduction that provides context for the research, explains its significance, and outlines the research question and objectives.
• The next section should be a literature review that provides an overview of existing research on the topic and highlights the gaps in knowledge that the current research seeks to address.
• The methodology section should provide a detailed explanation of the research design, including the sample size, data collection methods, and analytical techniques used.
• Present the research results in a clear and concise manner, using graphs, tables, and figures to illustrate the findings.
• Discuss the implications of the research results, including how they contribute to the existing body of knowledge on the topic and what further research is needed.
• Conclude the paper by summarizing the main findings, reiterating the significance of the research, and offering suggestions for future research.

Purpose of Research Results

The purposes of Research Results are as follows:

• Informing policy and practice: Research results can provide evidence-based information to inform policy decisions, such as in the fields of healthcare, education, and environmental regulation. They can also inform best practices in fields such as business, engineering, and social work.
• Addressing societal problems : Research results can be used to help address societal problems, such as reducing poverty, improving public health, and promoting social justice.
• Generating economic benefits : Research results can lead to the development of new products, services, and technologies that can create economic value and improve quality of life.
• Supporting academic and professional development : Research results can be used to support academic and professional development by providing opportunities for students, researchers, and practitioners to learn about new findings and methodologies in their field.
• Enhancing public understanding: Research results can help to educate the public about important issues and promote scientific literacy, leading to more informed decision-making and better public policy.
• Evaluating interventions: Research results can be used to evaluate the effectiveness of interventions, such as treatments, educational programs, and social policies. This can help to identify areas where improvements are needed and guide future interventions.
• Contributing to scientific progress: Research results can contribute to the advancement of science by providing new insights and discoveries that can lead to new theories, methods, and techniques.
• Informing decision-making : Research results can provide decision-makers with the information they need to make informed decisions. This can include decision-making at the individual, organizational, or governmental levels.
• Fostering collaboration : Research results can facilitate collaboration between researchers and practitioners, leading to new partnerships, interdisciplinary approaches, and innovative solutions to complex problems.

Advantages of Research Results

Some Advantages of Research Results are as follows:

• Improved decision-making: Research results can help inform decision-making in various fields, including medicine, business, and government. For example, research on the effectiveness of different treatments for a particular disease can help doctors make informed decisions about the best course of treatment for their patients.
• Innovation : Research results can lead to the development of new technologies, products, and services. For example, research on renewable energy sources can lead to the development of new and more efficient ways to harness renewable energy.
• Economic benefits: Research results can stimulate economic growth by providing new opportunities for businesses and entrepreneurs. For example, research on new materials or manufacturing techniques can lead to the development of new products and processes that can create new jobs and boost economic activity.
• Improved quality of life: Research results can contribute to improving the quality of life for individuals and society as a whole. For example, research on the causes of a particular disease can lead to the development of new treatments and cures, improving the health and well-being of millions of people.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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6 Steps to Write an Excellent Discussion in Your Manuscript

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Table of Contents

The discussion section in scientific manuscripts might be the last few paragraphs, but its role goes far beyond wrapping up. It’s the part of an article where scientists talk about what they found and what it means, where raw data turns into meaningful insights. Therefore, discussion is a vital component of the article.  

An excellent discussion is well-organized. We bring to you authors a classic 6-step method for writing discussion sections, with examples to illustrate the functions and specific writing logic of each step. Take a look at how you can impress journal reviewers with a concise and focused discussion section!  

Discussion frame structure   

Conventionally, a discussion section has three parts: an introductory paragraph, a few intermediate paragraphs, and a conclusion¹.  Please follow the steps below:  

1.Introduction—mention gaps in previous research¹⁻ ²

Here, you orient the reader to your study. In the first paragraph, it is advisable to mention the research gap your paper addresses.  

Example: This study investigated the cognitive effects of a meat-only diet on adults. While earlier studies have explored the impact of a carnivorous diet on physical attributes and agility, they have not explicitly addressed its influence on cognitively intense tasks involving memory and reasoning.  

2. Summarizing key findings—let your data speak ¹⁻ ²

After you have laid out the context for your study, recapitulate some of its key findings. Also, highlight key data and evidence supporting these findings.  

Example: We found that risk-taking behavior among teenagers correlates with their tendency to invest in cryptocurrencies. Risk takers in this study, as measured by the Cambridge Gambling Task, tended to have an inordinately higher proportion of their savings invested as crypto coins.  

3. Interpreting results—compare with other papers¹⁻²    

Here, you must analyze and interpret any results concerning the research question or hypothesis. How do the key findings of your study help verify or disprove the hypothesis? What practical relevance does your discovery have?  

Example: Our study suggests that higher daily caffeine intake is not associated with poor performance in major sporting events. Athletes may benefit from the cardiovascular benefits of daily caffeine intake without adversely impacting performance.    

Remember, unlike the results section, the discussion ideally focuses on locating your findings in the larger body of existing research. Hence, compare your results with those of other peer-reviewed papers.  

Example: Although Miller et al. (2020) found evidence of such political bias in a multicultural population, our findings suggest that the bias is weak or virtually non-existent among politically active citizens.  

4. Addressing limitations—their potential impact on the results¹⁻²    

Discuss the potential impact of limitations on the results. Most studies have limitations, and it is crucial to acknowledge them in the intermediary paragraphs of the discussion section. Limitations may include low sample size, suspected interference or noise in data, low effect size, etc.  

Example: This study explored a comprehensive list of adverse effects associated with the novel drug ‘X’. However, long-term studies may be needed to confirm its safety, especially regarding major cardiac events.  

5. Implications for future research—how to explore further¹⁻²    

Locate areas of your research where more investigation is needed. Concluding paragraphs of the discussion can explain what research will likely confirm your results or identify knowledge gaps your study left unaddressed.  

Example: Our study demonstrates that roads paved with the plastic-infused compound ‘Y’ are more resilient than asphalt. Future studies may explore economically feasible ways of producing compound Y in bulk.  

6. Conclusion—summarize content¹⁻²    

A good way to wind up the discussion section is by revisiting the research question mentioned in your introduction. Sign off by expressing the main findings of your study.  

Example: Recent observations suggest that the fish ‘Z’ is moving upriver in many parts of the Amazon basin. Our findings provide conclusive evidence that this phenomenon is associated with rising sea levels and climate change, not due to elevated numbers of invasive predators.  

A rigorous and concise discussion section is one of the keys to achieving an excellent paper. It serves as a critical platform for researchers to interpret and connect their findings with the broader scientific context. By detailing the results, carefully comparing them with existing research, and explaining the limitations of this study, you can effectively help reviewers and readers understand the entire research article more comprehensively and deeply¹⁻² , thereby helping your manuscript to be successfully published and gain wider dissemination.  

In addition to keeping this writing guide, you can also use Elsevier Language Services to improve the quality of your paper more deeply and comprehensively. We have a professional editing team covering multiple disciplines. With our profound disciplinary background and rich polishing experience, we can significantly optimize all paper modules including the discussion, effectively improve the fluency and rigor of your articles, and make your scientific research results consistent, with its value reflected more clearly. We are always committed to ensuring the quality of papers according to the standards of top journals, improving the publishing efficiency of scientific researchers, and helping you on the road to academic success. Check us out here !  

Type in wordcount for Standard Total: USD EUR JPY Follow this link if your manuscript is longer than 12,000 words. Upload  

References:   

• Masic, I. (2018). How to write an efficient discussion? Medical Archives , 72(3), 306. https://doi.org/10.5455/medarh.2018.72.306-307  
• Şanlı, Ö., Erdem, S., & Tefik, T. (2014). How to write a discussion section? Urology Research & Practice , 39(1), 20–24. https://doi.org/10.5152/tud.2013.049  

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Writing a discussion section: how to integrate substantive and statistical expertise

Michael höfler.

1 Institute of Clinical Psychology and Psychotherapy, Technische Universität Dresden, Dresden, Germany

5 Chair of Clinical Psychology and Behavioural Neuroscience, Institute of Clinical Psychology and Psychotherapy, Technische Universität Dresden, Dresden, Germany

2 Behavioral Epidemiology, Institute of Clinical Psychology and Psychotherapy, Technische Universität Dresden, Dresden, Germany

Sebastian Trautmann

Robert miller.

3 Faculty of Psychology, Technische Universität Dresden, Dresden, Germany

4 Department of Medical Epidemiology and Biostatistics, Karolinska Institute, Stockholm, Sweden

Associated Data

Not applicable.

When discussing results medical research articles often tear substantive and statistical (methodical) contributions apart, just as if both were independent. Consequently, reasoning on bias tends to be vague, unclear and superficial. This can lead to over-generalized, too narrow and misleading conclusions, especially for causal research questions.

To get the best possible conclusion, substantive and statistical expertise have to be integrated on the basis of reasonable assumptions. While statistics should raise questions on the mechanisms that have presumably created the data, substantive knowledge should answer them. Building on the related principle of Bayesian thinking, we make seven specific and four general proposals on writing a discussion section.

Misinterpretation could be reduced if authors explicitly discussed what can be concluded under which assumptions. Informed on the resulting conditional conclusions other researchers may, according to their knowledge and beliefs, follow a particular conclusion or, based on other conditions, arrive at another one. This could foster both an improved debate and a better understanding of the mechanisms behind the data and should therefore enable researchers to better address bias in future studies.

After a research article has presented the substantive background, the methods and the results, the discussion section assesses the validity of results and draws conclusions by interpreting them. The discussion puts the results into a broader context and reflects their implications for theoretical (e.g. etiological) and practical (e.g. interventional) purposes. As such, the discussion contains an article’s last words the reader is left with.

Common recommendations for the discussion section include general proposals for writing [ 1 ] and structuring (e.g. with a paragraph on a study’s strengths and weaknesses) [ 2 ], to avoid common statistical pitfalls (like misinterpreting non-significant findings as true null results) [ 3 ] and to “go beyond the data” when interpreting results [ 4 ]. Note that the latter includes much more than comparing an article’s results with the literature. If results and literature are consistent, this might be due to shared bias only. If they are not consistent, the question arises why inconsistency occurs – maybe because of bias acting differently across studies [ 5 – 7 ]. Recommendations like the CONSORT checklist do well in demanding all quantitative information on design, participation, compliance etc. to be reported in the methods and results section and “addressing sources of potential bias”, “limitations” and “considering other relevant evidence” in the discussion [ 8 , 9 ]. Similarly, the STROBE checklist for epidemiological research demands “a cautious overall interpretation of results” and "discussing the generalizability (external validity)" [ 10 , 11 ]. However, these guidelines do not clarify how to deal with the complex bias issue, and how to get to and report conclusions.

Consequently, suggestions on writing a discussion often remain vague by hardly addressing the role of the assumptions that have (often implicitly) been made when designing a study, analyzing the data and interpreting the results. Such assumptions involve mechanisms that have created the data and are related to sampling, measurement and treatment assignment (in observational studies common causes of factor and outcome) and, as a consequence, the bias this may produce [ 5 , 6 ]. They determine whether a result allows only an associational or a causal conclusion. Causal conclusions, if true, are of much higher relevance for etiology, prevention and intervention. However, they require much stronger assumptions. These have to be fully explicit and, therewith, essential part of the debate since they always involve subjectivity. Subjectivity is unavoidable because the mechanisms behind the data can never be fully estimated from the data themselves [ 12 ].

In this article, we argue that the conjunction of substantive and statistical (methodical) knowledge in the verbal integration of results and beliefs on mechanisms can be greatly improved in (medical) research papers. We illustrate this through the personal roles that a statistician (i.e. methods expert) and a substantive researcher should take. Doing so, we neither claim that usually just two people write a discussion, nor that one person lacks the knowledge of the other, nor that there were truly no researchers that have both kinds of expertise. As a metaphor, the division of these two roles into two persons describes the necessary integration of knowledge via the mode of a dialogue. Verbally, it addresses the finding of increased specialization of different study contributors in biomedical research. This has teared apart the two processes of statistical compilation of results and their verbal integration [ 13 ]. When this happens a statistician alone is limited to a study’s conditions (sampled population, experimental settings etc.), because he or she is unaware of the conditions’ generalizability. On the other hand, a A substantive expert alone is prone to over-generalize because he or she is not aware of the (mathematical) prerequisites for an interpretation.

The article addresses both (medical) researchers educated in basic statistics and research methods and statisticians who cooperate with them. Throughout the paper we exemplify our arguments with the finding of an association in a cross-tabulation between a binary X (factor) and a binary Y (outcome): those who are exposed to or treated with X have a statistically significantly elevated risk for Y as compared to the non-exposed or not (or otherwise) treated (for instance via the chi-squared independence test or logistic regression). Findings like this are frequent and raise the question which more profound conclusion is valid under what assumptions. Until some decades ago, statistics has largely avoided the related topic of causality and instead limited itself on describing observed distributions (here a two-by-two table between D = depression and LC = lung cancer) with well-fitting models.

We illustrate our arguments with the concrete example of the association found between the factor depression (D) and the outcome lung cancer (LC) [ 14 ]. Yet very different mechanisms could have produced such an association [ 7 ], and assumptions on these lead to the following fundamentally different conclusions (Fig. ​ (Fig.1 1 ):

• D causes LC (e.g. because smoking might constitute “self-medication” of depression symptoms)
• LC causes D (e.g. because LC patients are demoralized by their diagnosis)
• D and LC cause each other (e.g. because the arguments in both a. and b. apply)
• D and LC are the causal consequence of the same factor(s) (e.g. poor health behaviors - HB)
• D and LC only share measurement error (e.g. because a fraction of individuals that has either depression or lung cancer denies both in self-report measures).

Different conclusions about an association between D and LC. a D causes LC, b LC causes B, c D and LC cause each other, d D and LC are associated because of a shared factor (HB), e D and LC are associated because they have correlated errors

Note that we use the example purely for illustrative purposes. We do not make substantive claims on what of a. through e. is true but show how one should reflect on mechanisms in order to find the right answer. Besides, we do not consider research on the D-LC relation apart from the finding of association [ 14 ].

Assessing which of a. through e. truly applies requires substantive assumptions on mechanisms: the temporal order of D and LC (a causal effect requires that the cause occurs before the effect), shared factors, selection processes and measurement error. Questions on related mechanisms have to be brought up by statistical consideration, while substantive reasoning has to address them. Together this yields provisional assumptions for inferring that are subject to readers’ substantive consideration and refinement. In general, the integration of prior beliefs (anything beyond the data a conclusion depends on) and the results from the data themselves is formalized by Bayesian statistics [ 15 , 16 ]. This is beyond the scope of this article, still we argue that Bayesian thinking should govern the process of drawing conclusions.

Building on this idea, we provide seven specific and four general recommendations for the cooperative process of writing a discussion. The recommendations are intended to be suggestions rather than rules. They should be subject to further refinement and adjustment to specific requirements in different fields of medical and other research. Note that the order of the points is not meant to structure a discussion’s writing (besides 1.).

Recommendations for writing a discussion section

Specific recommendations.

Consider the example on the association between D and LC. Rather than starting with an in-depth (causal) interpretation a finding should firstly be taken as what it allows inferring without doubt: Under the usual assumptions that a statistical model makes (e.g. random sampling, independence or certain correlation structure between observations [ 17 ]), the association indicates that D (strictly speaking: measuring D) predicts an elevated LC risk (strictly speaking: measuring LC) in the population that one has managed to sample (source population). Assume that the sample has been randomly drawn from primary care settings. In this case the association is useful to recommend medical doctors to better look at an individual’s LC risk in case of D. If the association has been adjusted for age and gender (conveniently through a regression model), the conclusion modifies to: If the doctor knows a patient’s age and gender (what should always be the case) D has additional value in predicting an elevated LC risk.

In the above example, a substantive researcher might want to conclude that D and LC are associated in a general population instead of just inferring to patients in primary care settings (a.). Another researcher might even take the finding as evidence for D being a causal factor in the etiology of LC, meaning that prevention of D could reduce the incidence rate of LC (in whatever target population) (b.). In both cases, the substantive researcher should insist on assessing the desired interpretation that goes beyond the data [ 4 ], but the statistician immediately needs to bring up the next point.

The explanation of all the assumptions that lead from a data result to a conclusion enables a reader to assess whether he or she agrees with the authors’ inference or not. These conditions, however, often remain incomplete or unclear, in which case the reader can hardly assess whether he or she follows a path of argumentation and, thus, shares the conclusion this path leads to.

Consider conclusion a. and suppose that, instead of representative sampling in a general population (e.g. all U.S. citizens aged 18 or above), the investigators were only able to sample in primary care settings. Extrapolating the results to another population than the source population requires what is called “external validity”, “transportability” or the absence of “selection bias” [ 18 , 19 ]. No such bias occurs if the parameter of interest is equal in the source and the target population. Note that this is a weaker condition than the common belief that the sample must represent the target population in everything . If the parameter of interest is the difference in risk for LC between cases and non-cases of D, the condition translates into: the risk difference must be equal in target and source population.

For the causal conclusion b., however, sufficient assumptions are very strict. In an RCT, the conclusion is valid under random sampling from the target population, random allocation of X, perfect compliance in X, complete participation and no measurement error in outcome (for details see [ 20 ]). In practice, on the other hand, the derivations from such conditions might sometimes be modest what may produce little bias only. For instance, non-compliance in a specific drug intake (treatment) might occur only in a few individuals to little extent through a random process (e.g. sickness of a nurse being responsible for drug dispense) and yield just small (downward) bias [ 5 ]. The conclusion of downward bias might also be justified if non-compliance does not cause anything that has a larger effect on a Y than the drug itself. Another researcher, however, could believe that non-compliance leads to taking a more effective, alternative treatment. He or she could infer upward bias instead if well-informed on the line of argument.

In practice, researchers frequently use causal language yet without mentioning any assumptions. This does not imply that they truly have a causal effect in mind, often causal and associational wordings are carelessly used in synonymous way. For example, concluding “depression increases the risk of lung cancer” constitutes already causal wording because it implies that a change in the depression status would change the cancer risk. Associational language like “lung cancer risk is elevated if depression occurs”, however, would allow for an elevated lung cancer risk in depression cases just because LC and D share some causes (“inducing” or “removing” depression would not change the cancer risk here).

Often, it is unclear where the path of argumentation from assumptions to a conclusion leads when alternative assumptions are made. Consider again bias due to selection. A different effect in target and source population occurs if effect-modifying variables distribute differently in both populations. Accordingly, the statistician should ask which variables influence the effect of interest, and whether these can be assumed to distribute equally in the source population and the target population. The substantive researcher might answer that the causal risk difference between D and LC likely increases with age. Given that this is true, and if elder individuals have been oversampled (e.g. because elderly are over-represented in primary care settings), both together would conclude that sampling has led to over-estimation (despite other factors, Fig. ​ Fig.2 2 ).

If higher age is related to a larger effect (risk difference) of D on LC, a larger effect estimate is expected in an elder sample

However, the statistician might add, if effect modification is weak, or the difference in the age distributions is modest (e.g. mean 54 vs. 52 years), selection is unlikely to have produced large (here: upward) bias. In turn, another substantive researcher, who reads the resulting discussion, might instead assume a decrease of effect with increasing age and thus infer downward bias.

In practice, researchers should be extremely sensitive for bias due to selection if a sample has been drawn conditionally on a common consequence of factor and outcome or a variable associated with such a consequence [19 and references therein]. For instance, hospitalization might be influenced by both D and LC, and thus sampling from hospitals might introduce a false association or change an association’s sign; particularly D and LC may appear to be negatively associated although the association is positive in the general population (Fig. ​ (Fig.3 3 ).

If hospitalization (H) is a common cause of D and LC, sampling conditionally on H can introduce a spurious association between D and LC ("conditioning on a collider")

Usually, only some kinds of bias are discussed, while the consequences of others are ignored [ 5 ]. Besides selection the main sources of bias are often measurement and confounding. If one is only interested in association, confounding is irrelevant. For causal conclusions, however, assumptions on all three kinds of bias are necessary.

Measurement error means that the measurement of a factor and/or outcome deviates from the true value, at least in some individuals. Bias due to measurement is known under many other terms that describe the reasons why such error occurs (e.g. “recall bias” and “reporting bias”). In contrast to conventional wisdom, measurement error does not always bias association and effect estimates downwards [ 5 , 6 ]. It does, for instance, if only the factor (e.g. depression) is measured with error and the errors occur independently from the outcome (e.g. lung cancer), or vice versa (“non-differential misclassification”) [22 and references therein]. However, many lung cancer cases might falsely report depression symptoms (e.g. to express need for care). Such false positives (non-cases of depression classified as cases) may also occur in non-cases of lung cancer but to a lesser extent (a special case of “differential misclassification”). Here, bias might be upward as well. Importantly, false positives cause larger bias than false negatives (non-cases of depression falsely classified as depression cases) as long as the relative frequency of a factor is lower than 50% [ 21 ]. Therefore, they should receive more attention in discussion. If measurement error occurs in depression and lung cancer, the direction of bias also depends on the correlation between both errors [ 21 ].

Note that what is in line with common standards of “good” measurement (e.g. a Kappa value measuring validity or reliability of 0.7) might anyway produce large bias. This applies to estimates of prevalence, association and effect. The reason is that while indices of measurement are one-dimensional, bias depends on two parameters (sensitivity and specificity) [ 21 , 22 ]. Moreover, estimates of such indices are often extrapolated to different kinds of populations (typically from a clinical to general population), what may be inadequate. Note that the different kinds of bias often interact, e.g. bias due to measurement might depend on selection (e.g. measurement error might differ between a clinical and a general population) [ 5 , 6 ].

Assessment of bias due to confounding variables (roughly speaking: common causes of factor and outcome) requires assumptions on the entire system of variables that affect both factor and outcome. For example, D and LC might share several causes such as stressful life events or socioeconomic status. If these influence D and LC with the same effect direction, this leads to overestimation, otherwise (different effect directions) the causal effect is underestimated. In the medical field, many unfavorable conditions may be positively related. If this holds true for all common factors of D and LC, upward bias can be assumed. However, not all confounders have to be taken into account. Within the framework of “causal graphs”, the “backdoor criterion” [ 7 ] provides a graphical rule for sets of confounders to be sufficient when adjusted for. Practically, such a causal graph must include all factors that directly or indirectly affect both D and LC. Then, adjustment for a set of confounders that meets the “backdoor criterion” in the graph completely removes bias due to confounding. In the example of Fig. ​ Fig.4 4 it is sufficient to adjust for Z 1 and Z 2 because this “blocks” all paths that otherwise lead backwards from D to LC. Note that fully eliminating bias due to confounding also requires that the confounders have been collected without measurement error [ 5 , 6 , 23 ]. Therefore, the advice is always to concede at least some “residual” bias and reflect on the direction this might have (could be downward if such error is not stronger related to D and LC than a confounder itself).

Causal graph for the effect of D on LC and confounders Z 1 , Z 2 and Z 3

Whereas the statistician should pinpoint to the mathematical insight of the backdoor criterion, its application requires profound substantive input and literature review. Of course, there are numerous relevant factors in the medical field. Hence, one should practically focus on those with the highest prevalence (a very seldom factor can hardly cause large bias) and large assumed effects on both X and Y.

If knowledge on any of the three kinds of bias is poor or very uncertain, researchers should admit that this adds uncertainty in a conclusion: systematic error on top of random error. In the Bayesian framework, quantitative bias analysis formalizes this through the result of larger variance in an estimate. Technically, this additional variance is introduced via the variances of distributions assigned to “bias parameters”; for instance a misclassification probability (e.g. classifying a true depression case as non-case) or the prevalence of a binary confounder and its effects on X and Y. Of course, bias analysis also changes point estimates (hopefully reducing bias considerably). Note that conventional frequentist analysis, as regarded from the Bayesian perspective, assumes that all bias parameters were zero with a probability of one [ 5 , 6 , 23 ]. The only exceptions (bias addressed in conventional analyses) are adjustment on variables to hopefully reduce bias due to confounding and weighting the individuals (according to variables related to participation) to take into account bias due to selection.

If the substantive investigator understands the processes of selection, measurement and confounding only poorly, such strict analysis numerically reveals that little to nothing is known on the effect of X on Y, no matter how large an observed association and a sample (providing small random error) may be [ 5 , 6 , 23 ]). This insight has to be brought up by the statistician. Although such an analysis is complicated, itself very sensitive to how it is conducted [ 5 , 6 ] and rarely done, the Bayesian thinking behind it forces researchers to better understand the processes behind the data. Otherwise, he or she cannot make any assumptions and, in turn, no conclusion on causality.

Usually articles end with statements that only go little further than the always true but never informative statement “more research is needed”. Moreover, larger samples and better measurements are frequently proposed. If an association has been found, a RCT or other interventional study is usually proposed to investigate causality. In our example, this recommendation disregards that: (1) onset of D might have a different effect on LC risk than an intervention against D (the effect of onset cannot be investigated in any interventional study), (2) the effects of onset and intervention concern different populations (those without vs. those with depression), (3) an intervention effect depends on the mode of intervention [ 24 ], and (4) (applying the backdoor criterion) a well-designed observational study may approximatively yield the same result as a randomized study would [ 25 – 27 ]. If the effect of “removing” depression is actually of interest, one could propose an RCT that investigates the effect of treating depression in a strictly defined way and in a strictly defined population (desirably in all who meet the criteria of depression). Ideally, this population is sampled randomly, and non-participants and dropouts are investigated with respect to assumed effect-modifiers (differences in their distributions between participants and non-participants can then be addressed e.g. by weighting [ 27 ]). In a non-randomized study, one should collect variables supposed to meet the backdoor-criterion with the best instruments possible.

General recommendations

Yet when considering 1) through 7); i.e. carefully reflecting on the mechanisms that have created the data, discussions on statistical results can be very misleading, because the basic statistical methods are mis-interpreted or inadequately worded.

A common pitfall is to consider the lack of evidence for the alternative hypothesis (e.g. association between D and LC) as evidence for the null hypothesis (no association). In fact, such inference requires an a-priori calculated sample-size to ensure that the type-two error probability does not exceed a pre-specified limit (typically 20% or 10%, given the other necessary assumptions, e.g. on the true magnitude of association). Otherwise, the type-two error is unknown and in practice often large. This may put a “false negative result” into the scientific public that turns out to be “unreplicable” – what would be falsely interpreted as part of the “replication crisis”. Such results are neither positive nor negative but uninformative . In this case, the wording “there is no evidence for an association” is adequate because it does not claim that there is no association.

Frequently, it remains unclear which hypotheses have been a-priori specified and which have been brought up only after some data analysis. This, of course, is scientific malpractice because it does not enable the readership to assess the random error emerging from explorative data analysis. Accordingly, the variance of results across statistical methods is often misused to filter out the analysis that yields a significant result (“ p -hacking”, [ 28 ]). Pre-planned tests (via writing a grant) leave at least less room for p-hacking because they specify a-priori which analysis is to be conducted.

On the other hand, post-hoc analyses can be extremely useful for identifying unexpected phenomena and creating new hypotheses. Verbalization in the discussion section should therefore sharply separate between conclusions from hypothesis testing and new hypotheses created from data exploration. The distinction is profound, since a newly proposed hypothesis just makes a new claim. Suggesting new hypotheses cannot be wrong, this can only be inefficient if many hypotheses turn out to be wrong. Therefore, we suggest proposing only a limited number of new hypotheses that appear promising to stimulate further research and scientific progress. They are to be confirmed or falsified with future studies. A present discussion, however, should yet explicate the testable predictions a new hypothesis entails, and how a future study should be designed to keep bias in related analyses as small as possible.

Confidence intervals address the problem of reducing results to the dichotomy of significant and non-significant through providing a range of values that are compatible with the data at the given confidence level, usually 95% [ 29 ].

This is also addressed by Bayesian statistics that allows calculating what frequentist p -values are often misinterpreted to be: the probability that the alternative (or null) hypothesis is true [ 17 ]. Moreover, one can calculate how likely it is that the parameter lies within any specified range (e.g. the risk difference being greater than .05, a lower boundary for practical significance) [ 15 , 16 ]. To gain these benefits, one needs to specify how the parameter of interest (e.g. causal risk difference between D and LC) is distributed before inspecting the data. In Bayesian statistics (unlike frequentist statistics) a parameter is a random number that expresses prior beliefs via a “prior distribution”. Such a “prior” is combined with the data result to a “posterior distribution”. This integrates both sources of information.

Note that confidence intervals also can be interpreted from the Bayesian perspective (then called “credibility interval”). This assumes that all parameter values were equally likely (uniformly distributed, strictly speaking) before analyzing the data [ 5 , 6 , 20 ].

Testing just for a non-zero association can only yield evidence for an association deviating from zero. A better indicator for the true impact of an effect/association for clinical, economic, political, or research purposes is its magnitude. If an association between D and LC after adjusting for age and gender has been discovered, then the knowledge of D has additional value in predicting an elevated LC probability beyond age and gender. However, there may be many other factors that stronger predict LC and thus should receive higher priority in a doctor’s assessment. Besides, if an association is small, it may yet be explained by modest (upward) bias. Especially large samples often yield significant results with little practical value. The p -value does not measure strength of association [ 17 ]. For instance, in a large sample, a Pearson correlation between two dimensional variables could equal 0.1 only but with a p -value <.001. A further problem arises if the significance threshold of .05 is weakened post-hoc to allow for “statistical trends” ( p between .05 and .10) because a result has “failed to reach significance” (this wording claims that there is truly an association. If this was known, no research would be necessary).

It is usually the statistician’s job to insist not only on removing the attention from pure statistical significance to confidence intervals or even Bayesian interpretation, but also to point out the necessity of a meaningful cutoff for practical significance. The substantive researcher then has to provide this cutoff.

Researchers should not draw conclusions that have not been explicitly tested for. For example, one may have found a positive association between D and LC (e.g. p  = .049), but this association is not significant (e.g. p  = .051), when adjusting for “health behavior”. This does not imply that “health behavior” “explains” the association (yet fully). The difference in magnitude of association in both analyses compared here (without and with adjustment on HB) may be very small and the difference in p -values (“borderline significance” after adjustment) likely to emerge from random error. This often applies to larger differences in p as well.

Investigators, however, might find patterns in their results that they consider worth mentioning for creating hypotheses. In the example above, adding the words “in the sample”, would clarify that they refer just to the difference of two point estimates . By default, “association” in hypotheses testing should mean “statistically significant association” (explorative analyses should instead refer to “suggestive associations”).

Conclusions

Some issues of discussing results not mentioned yet appear to require only substantive reasoning. For instance, Bradford Hill’s consideration on “plausibility” claims that a causal effect is more likely, if it is in line with biological (substantive) knowledge, or if a dose-response relation has been found [ 30 ]. However, the application of these considerations itself depends on the trueness of assumptions. For instance, bias might act differently across the dose of exposure (e.g. larger measurement error in outcome among those with higher dosage). As a consequence, a pattern observed across dose may mask a true or pretend a wrong dose-response relation [ 30 ]. This again has to be brought up by statistical expertise.

There are, however, some practical issues that hinder the cooperation we suggest. First, substantive researchers often feel discomfort when urged to make assumptions on the mechanisms behind the data, presumably because they fear to be wrong. Here, the statistician needs to insist: “If you are unable to make any assumptions, you cannot conclude anything!” And: “As a scientist you have to understand the processes that create your data.” See [ 31 ] for practical advice on how to arrive at meaningful assumptions.

Second, statisticians have long been skeptical against causal inference. Still, most of them focus solely on describing observed data with distributional models, probably because estimating causal effects has long been regarded as unfeasible with scientific methods. Training in causality remains rather new, since strict mathematical methods have been developed only in the last decades [ 7 ].

The cooperation could be improved if education in both fields focused on the insight that one cannot succeed without the other. Academic education should demonstrate that in-depth conclusions from data unavoidably involve prior beliefs. Such education should say: Data do not “speak for themselves”, because they “speak” only ambiguously and little, since they have been filtered through various biases [ 32 ]. The subjectivity introduced by addressing bias, however, unsettles many researchers. On the other hand, conventional frequentist statistics just pretends to be objective. Instead of accepting the variety of possible assumptions, it makes the absurd assumption of “no bias with probability of one”. Or it avoids causal conclusions at all if no randomized study is possible. This limits science to investigating just associations for all factors that can never be randomized (e.g. onset of depression). However, the alternative of Bayesian statistics and thinking are themselves prone to fundamental cognitive biases which should as well be subject of interdisciplinary teaching [ 33 ].

Readers may take this article as an invitation to read further papers’ discussions differently while evaluating our claims. Rather than sharing a provided conclusion (or not) they could ask themselves whether a discussion enables them to clearly specify why they share it (or not). If the result is uncertainty, this might motivate them to write their next discussion differently. The proposals made in this article could help shifting scientific debates to where they belong. Rather than arguing on misunderstandings caused by ambiguity in a conclusion’s assumptions one should argue on the assumptions themselves.

Acknowledgements

We acknowledge support by the German Research Foundation and the Open Access Publication Funds of the TU Dresden. We wish to thank Pia Grabbe and Helen Steiner for language editing and the cited authors for their outstanding work that our proposals build on.

John Venz is funded by the German Federal Ministry of Education and Research (BMBF) project no. 01ER1303 and 01ER1703. He has contributed to this manuscript outside of time funded by these projects.

Availability of data and materials

Abbreviations, authors’ contributions.

MH and RM had the initial idea on the article. MH has taken the lead in writing. JV has contributed to the statistical parts, especially the Bayesian aspects. RM has refined the paragraphs on statistical inference. ST joined later and has added many clarifications related to the perspective of the substantive researcher. All authors have contributed to the final wording of all sections and the article’s revision. All authors read and approved the final manuscript.

Ethics approval and consent to participate

Consent for publication, competing interests.

The authors declare that they have no competing interests.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Writing a scientific paper.

• Writing a lab report
• INTRODUCTION

Writing a "good" results section

Figures and Captions in Lab Reports

"Results Checklist" from: How to Write a Good Scientific Paper. Chris A. Mack. SPIE. 2018.

Additional tips for results sections.

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

This is the core of the paper. Don't start the results sections with methods you left out of the Materials and Methods section. You need to give an overall description of the experiments and present the data you found.

• Factual statements supported by evidence. Short and sweet without excess words
• Present representative data rather than endlessly repetitive data
• Discuss variables only if they had an effect (positive or negative)
• Use meaningful statistics
• Avoid redundancy. If it is in the tables or captions you may not need to repeat it

A short article by Dr. Brett Couch and Dr. Deena Wassenberg, Biology Program, University of Minnesota

• Present the results of the paper, in logical order, using tables and graphs as necessary.
• Explain the results and show how they help to answer the research questions posed in the Introduction. Evidence does not explain itself; the results must be presented and then explained. 
• Avoid: presenting results that are never discussed;  presenting results in chronological order rather than logical order; ignoring results that do not support the conclusions; 
• Number tables and figures separately beginning with 1 (i.e. Table 1, Table 2, Figure 1, etc.).
• Do not attempt to evaluate the results in this section. Report only what you found; hold all discussion of the significance of the results for the Discussion section.
• It is not necessary to describe every step of your statistical analyses. Scientists understand all about null hypotheses, rejection rules, and so forth and do not need to be reminded of them. Just say something like, "Honeybees did not use the flowers in proportion to their availability (X2 = 7.9, p<0.05, d.f.= 4, chi-square test)." Likewise, cite tables and figures without describing in detail how the data were manipulated. Explanations of this sort should appear in a legend or caption written on the same page as the figure or table.
• You must refer in the text to each figure or table you include in your paper.
• Tables generally should report summary-level data, such as means ± standard deviations, rather than all your raw data.  A long list of all your individual observations will mean much less than a few concise, easy-to-read tables or figures that bring out the main findings of your study.  
• Only use a figure (graph) when the data lend themselves to a good visual representation.  Avoid using figures that show too many variables or trends at once, because they can be hard to understand.

From:  https://writingcenter.gmu.edu/guides/imrad-results-discussion

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How to Write the Results/Findings Section in Research

What is the research paper Results section and what does it do?

The Results section of a scientific research paper represents the core findings of a study derived from the methods applied to gather and analyze information. It presents these findings in a logical sequence without bias or interpretation from the author, setting up the reader for later interpretation and evaluation in the Discussion section. A major purpose of the Results section is to break down the data into sentences that show its significance to the research question(s).

The Results section appears third in the section sequence in most scientific papers. It follows the presentation of the Methods and Materials and is presented before the Discussion section —although the Results and Discussion are presented together in many journals. This section answers the basic question “What did you find in your research?”

What is included in the Results section?

The Results section should include the findings of your study and ONLY the findings of your study. The findings include:

• Data presented in tables, charts, graphs, and other figures (may be placed into the text or on separate pages at the end of the manuscript)
• A contextual analysis of this data explaining its meaning in sentence form
• All data that corresponds to the central research question(s)
• All secondary findings (secondary outcomes, subgroup analyses, etc.)

If the scope of the study is broad, or if you studied a variety of variables, or if the methodology used yields a wide range of different results, the author should present only those results that are most relevant to the research question stated in the Introduction section .

As a general rule, any information that does not present the direct findings or outcome of the study should be left out of this section. Unless the journal requests that authors combine the Results and Discussion sections, explanations and interpretations should be omitted from the Results.

How are the results organized?

The best way to organize your Results section is “logically.” One logical and clear method of organizing research results is to provide them alongside the research questions—within each research question, present the type of data that addresses that research question.

Let’s look at an example. Your research question is based on a survey among patients who were treated at a hospital and received postoperative care. Let’s say your first research question is:

“What do hospital patients over age 55 think about postoperative care?”

This can actually be represented as a heading within your Results section, though it might be presented as a statement rather than a question:

Attitudes towards postoperative care in patients over the age of 55

Now present the results that address this specific research question first. In this case, perhaps a table illustrating data from a survey. Likert items can be included in this example. Tables can also present standard deviations, probabilities, correlation matrices, etc.

Following this, present a content analysis, in words, of one end of the spectrum of the survey or data table. In our example case, start with the POSITIVE survey responses regarding postoperative care, using descriptive phrases. For example:

“Sixty-five percent of patients over 55 responded positively to the question “ Are you satisfied with your hospital’s postoperative care ?” (Fig. 2)

Include other results such as subcategory analyses. The amount of textual description used will depend on how much interpretation of tables and figures is necessary and how many examples the reader needs in order to understand the significance of your research findings.

Next, present a content analysis of another part of the spectrum of the same research question, perhaps the NEGATIVE or NEUTRAL responses to the survey. For instance:

  “As Figure 1 shows, 15 out of 60 patients in Group A responded negatively to Question 2.”

After you have assessed the data in one figure and explained it sufficiently, move on to your next research question. For example:

  “How does patient satisfaction correspond to in-hospital improvements made to postoperative care?”

This kind of data may be presented through a figure or set of figures (for instance, a paired T-test table).

Explain the data you present, here in a table, with a concise content analysis:

“The p-value for the comparison between the before and after groups of patients was .03% (Fig. 2), indicating that the greater the dissatisfaction among patients, the more frequent the improvements that were made to postoperative care.”

Let’s examine another example of a Results section from a study on plant tolerance to heavy metal stress . In the Introduction section, the aims of the study are presented as “determining the physiological and morphological responses of Allium cepa L. towards increased cadmium toxicity” and “evaluating its potential to accumulate the metal and its associated environmental consequences.” The Results section presents data showing how these aims are achieved in tables alongside a content analysis, beginning with an overview of the findings:

“Cadmium caused inhibition of root and leave elongation, with increasing effects at higher exposure doses (Fig. 1a-c).”

The figure containing this data is cited in parentheses. Note that this author has combined three graphs into one single figure. Separating the data into separate graphs focusing on specific aspects makes it easier for the reader to assess the findings, and consolidating this information into one figure saves space and makes it easy to locate the most relevant results.

Following this overall summary, the relevant data in the tables is broken down into greater detail in text form in the Results section.

• “Results on the bio-accumulation of cadmium were found to be the highest (17.5 mg kgG1) in the bulb, when the concentration of cadmium in the solution was 1×10G2 M and lowest (0.11 mg kgG1) in the leaves when the concentration was 1×10G3 M.”

Captioning and Referencing Tables and Figures

Tables and figures are central components of your Results section and you need to carefully think about the most effective way to use graphs and tables to present your findings . Therefore, it is crucial to know how to write strong figure captions and to refer to them within the text of the Results section.

The most important advice one can give here as well as throughout the paper is to check the requirements and standards of the journal to which you are submitting your work. Every journal has its own design and layout standards, which you can find in the author instructions on the target journal’s website. Perusing a journal’s published articles will also give you an idea of the proper number, size, and complexity of your figures.

Regardless of which format you use, the figures should be placed in the order they are referenced in the Results section and be as clear and easy to understand as possible. If there are multiple variables being considered (within one or more research questions), it can be a good idea to split these up into separate figures. Subsequently, these can be referenced and analyzed under separate headings and paragraphs in the text.

To create a caption, consider the research question being asked and change it into a phrase. For instance, if one question is “Which color did participants choose?”, the caption might be “Color choice by participant group.” Or in our last research paper example, where the question was “What is the concentration of cadmium in different parts of the onion after 14 days?” the caption reads:

 “Fig. 1(a-c): Mean concentration of Cd determined in (a) bulbs, (b) leaves, and (c) roots of onions after a 14-day period.”

Steps for Composing the Results Section

Because each study is unique, there is no one-size-fits-all approach when it comes to designing a strategy for structuring and writing the section of a research paper where findings are presented. The content and layout of this section will be determined by the specific area of research, the design of the study and its particular methodologies, and the guidelines of the target journal and its editors. However, the following steps can be used to compose the results of most scientific research studies and are essential for researchers who are new to preparing a manuscript for publication or who need a reminder of how to construct the Results section.

Step 1 : Consult the guidelines or instructions that the target journal or publisher provides authors and read research papers it has published, especially those with similar topics, methods, or results to your study.

• The guidelines will generally outline specific requirements for the results or findings section, and the published articles will provide sound examples of successful approaches.
• Note length limitations on restrictions on content. For instance, while many journals require the Results and Discussion sections to be separate, others do not—qualitative research papers often include results and interpretations in the same section (“Results and Discussion”).
• Reading the aims and scope in the journal’s “ guide for authors ” section and understanding the interests of its readers will be invaluable in preparing to write the Results section.

Step 2 : Consider your research results in relation to the journal’s requirements and catalogue your results.

• Focus on experimental results and other findings that are especially relevant to your research questions and objectives and include them even if they are unexpected or do not support your ideas and hypotheses.
• Catalogue your findings—use subheadings to streamline and clarify your report. This will help you avoid excessive and peripheral details as you write and also help your reader understand and remember your findings. Create appendices that might interest specialists but prove too long or distracting for other readers.
• Decide how you will structure of your results. You might match the order of the research questions and hypotheses to your results, or you could arrange them according to the order presented in the Methods section. A chronological order or even a hierarchy of importance or meaningful grouping of main themes or categories might prove effective. Consider your audience, evidence, and most importantly, the objectives of your research when choosing a structure for presenting your findings.

Step 3 : Design figures and tables to present and illustrate your data.

• Tables and figures should be numbered according to the order in which they are mentioned in the main text of the paper.
• Information in figures should be relatively self-explanatory (with the aid of captions), and their design should include all definitions and other information necessary for readers to understand the findings without reading all of the text.
• Use tables and figures as a focal point to tell a clear and informative story about your research and avoid repeating information. But remember that while figures clarify and enhance the text, they cannot replace it.

Step 4 : Draft your Results section using the findings and figures you have organized.

• The goal is to communicate this complex information as clearly and precisely as possible; precise and compact phrases and sentences are most effective.
• In the opening paragraph of this section, restate your research questions or aims to focus the reader’s attention to what the results are trying to show. It is also a good idea to summarize key findings at the end of this section to create a logical transition to the interpretation and discussion that follows.
• Try to write in the past tense and the active voice to relay the findings since the research has already been done and the agent is usually clear. This will ensure that your explanations are also clear and logical.
• Make sure that any specialized terminology or abbreviation you have used here has been defined and clarified in the  Introduction section .

Step 5 : Review your draft; edit and revise until it reports results exactly as you would like to have them reported to your readers.

• Double-check the accuracy and consistency of all the data, as well as all of the visual elements included.
• Read your draft aloud to catch language errors (grammar, spelling, and mechanics), awkward phrases, and missing transitions.
• Ensure that your results are presented in the best order to focus on objectives and prepare readers for interpretations, valuations, and recommendations in the Discussion section . Look back over the paper’s Introduction and background while anticipating the Discussion and Conclusion sections to ensure that the presentation of your results is consistent and effective.
• Consider seeking additional guidance on your paper. Find additional readers to look over your Results section and see if it can be improved in any way. Peers, professors, or qualified experts can provide valuable insights.

One excellent option is to use a professional English proofreading and editing service  such as Wordvice, including our paper editing service . With hundreds of qualified editors from dozens of scientific fields, Wordvice has helped thousands of authors revise their manuscripts and get accepted into their target journals. Read more about the  proofreading and editing process  before proceeding with getting academic editing services and manuscript editing services for your manuscript.

As the representation of your study’s data output, the Results section presents the core information in your research paper. By writing with clarity and conciseness and by highlighting and explaining the crucial findings of their study, authors increase the impact and effectiveness of their research manuscripts.

For more articles and videos on writing your research manuscript, visit Wordvice’s Resources page.

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• A Research Guide
• Research Paper Guide

How to Write a Discussion Section of a Research Paper

• The purpose of the discussion section

Structure and Writing Style

• Step-by-step writing guide
• Tips for writing a discussion
• Discussion section example

The Purpose of the Discussion Section in a Research Paper

• A summary of your work. Don’t rewrite the results section. Briefly summarize what you’ve explored, and remind readers about that.
• Interpretation of your result. The following important part of the discussion section is to talk about what your results mean. What are the results of your research?
• Your recommendations. Tell readers about what suggestions you give in connection with the results obtained. Perhaps locally to solve the problem or in general some preventive measures. But be careful! Do not give any speculative recommendations that are not supported by your research. Also, do not focus on what did not work out or where mistakes were made.
• Be concise, and don’t repeat yourself. Express your thoughts clearly and consistently so the reader immediately understands what you are discussing. Do not repeat sections of your work or retell the same idea several times in different words.
• Avoid using jargon or complex, obscure words. Everyone who reads your work should understand what you want to say without a dictionary or additional books.
• Be bold and cite other authors and studies to support your conclusions and thoughts.
• If your discussion section is too long, you can use subheadings to group ideas together so you don’t forget anything while writing.
• Comment on your results , even if they were unexpected or random. Feel free to go into details.
• You can add hypotheses or assumptions that will be explored in your following works. This way, you show the depth of the results and their significance.
• You can start writing a discussion in scientific paper from general problems and perspectives on solving them to specific aspects. You can also offer some options for practical solutions to issues.
• Remember to describe general patterns, principles, and relationships in the problem under study.
• If you find some unexpected result, describe how you came to it and how it will affect the question.
• At the end of the discussion section, you should state why the results are significant and how they affect broader research topics.

6 Steps to Write a Discussion in Research Paper

Step 1. write down the conclusions you want to make in the discussion section, step 2. start the discussion with the problem and results, step 3: formulate your interpretations of the research paper discussion, step 4. describe the consequences in the discussion section, step 5. talk about limitations in your discussion part, step 6. summarize and share recommendations in the discussion section, tips for writing a discussion section.

• Once you have established the context, presenting a well-supported argument with relevant evidence and examples is essential. It means you should analyze the data collected during your research and use it to support your claims. Provide specific examples and use straightforward language to explain your findings.
• Ensuring that your discussion is easy to follow and understand is crucial. Avoid using technical jargon, and break up complex ideas into smaller, more manageable chunks. It will help your readers stay engaged and easily follow your argument.
• Visual aids such as graphs, charts, or tables can also be beneficial, allowing you to present data clearly and concisely. These visual aids can help to illustrate your points and make your argument more compelling.
• Finally, engaging with your audience and creating a sense of dialogue throughout your writing is essential. It can be achieved by addressing counterarguments and inviting feedback and discussion from your readers. Doing so can create a more engaging and thought-provoking discussion section.

Example of Discussion in Research Paper

In the discussion section, we will delve deeper into the findings of our study and explore their implications. Our research showed a strong correlation between regular exercise and improved mental health. This finding is consistent with previous studies in the field and reinforces the importance of physical activity for overall well-being.

We also found that social support plays a significant role in promoting exercise adherence and mental health outcomes. Participants who reported having supportive friends and family members were more likely to exercise regularly and experience positive mental health outcomes.

However, our study had limitations that should be acknowledged. Firstly, our sample size was small, and we only recruited participants from one location. Future studies should aim to recruit a more extensive and more diverse sample. Secondly, our study relied on self-reported measures of exercise and mental health, which can be subject to bias.

Overall, our findings suggest that promoting regular exercise and social support can effectively improve mental health outcomes. Further research is needed to explore the mechanisms underlying these relationships and to identify specific interventions that can be implemented to promote exercise and social support.

• Writing a Research Paper
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Results & Discussion

Characteristics of results & discussion.

• Results section contains data collected by scientists from experiments that they conducted.
• Data can be measurements, numbers, descriptions and/or observations.
• Scientific data is typically described using graphs, tables, figures, diagrams, maps, charts, photographs and/or equations.
• Discussion section provides an interpretation of the data, especially in context to previously published research.

The Results and Discussion sections can be written as separate sections (as shown in Fig. 2 ), but are often combined in a poster into one section called Results and Discussion.   This is done in order to (1) save precious space on a poster for the many pieces of information that a scientist would like to tell their audience and (2) by combining the two sections, it becomes easier for the audience to understand the significance of the research.   Combining the Results section and Discussion section in a poster is different for what is typically done for a scientific journal article.   In most journal articles, the Results section is separated from the Discussion section.   Journal articles are different from posters in that a scientist is not standing next to their journal article explaining it to a reader.   Therefore, in a journal article, an author needs to provide more detailed information so that the reader can understand the research independently.   Separating the Results section and Discussion section allows an author the space necessary to write a lengthier description of the research. Journal articles typically contain more text and more content (e.g., figures, tables) than posters.

The Results and Discussion section should contain data, typically in the form of a graph, histogram, chart, image, color-coded map or table ( Figs. 1 & 4 ).   Very often data means numbers that scientists collect from making measurements.   These data are typically presented to an audience in the form of graphs and charts to show a reader how these numbers change over time, space or experimental conditions ( Fig. 7 ).   Numbers can increase, decrease or stay the same and a graph, or another type of figure, can be effectively used to convey this information to a reader in a visual format ( Fig. 7 ).      

Figure 7. Example of a Graph

An audience will be attracted to a poster because of its figures and so it is very important for the author to pay particular attention to the creation, design and placement of the figures in a poster ( Figs. 1 & 4 ).   A good figure is one that is informative, easy to comprehend and allows the reader to understand the significance of the data and experiment.   Very often an author will use color to draw attention to a figure.      

The Discussion section should state the importance of the research that is presented in the poster.   It should provide an interpretation of the results, especially in context to previously published research.   It may propose future experiments that need to be conducted as a result of the research presented in the poster.   It should clearly illustrate the significance of the research with regards to new knowledge, understanding and/or discoveries that were made as part of the research.

Scientific Posters: A Learner's Guide Copyright © 2020 by Ella Weaver; Kylienne A. Shaul; Henry Griffy; and Brian H. Lower is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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• How to Write a Discussion Section | Tips & Examples

How to Write a Discussion Section | Tips & Examples

Published on 21 August 2022 by Shona McCombes . Revised on 25 October 2022.

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 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: summarise 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.

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 emphasise weaknesses or failures.

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Start this section by reiterating your research problem  and concisely summarising your major 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
• Contextualising 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 organise 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 hypothesised association …
• The results contradict the claims of Smith (2007) that …
• The results might suggest that x . However, based on the findings of similar studies, a more plausible explanation is x .

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 .

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 generalisability is limited.
• If you encountered problems when gathering or analysing 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 generalisability 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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• Published: 26 March 2024

Predicting and improving complex beer flavor through machine learning

• Michiel Schreurs   ORCID: orcid.org/0000-0002-9449-5619 1 , 2 , 3   na1 ,
• Supinya Piampongsant 1 , 2 , 3   na1 ,
• Miguel Roncoroni   ORCID: orcid.org/0000-0001-7461-1427 1 , 2 , 3   na1 ,
• Lloyd Cool   ORCID: orcid.org/0000-0001-9936-3124 1 , 2 , 3 , 4 ,
• Beatriz Herrera-Malaver   ORCID: orcid.org/0000-0002-5096-9974 1 , 2 , 3 ,
• Christophe Vanderaa   ORCID: orcid.org/0000-0001-7443-5427 4 ,
• Florian A. Theßeling 1 , 2 , 3 ,
• Łukasz Kreft   ORCID: orcid.org/0000-0001-7620-4657 5 ,
• Alexander Botzki   ORCID: orcid.org/0000-0001-6691-4233 5 ,
• Philippe Malcorps 6 ,
• Luk Daenen 6 ,
• Tom Wenseleers   ORCID: orcid.org/0000-0002-1434-861X 4 &
• Kevin J. Verstrepen   ORCID: orcid.org/0000-0002-3077-6219 1 , 2 , 3  

Nature Communications volume  15 , Article number:  2368 ( 2024 ) Cite this article

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• Chemical engineering
• Gas chromatography
• Machine learning
• Metabolomics
• Taste receptors

The perception and appreciation of food flavor depends on many interacting chemical compounds and external factors, and therefore proves challenging to understand and predict. Here, we combine extensive chemical and sensory analyses of 250 different beers to train machine learning models that allow predicting flavor and consumer appreciation. For each beer, we measure over 200 chemical properties, perform quantitative descriptive sensory analysis with a trained tasting panel and map data from over 180,000 consumer reviews to train 10 different machine learning models. The best-performing algorithm, Gradient Boosting, yields models that significantly outperform predictions based on conventional statistics and accurately predict complex food features and consumer appreciation from chemical profiles. Model dissection allows identifying specific and unexpected compounds as drivers of beer flavor and appreciation. Adding these compounds results in variants of commercial alcoholic and non-alcoholic beers with improved consumer appreciation. Together, our study reveals how big data and machine learning uncover complex links between food chemistry, flavor and consumer perception, and lays the foundation to develop novel, tailored foods with superior flavors.

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Introduction

Predicting and understanding food perception and appreciation is one of the major challenges in food science. Accurate modeling of food flavor and appreciation could yield important opportunities for both producers and consumers, including quality control, product fingerprinting, counterfeit detection, spoilage detection, and the development of new products and product combinations (food pairing) 1 , 2 , 3 , 4 , 5 , 6 . Accurate models for flavor and consumer appreciation would contribute greatly to our scientific understanding of how humans perceive and appreciate flavor. Moreover, accurate predictive models would also facilitate and standardize existing food assessment methods and could supplement or replace assessments by trained and consumer tasting panels, which are variable, expensive and time-consuming 7 , 8 , 9 . Lastly, apart from providing objective, quantitative, accurate and contextual information that can help producers, models can also guide consumers in understanding their personal preferences 10 .

Despite the myriad of applications, predicting food flavor and appreciation from its chemical properties remains a largely elusive goal in sensory science, especially for complex food and beverages 11 , 12 . A key obstacle is the immense number of flavor-active chemicals underlying food flavor. Flavor compounds can vary widely in chemical structure and concentration, making them technically challenging and labor-intensive to quantify, even in the face of innovations in metabolomics, such as non-targeted metabolic fingerprinting 13 , 14 . Moreover, sensory analysis is perhaps even more complicated. Flavor perception is highly complex, resulting from hundreds of different molecules interacting at the physiochemical and sensorial level. Sensory perception is often non-linear, characterized by complex and concentration-dependent synergistic and antagonistic effects 15 , 16 , 17 , 18 , 19 , 20 , 21 that are further convoluted by the genetics, environment, culture and psychology of consumers 22 , 23 , 24 . Perceived flavor is therefore difficult to measure, with problems of sensitivity, accuracy, and reproducibility that can only be resolved by gathering sufficiently large datasets 25 . Trained tasting panels are considered the prime source of quality sensory data, but require meticulous training, are low throughput and high cost. Public databases containing consumer reviews of food products could provide a valuable alternative, especially for studying appreciation scores, which do not require formal training 25 . Public databases offer the advantage of amassing large amounts of data, increasing the statistical power to identify potential drivers of appreciation. However, public datasets suffer from biases, including a bias in the volunteers that contribute to the database, as well as confounding factors such as price, cult status and psychological conformity towards previous ratings of the product.

Classical multivariate statistics and machine learning methods have been used to predict flavor of specific compounds by, for example, linking structural properties of a compound to its potential biological activities or linking concentrations of specific compounds to sensory profiles 1 , 26 . Importantly, most previous studies focused on predicting organoleptic properties of single compounds (often based on their chemical structure) 27 , 28 , 29 , 30 , 31 , 32 , 33 , thus ignoring the fact that these compounds are present in a complex matrix in food or beverages and excluding complex interactions between compounds. Moreover, the classical statistics commonly used in sensory science 34 , 35 , 36 , 37 , 38 , 39 require a large sample size and sufficient variance amongst predictors to create accurate models. They are not fit for studying an extensive set of hundreds of interacting flavor compounds, since they are sensitive to outliers, have a high tendency to overfit and are less suited for non-linear and discontinuous relationships 40 .

In this study, we combine extensive chemical analyses and sensory data of a set of different commercial beers with machine learning approaches to develop models that predict taste, smell, mouthfeel and appreciation from compound concentrations. Beer is particularly suited to model the relationship between chemistry, flavor and appreciation. First, beer is a complex product, consisting of thousands of flavor compounds that partake in complex sensory interactions 41 , 42 , 43 . This chemical diversity arises from the raw materials (malt, yeast, hops, water and spices) and biochemical conversions during the brewing process (kilning, mashing, boiling, fermentation, maturation and aging) 44 , 45 . Second, the advent of the internet saw beer consumers embrace online review platforms, such as RateBeer (ZX Ventures, Anheuser-Busch InBev SA/NV) and BeerAdvocate (Next Glass, inc.). In this way, the beer community provides massive data sets of beer flavor and appreciation scores, creating extraordinarily large sensory databases to complement the analyses of our professional sensory panel. Specifically, we characterize over 200 chemical properties of 250 commercial beers, spread across 22 beer styles, and link these to the descriptive sensory profiling data of a 16-person in-house trained tasting panel and data acquired from over 180,000 public consumer reviews. These unique and extensive datasets enable us to train a suite of machine learning models to predict flavor and appreciation from a beer’s chemical profile. Dissection of the best-performing models allows us to pinpoint specific compounds as potential drivers of beer flavor and appreciation. Follow-up experiments confirm the importance of these compounds and ultimately allow us to significantly improve the flavor and appreciation of selected commercial beers. Together, our study represents a significant step towards understanding complex flavors and reinforces the value of machine learning to develop and refine complex foods. In this way, it represents a stepping stone for further computer-aided food engineering applications 46 .

To generate a comprehensive dataset on beer flavor, we selected 250 commercial Belgian beers across 22 different beer styles (Supplementary Fig.  S1 ). Beers with ≤ 4.2% alcohol by volume (ABV) were classified as non-alcoholic and low-alcoholic. Blonds and Tripels constitute a significant portion of the dataset (12.4% and 11.2%, respectively) reflecting their presence on the Belgian beer market and the heterogeneity of beers within these styles. By contrast, lager beers are less diverse and dominated by a handful of brands. Rare styles such as Brut or Faro make up only a small fraction of the dataset (2% and 1%, respectively) because fewer of these beers are produced and because they are dominated by distinct characteristics in terms of flavor and chemical composition.

Extensive analysis identifies relationships between chemical compounds in beer

For each beer, we measured 226 different chemical properties, including common brewing parameters such as alcohol content, iso-alpha acids, pH, sugar concentration 47 , and over 200 flavor compounds (Methods, Supplementary Table  S1 ). A large portion (37.2%) are terpenoids arising from hopping, responsible for herbal and fruity flavors 16 , 48 . A second major category are yeast metabolites, such as esters and alcohols, that result in fruity and solvent notes 48 , 49 , 50 . Other measured compounds are primarily derived from malt, or other microbes such as non- Saccharomyces yeasts and bacteria (‘wild flora’). Compounds that arise from spices or staling are labeled under ‘Others’. Five attributes (caloric value, total acids and total ester, hop aroma and sulfur compounds) are calculated from multiple individually measured compounds.

As a first step in identifying relationships between chemical properties, we determined correlations between the concentrations of the compounds (Fig.  1 , upper panel, Supplementary Data  1 and 2 , and Supplementary Fig.  S2 . For the sake of clarity, only a subset of the measured compounds is shown in Fig.  1 ). Compounds of the same origin typically show a positive correlation, while absence of correlation hints at parameters varying independently. For example, the hop aroma compounds citronellol, and alpha-terpineol show moderate correlations with each other (Spearman’s rho=0.39 and 0.57), but not with the bittering hop component iso-alpha acids (Spearman’s rho=0.16 and −0.07). This illustrates how brewers can independently modify hop aroma and bitterness by selecting hop varieties and dosage time. If hops are added early in the boiling phase, chemical conversions increase bitterness while aromas evaporate, conversely, late addition of hops preserves aroma but limits bitterness 51 . Similarly, hop-derived iso-alpha acids show a strong anti-correlation with lactic acid and acetic acid, likely reflecting growth inhibition of lactic acid and acetic acid bacteria, or the consequent use of fewer hops in sour beer styles, such as West Flanders ales and Fruit beers, that rely on these bacteria for their distinct flavors 52 . Finally, yeast-derived esters (ethyl acetate, ethyl decanoate, ethyl hexanoate, ethyl octanoate) and alcohols (ethanol, isoamyl alcohol, isobutanol, and glycerol), correlate with Spearman coefficients above 0.5, suggesting that these secondary metabolites are correlated with the yeast genetic background and/or fermentation parameters and may be difficult to influence individually, although the choice of yeast strain may offer some control 53 .

Spearman rank correlations are shown. Descriptors are grouped according to their origin (malt (blue), hops (green), yeast (red), wild flora (yellow), Others (black)), and sensory aspect (aroma, taste, palate, and overall appreciation). Please note that for the chemical compounds, for the sake of clarity, only a subset of the total number of measured compounds is shown, with an emphasis on the key compounds for each source. For more details, see the main text and Methods section. Chemical data can be found in Supplementary Data  1 , correlations between all chemical compounds are depicted in Supplementary Fig.  S2 and correlation values can be found in Supplementary Data  2 . See Supplementary Data  4 for sensory panel assessments and Supplementary Data  5 for correlation values between all sensory descriptors.

Interestingly, different beer styles show distinct patterns for some flavor compounds (Supplementary Fig.  S3 ). These observations agree with expectations for key beer styles, and serve as a control for our measurements. For instance, Stouts generally show high values for color (darker), while hoppy beers contain elevated levels of iso-alpha acids, compounds associated with bitter hop taste. Acetic and lactic acid are not prevalent in most beers, with notable exceptions such as Kriek, Lambic, Faro, West Flanders ales and Flanders Old Brown, which use acid-producing bacteria ( Lactobacillus and Pediococcus ) or unconventional yeast ( Brettanomyces ) 54 , 55 . Glycerol, ethanol and esters show similar distributions across all beer styles, reflecting their common origin as products of yeast metabolism during fermentation 45 , 53 . Finally, low/no-alcohol beers contain low concentrations of glycerol and esters. This is in line with the production process for most of the low/no-alcohol beers in our dataset, which are produced through limiting fermentation or by stripping away alcohol via evaporation or dialysis, with both methods having the unintended side-effect of reducing the amount of flavor compounds in the final beer 56 , 57 .

Besides expected associations, our data also reveals less trivial associations between beer styles and specific parameters. For example, geraniol and citronellol, two monoterpenoids responsible for citrus, floral and rose flavors and characteristic of Citra hops, are found in relatively high amounts in Christmas, Saison, and Brett/co-fermented beers, where they may originate from terpenoid-rich spices such as coriander seeds instead of hops 58 .

Tasting panel assessments reveal sensorial relationships in beer

To assess the sensory profile of each beer, a trained tasting panel evaluated each of the 250 beers for 50 sensory attributes, including different hop, malt and yeast flavors, off-flavors and spices. Panelists used a tasting sheet (Supplementary Data  3 ) to score the different attributes. Panel consistency was evaluated by repeating 12 samples across different sessions and performing ANOVA. In 95% of cases no significant difference was found across sessions ( p  > 0.05), indicating good panel consistency (Supplementary Table  S2 ).

Aroma and taste perception reported by the trained panel are often linked (Fig.  1 , bottom left panel and Supplementary Data  4 and 5 ), with high correlations between hops aroma and taste (Spearman’s rho=0.83). Bitter taste was found to correlate with hop aroma and taste in general (Spearman’s rho=0.80 and 0.69), and particularly with “grassy” noble hops (Spearman’s rho=0.75). Barnyard flavor, most often associated with sour beers, is identified together with stale hops (Spearman’s rho=0.97) that are used in these beers. Lactic and acetic acid, which often co-occur, are correlated (Spearman’s rho=0.66). Interestingly, sweetness and bitterness are anti-correlated (Spearman’s rho = −0.48), confirming the hypothesis that they mask each other 59 , 60 . Beer body is highly correlated with alcohol (Spearman’s rho = 0.79), and overall appreciation is found to correlate with multiple aspects that describe beer mouthfeel (alcohol, carbonation; Spearman’s rho= 0.32, 0.39), as well as with hop and ester aroma intensity (Spearman’s rho=0.39 and 0.35).

Similar to the chemical analyses, sensorial analyses confirmed typical features of specific beer styles (Supplementary Fig.  S4 ). For example, sour beers (Faro, Flanders Old Brown, Fruit beer, Kriek, Lambic, West Flanders ale) were rated acidic, with flavors of both acetic and lactic acid. Hoppy beers were found to be bitter and showed hop-associated aromas like citrus and tropical fruit. Malt taste is most detected among scotch, stout/porters, and strong ales, while low/no-alcohol beers, which often have a reputation for being ‘worty’ (reminiscent of unfermented, sweet malt extract) appear in the middle. Unsurprisingly, hop aromas are most strongly detected among hoppy beers. Like its chemical counterpart (Supplementary Fig.  S3 ), acidity shows a right-skewed distribution, with the most acidic beers being Krieks, Lambics, and West Flanders ales.

Tasting panel assessments of specific flavors correlate with chemical composition

We find that the concentrations of several chemical compounds strongly correlate with specific aroma or taste, as evaluated by the tasting panel (Fig.  2 , Supplementary Fig.  S5 , Supplementary Data  6 ). In some cases, these correlations confirm expectations and serve as a useful control for data quality. For example, iso-alpha acids, the bittering compounds in hops, strongly correlate with bitterness (Spearman’s rho=0.68), while ethanol and glycerol correlate with tasters’ perceptions of alcohol and body, the mouthfeel sensation of fullness (Spearman’s rho=0.82/0.62 and 0.72/0.57 respectively) and darker color from roasted malts is a good indication of malt perception (Spearman’s rho=0.54).

Heatmap colors indicate Spearman’s Rho. Axes are organized according to sensory categories (aroma, taste, mouthfeel, overall), chemical categories and chemical sources in beer (malt (blue), hops (green), yeast (red), wild flora (yellow), Others (black)). See Supplementary Data  6 for all correlation values.

Interestingly, for some relationships between chemical compounds and perceived flavor, correlations are weaker than expected. For example, the rose-smelling phenethyl acetate only weakly correlates with floral aroma. This hints at more complex relationships and interactions between compounds and suggests a need for a more complex model than simple correlations. Lastly, we uncovered unexpected correlations. For instance, the esters ethyl decanoate and ethyl octanoate appear to correlate slightly with hop perception and bitterness, possibly due to their fruity flavor. Iron is anti-correlated with hop aromas and bitterness, most likely because it is also anti-correlated with iso-alpha acids. This could be a sign of metal chelation of hop acids 61 , given that our analyses measure unbound hop acids and total iron content, or could result from the higher iron content in dark and Fruit beers, which typically have less hoppy and bitter flavors 62 .

Public consumer reviews complement expert panel data

To complement and expand the sensory data of our trained tasting panel, we collected 180,000 reviews of our 250 beers from the online consumer review platform RateBeer. This provided numerical scores for beer appearance, aroma, taste, palate, overall quality as well as the average overall score.

Public datasets are known to suffer from biases, such as price, cult status and psychological conformity towards previous ratings of a product. For example, prices correlate with appreciation scores for these online consumer reviews (rho=0.49, Supplementary Fig.  S6 ), but not for our trained tasting panel (rho=0.19). This suggests that prices affect consumer appreciation, which has been reported in wine 63 , while blind tastings are unaffected. Moreover, we observe that some beer styles, like lagers and non-alcoholic beers, generally receive lower scores, reflecting that online reviewers are mostly beer aficionados with a preference for specialty beers over lager beers. In general, we find a modest correlation between our trained panel’s overall appreciation score and the online consumer appreciation scores (Fig.  3 , rho=0.29). Apart from the aforementioned biases in the online datasets, serving temperature, sample freshness and surroundings, which are all tightly controlled during the tasting panel sessions, can vary tremendously across online consumers and can further contribute to (among others, appreciation) differences between the two categories of tasters. Importantly, in contrast to the overall appreciation scores, for many sensory aspects the results from the professional panel correlated well with results obtained from RateBeer reviews. Correlations were highest for features that are relatively easy to recognize even for untrained tasters, like bitterness, sweetness, alcohol and malt aroma (Fig.  3 and below).

RateBeer text mining results can be found in Supplementary Data  7 . Rho values shown are Spearman correlation values, with asterisks indicating significant correlations ( p  < 0.05, two-sided). All p values were smaller than 0.001, except for Esters aroma (0.0553), Esters taste (0.3275), Esters aroma—banana (0.0019), Coriander (0.0508) and Diacetyl (0.0134).

Besides collecting consumer appreciation from these online reviews, we developed automated text analysis tools to gather additional data from review texts (Supplementary Data  7 ). Processing review texts on the RateBeer database yielded comparable results to the scores given by the trained panel for many common sensory aspects, including acidity, bitterness, sweetness, alcohol, malt, and hop tastes (Fig.  3 ). This is in line with what would be expected, since these attributes require less training for accurate assessment and are less influenced by environmental factors such as temperature, serving glass and odors in the environment. Consumer reviews also correlate well with our trained panel for 4-vinyl guaiacol, a compound associated with a very characteristic aroma. By contrast, correlations for more specific aromas like ester, coriander or diacetyl are underrepresented in the online reviews, underscoring the importance of using a trained tasting panel and standardized tasting sheets with explicit factors to be scored for evaluating specific aspects of a beer. Taken together, our results suggest that public reviews are trustworthy for some, but not all, flavor features and can complement or substitute taste panel data for these sensory aspects.

Models can predict beer sensory profiles from chemical data

The rich datasets of chemical analyses, tasting panel assessments and public reviews gathered in the first part of this study provided us with a unique opportunity to develop predictive models that link chemical data to sensorial features. Given the complexity of beer flavor, basic statistical tools such as correlations or linear regression may not always be the most suitable for making accurate predictions. Instead, we applied different machine learning models that can model both simple linear and complex interactive relationships. Specifically, we constructed a set of regression models to predict (a) trained panel scores for beer flavor and quality and (b) public reviews’ appreciation scores from beer chemical profiles. We trained and tested 10 different models (Methods), 3 linear regression-based models (simple linear regression with first-order interactions (LR), lasso regression with first-order interactions (Lasso), partial least squares regressor (PLSR)), 5 decision tree models (AdaBoost regressor (ABR), extra trees (ET), gradient boosting regressor (GBR), random forest (RF) and XGBoost regressor (XGBR)), 1 support vector regression (SVR), and 1 artificial neural network (ANN) model.

To compare the performance of our machine learning models, the dataset was randomly split into a training and test set, stratified by beer style. After a model was trained on data in the training set, its performance was evaluated on its ability to predict the test dataset obtained from multi-output models (based on the coefficient of determination, see Methods). Additionally, individual-attribute models were ranked per descriptor and the average rank was calculated, as proposed by Korneva et al. 64 . Importantly, both ways of evaluating the models’ performance agreed in general. Performance of the different models varied (Table  1 ). It should be noted that all models perform better at predicting RateBeer results than results from our trained tasting panel. One reason could be that sensory data is inherently variable, and this variability is averaged out with the large number of public reviews from RateBeer. Additionally, all tree-based models perform better at predicting taste than aroma. Linear models (LR) performed particularly poorly, with negative R 2 values, due to severe overfitting (training set R 2  = 1). Overfitting is a common issue in linear models with many parameters and limited samples, especially with interaction terms further amplifying the number of parameters. L1 regularization (Lasso) successfully overcomes this overfitting, out-competing multiple tree-based models on the RateBeer dataset. Similarly, the dimensionality reduction of PLSR avoids overfitting and improves performance, to some extent. Still, tree-based models (ABR, ET, GBR, RF and XGBR) show the best performance, out-competing the linear models (LR, Lasso, PLSR) commonly used in sensory science 65 .

GBR models showed the best overall performance in predicting sensory responses from chemical information, with R 2 values up to 0.75 depending on the predicted sensory feature (Supplementary Table  S4 ). The GBR models predict consumer appreciation (RateBeer) better than our trained panel’s appreciation (R 2 value of 0.67 compared to R 2 value of 0.09) (Supplementary Table  S3 and Supplementary Table  S4 ). ANN models showed intermediate performance, likely because neural networks typically perform best with larger datasets 66 . The SVR shows intermediate performance, mostly due to the weak predictions of specific attributes that lower the overall performance (Supplementary Table  S4 ).

Model dissection identifies specific, unexpected compounds as drivers of consumer appreciation

Next, we leveraged our models to infer important contributors to sensory perception and consumer appreciation. Consumer preference is a crucial sensory aspects, because a product that shows low consumer appreciation scores often does not succeed commercially 25 . Additionally, the requirement for a large number of representative evaluators makes consumer trials one of the more costly and time-consuming aspects of product development. Hence, a model for predicting chemical drivers of overall appreciation would be a welcome addition to the available toolbox for food development and optimization.

Since GBR models on our RateBeer dataset showed the best overall performance, we focused on these models. Specifically, we used two approaches to identify important contributors. First, rankings of the most important predictors for each sensorial trait in the GBR models were obtained based on impurity-based feature importance (mean decrease in impurity). High-ranked parameters were hypothesized to be either the true causal chemical properties underlying the trait, to correlate with the actual causal properties, or to take part in sensory interactions affecting the trait 67 (Fig.  4A ). In a second approach, we used SHAP 68 to determine which parameters contributed most to the model for making predictions of consumer appreciation (Fig.  4B ). SHAP calculates parameter contributions to model predictions on a per-sample basis, which can be aggregated into an importance score.

A The impurity-based feature importance (mean deviance in impurity, MDI) calculated from the Gradient Boosting Regression (GBR) model predicting RateBeer appreciation scores. The top 15 highest ranked chemical properties are shown. B SHAP summary plot for the top 15 parameters contributing to our GBR model. Each point on the graph represents a sample from our dataset. The color represents the concentration of that parameter, with bluer colors representing low values and redder colors representing higher values. Greater absolute values on the horizontal axis indicate a higher impact of the parameter on the prediction of the model. C Spearman correlations between the 15 most important chemical properties and consumer overall appreciation. Numbers indicate the Spearman Rho correlation coefficient, and the rank of this correlation compared to all other correlations. The top 15 important compounds were determined using SHAP (panel B).

Both approaches identified ethyl acetate as the most predictive parameter for beer appreciation (Fig.  4 ). Ethyl acetate is the most abundant ester in beer with a typical ‘fruity’, ‘solvent’ and ‘alcoholic’ flavor, but is often considered less important than other esters like isoamyl acetate. The second most important parameter identified by SHAP is ethanol, the most abundant beer compound after water. Apart from directly contributing to beer flavor and mouthfeel, ethanol drastically influences the physical properties of beer, dictating how easily volatile compounds escape the beer matrix to contribute to beer aroma 69 . Importantly, it should also be noted that the importance of ethanol for appreciation is likely inflated by the very low appreciation scores of non-alcoholic beers (Supplementary Fig.  S4 ). Despite not often being considered a driver of beer appreciation, protein level also ranks highly in both approaches, possibly due to its effect on mouthfeel and body 70 . Lactic acid, which contributes to the tart taste of sour beers, is the fourth most important parameter identified by SHAP, possibly due to the generally high appreciation of sour beers in our dataset.

Interestingly, some of the most important predictive parameters for our model are not well-established as beer flavors or are even commonly regarded as being negative for beer quality. For example, our models identify methanethiol and ethyl phenyl acetate, an ester commonly linked to beer staling 71 , as a key factor contributing to beer appreciation. Although there is no doubt that high concentrations of these compounds are considered unpleasant, the positive effects of modest concentrations are not yet known 72 , 73 .

To compare our approach to conventional statistics, we evaluated how well the 15 most important SHAP-derived parameters correlate with consumer appreciation (Fig.  4C ). Interestingly, only 6 of the properties derived by SHAP rank amongst the top 15 most correlated parameters. For some chemical compounds, the correlations are so low that they would have likely been considered unimportant. For example, lactic acid, the fourth most important parameter, shows a bimodal distribution for appreciation, with sour beers forming a separate cluster, that is missed entirely by the Spearman correlation. Additionally, the correlation plots reveal outliers, emphasizing the need for robust analysis tools. Together, this highlights the need for alternative models, like the Gradient Boosting model, that better grasp the complexity of (beer) flavor.

Finally, to observe the relationships between these chemical properties and their predicted targets, partial dependence plots were constructed for the six most important predictors of consumer appreciation 74 , 75 , 76 (Supplementary Fig.  S7 ). One-way partial dependence plots show how a change in concentration affects the predicted appreciation. These plots reveal an important limitation of our models: appreciation predictions remain constant at ever-increasing concentrations. This implies that once a threshold concentration is reached, further increasing the concentration does not affect appreciation. This is false, as it is well-documented that certain compounds become unpleasant at high concentrations, including ethyl acetate (‘nail polish’) 77 and methanethiol (‘sulfury’ and ‘rotten cabbage’) 78 . The inability of our models to grasp that flavor compounds have optimal levels, above which they become negative, is a consequence of working with commercial beer brands where (off-)flavors are rarely too high to negatively impact the product. The two-way partial dependence plots show how changing the concentration of two compounds influences predicted appreciation, visualizing their interactions (Supplementary Fig.  S7 ). In our case, the top 5 parameters are dominated by additive or synergistic interactions, with high concentrations for both compounds resulting in the highest predicted appreciation.

To assess the robustness of our best-performing models and model predictions, we performed 100 iterations of the GBR, RF and ET models. In general, all iterations of the models yielded similar performance (Supplementary Fig.  S8 ). Moreover, the main predictors (including the top predictors ethanol and ethyl acetate) remained virtually the same, especially for GBR and RF. For the iterations of the ET model, we did observe more variation in the top predictors, which is likely a consequence of the model’s inherent random architecture in combination with co-correlations between certain predictors. However, even in this case, several of the top predictors (ethanol and ethyl acetate) remain unchanged, although their rank in importance changes (Supplementary Fig.  S8 ).

Next, we investigated if a combination of RateBeer and trained panel data into one consolidated dataset would lead to stronger models, under the hypothesis that such a model would suffer less from bias in the datasets. A GBR model was trained to predict appreciation on the combined dataset. This model underperformed compared to the RateBeer model, both in the native case and when including a dataset identifier (R 2  = 0.67, 0.26 and 0.42 respectively). For the latter, the dataset identifier is the most important feature (Supplementary Fig.  S9 ), while most of the feature importance remains unchanged, with ethyl acetate and ethanol ranking highest, like in the original model trained only on RateBeer data. It seems that the large variation in the panel dataset introduces noise, weakening the models’ performances and reliability. In addition, it seems reasonable to assume that both datasets are fundamentally different, with the panel dataset obtained by blind tastings by a trained professional panel.

Lastly, we evaluated whether beer style identifiers would further enhance the model’s performance. A GBR model was trained with parameters that explicitly encoded the styles of the samples. This did not improve model performance (R2 = 0.66 with style information vs R2 = 0.67). The most important chemical features are consistent with the model trained without style information (eg. ethanol and ethyl acetate), and with the exception of the most preferred (strong ale) and least preferred (low/no-alcohol) styles, none of the styles were among the most important features (Supplementary Fig.  S9 , Supplementary Table  S5 and S6 ). This is likely due to a combination of style-specific chemical signatures, such as iso-alpha acids and lactic acid, that implicitly convey style information to the original models, as well as the low number of samples belonging to some styles, making it difficult for the model to learn style-specific patterns. Moreover, beer styles are not rigorously defined, with some styles overlapping in features and some beers being misattributed to a specific style, all of which leads to more noise in models that use style parameters.

Model validation

To test if our predictive models give insight into beer appreciation, we set up experiments aimed at improving existing commercial beers. We specifically selected overall appreciation as the trait to be examined because of its complexity and commercial relevance. Beer flavor comprises a complex bouquet rather than single aromas and tastes 53 . Hence, adding a single compound to the extent that a difference is noticeable may lead to an unbalanced, artificial flavor. Therefore, we evaluated the effect of combinations of compounds. Because Blond beers represent the most extensive style in our dataset, we selected a beer from this style as the starting material for these experiments (Beer 64 in Supplementary Data  1 ).

In the first set of experiments, we adjusted the concentrations of compounds that made up the most important predictors of overall appreciation (ethyl acetate, ethanol, lactic acid, ethyl phenyl acetate) together with correlated compounds (ethyl hexanoate, isoamyl acetate, glycerol), bringing them up to 95 th percentile ethanol-normalized concentrations (Methods) within the Blond group (‘Spiked’ concentration in Fig.  5A ). Compared to controls, the spiked beers were found to have significantly improved overall appreciation among trained panelists, with panelist noting increased intensity of ester flavors, sweetness, alcohol, and body fullness (Fig.  5B ). To disentangle the contribution of ethanol to these results, a second experiment was performed without the addition of ethanol. This resulted in a similar outcome, including increased perception of alcohol and overall appreciation.

Adding the top chemical compounds, identified as best predictors of appreciation by our model, into poorly appreciated beers results in increased appreciation from our trained panel. Results of sensory tests between base beers and those spiked with compounds identified as the best predictors by the model. A Blond and Non/Low-alcohol (0.0% ABV) base beers were brought up to 95th-percentile ethanol-normalized concentrations within each style. B For each sensory attribute, tasters indicated the more intense sample and selected the sample they preferred. The numbers above the bars correspond to the p values that indicate significant changes in perceived flavor (two-sided binomial test: alpha 0.05, n  = 20 or 13).

In a last experiment, we tested whether using the model’s predictions can boost the appreciation of a non-alcoholic beer (beer 223 in Supplementary Data  1 ). Again, the addition of a mixture of predicted compounds (omitting ethanol, in this case) resulted in a significant increase in appreciation, body, ester flavor and sweetness.

Predicting flavor and consumer appreciation from chemical composition is one of the ultimate goals of sensory science. A reliable, systematic and unbiased way to link chemical profiles to flavor and food appreciation would be a significant asset to the food and beverage industry. Such tools would substantially aid in quality control and recipe development, offer an efficient and cost-effective alternative to pilot studies and consumer trials and would ultimately allow food manufacturers to produce superior, tailor-made products that better meet the demands of specific consumer groups more efficiently.

A limited set of studies have previously tried, to varying degrees of success, to predict beer flavor and beer popularity based on (a limited set of) chemical compounds and flavors 79 , 80 . Current sensitive, high-throughput technologies allow measuring an unprecedented number of chemical compounds and properties in a large set of samples, yielding a dataset that can train models that help close the gaps between chemistry and flavor, even for a complex natural product like beer. To our knowledge, no previous research gathered data at this scale (250 samples, 226 chemical parameters, 50 sensory attributes and 5 consumer scores) to disentangle and validate the chemical aspects driving beer preference using various machine-learning techniques. We find that modern machine learning models outperform conventional statistical tools, such as correlations and linear models, and can successfully predict flavor appreciation from chemical composition. This could be attributed to the natural incorporation of interactions and non-linear or discontinuous effects in machine learning models, which are not easily grasped by the linear model architecture. While linear models and partial least squares regression represent the most widespread statistical approaches in sensory science, in part because they allow interpretation 65 , 81 , 82 , modern machine learning methods allow for building better predictive models while preserving the possibility to dissect and exploit the underlying patterns. Of the 10 different models we trained, tree-based models, such as our best performing GBR, showed the best overall performance in predicting sensory responses from chemical information, outcompeting artificial neural networks. This agrees with previous reports for models trained on tabular data 83 . Our results are in line with the findings of Colantonio et al. who also identified the gradient boosting architecture as performing best at predicting appreciation and flavor (of tomatoes and blueberries, in their specific study) 26 . Importantly, besides our larger experimental scale, we were able to directly confirm our models’ predictions in vivo.

Our study confirms that flavor compound concentration does not always correlate with perception, suggesting complex interactions that are often missed by more conventional statistics and simple models. Specifically, we find that tree-based algorithms may perform best in developing models that link complex food chemistry with aroma. Furthermore, we show that massive datasets of untrained consumer reviews provide a valuable source of data, that can complement or even replace trained tasting panels, especially for appreciation and basic flavors, such as sweetness and bitterness. This holds despite biases that are known to occur in such datasets, such as price or conformity bias. Moreover, GBR models predict taste better than aroma. This is likely because taste (e.g. bitterness) often directly relates to the corresponding chemical measurements (e.g., iso-alpha acids), whereas such a link is less clear for aromas, which often result from the interplay between multiple volatile compounds. We also find that our models are best at predicting acidity and alcohol, likely because there is a direct relation between the measured chemical compounds (acids and ethanol) and the corresponding perceived sensorial attribute (acidity and alcohol), and because even untrained consumers are generally able to recognize these flavors and aromas.

The predictions of our final models, trained on review data, hold even for blind tastings with small groups of trained tasters, as demonstrated by our ability to validate specific compounds as drivers of beer flavor and appreciation. Since adding a single compound to the extent of a noticeable difference may result in an unbalanced flavor profile, we specifically tested our identified key drivers as a combination of compounds. While this approach does not allow us to validate if a particular single compound would affect flavor and/or appreciation, our experiments do show that this combination of compounds increases consumer appreciation.

It is important to stress that, while it represents an important step forward, our approach still has several major limitations. A key weakness of the GBR model architecture is that amongst co-correlating variables, the largest main effect is consistently preferred for model building. As a result, co-correlating variables often have artificially low importance scores, both for impurity and SHAP-based methods, like we observed in the comparison to the more randomized Extra Trees models. This implies that chemicals identified as key drivers of a specific sensory feature by GBR might not be the true causative compounds, but rather co-correlate with the actual causative chemical. For example, the high importance of ethyl acetate could be (partially) attributed to the total ester content, ethanol or ethyl hexanoate (rho=0.77, rho=0.72 and rho=0.68), while ethyl phenylacetate could hide the importance of prenyl isobutyrate and ethyl benzoate (rho=0.77 and rho=0.76). Expanding our GBR model to include beer style as a parameter did not yield additional power or insight. This is likely due to style-specific chemical signatures, such as iso-alpha acids and lactic acid, that implicitly convey style information to the original model, as well as the smaller sample size per style, limiting the power to uncover style-specific patterns. This can be partly attributed to the curse of dimensionality, where the high number of parameters results in the models mainly incorporating single parameter effects, rather than complex interactions such as style-dependent effects 67 . A larger number of samples may overcome some of these limitations and offer more insight into style-specific effects. On the other hand, beer style is not a rigid scientific classification, and beers within one style often differ a lot, which further complicates the analysis of style as a model factor.

Our study is limited to beers from Belgian breweries. Although these beers cover a large portion of the beer styles available globally, some beer styles and consumer patterns may be missing, while other features might be overrepresented. For example, many Belgian ales exhibit yeast-driven flavor profiles, which is reflected in the chemical drivers of appreciation discovered by this study. In future work, expanding the scope to include diverse markets and beer styles could lead to the identification of even more drivers of appreciation and better models for special niche products that were not present in our beer set.

In addition to inherent limitations of GBR models, there are also some limitations associated with studying food aroma. Even if our chemical analyses measured most of the known aroma compounds, the total number of flavor compounds in complex foods like beer is still larger than the subset we were able to measure in this study. For example, hop-derived thiols, that influence flavor at very low concentrations, are notoriously difficult to measure in a high-throughput experiment. Moreover, consumer perception remains subjective and prone to biases that are difficult to avoid. It is also important to stress that the models are still immature and that more extensive datasets will be crucial for developing more complete models in the future. Besides more samples and parameters, our dataset does not include any demographic information about the tasters. Including such data could lead to better models that grasp external factors like age and culture. Another limitation is that our set of beers consists of high-quality end-products and lacks beers that are unfit for sale, which limits the current model in accurately predicting products that are appreciated very badly. Finally, while models could be readily applied in quality control, their use in sensory science and product development is restrained by their inability to discern causal relationships. Given that the models cannot distinguish compounds that genuinely drive consumer perception from those that merely correlate, validation experiments are essential to identify true causative compounds.

Despite the inherent limitations, dissection of our models enabled us to pinpoint specific molecules as potential drivers of beer aroma and consumer appreciation, including compounds that were unexpected and would not have been identified using standard approaches. Important drivers of beer appreciation uncovered by our models include protein levels, ethyl acetate, ethyl phenyl acetate and lactic acid. Currently, many brewers already use lactic acid to acidify their brewing water and ensure optimal pH for enzymatic activity during the mashing process. Our results suggest that adding lactic acid can also improve beer appreciation, although its individual effect remains to be tested. Interestingly, ethanol appears to be unnecessary to improve beer appreciation, both for blond beer and alcohol-free beer. Given the growing consumer interest in alcohol-free beer, with a predicted annual market growth of >7% 84 , it is relevant for brewers to know what compounds can further increase consumer appreciation of these beers. Hence, our model may readily provide avenues to further improve the flavor and consumer appreciation of both alcoholic and non-alcoholic beers, which is generally considered one of the key challenges for future beer production.

Whereas we see a direct implementation of our results for the development of superior alcohol-free beverages and other food products, our study can also serve as a stepping stone for the development of novel alcohol-containing beverages. We want to echo the growing body of scientific evidence for the negative effects of alcohol consumption, both on the individual level by the mutagenic, teratogenic and carcinogenic effects of ethanol 85 , 86 , as well as the burden on society caused by alcohol abuse and addiction. We encourage the use of our results for the production of healthier, tastier products, including novel and improved beverages with lower alcohol contents. Furthermore, we strongly discourage the use of these technologies to improve the appreciation or addictive properties of harmful substances.

The present work demonstrates that despite some important remaining hurdles, combining the latest developments in chemical analyses, sensory analysis and modern machine learning methods offers exciting avenues for food chemistry and engineering. Soon, these tools may provide solutions in quality control and recipe development, as well as new approaches to sensory science and flavor research.

Beer selection

250 commercial Belgian beers were selected to cover the broad diversity of beer styles and corresponding diversity in chemical composition and aroma. See Supplementary Fig.  S1 .

Chemical dataset

Sample preparation.

Beers within their expiration date were purchased from commercial retailers. Samples were prepared in biological duplicates at room temperature, unless explicitly stated otherwise. Bottle pressure was measured with a manual pressure device (Steinfurth Mess-Systeme GmbH) and used to calculate CO 2 concentration. The beer was poured through two filter papers (Macherey-Nagel, 500713032 MN 713 ¼) to remove carbon dioxide and prevent spontaneous foaming. Samples were then prepared for measurements by targeted Headspace-Gas Chromatography-Flame Ionization Detector/Flame Photometric Detector (HS-GC-FID/FPD), Headspace-Solid Phase Microextraction-Gas Chromatography-Mass Spectrometry (HS-SPME-GC-MS), colorimetric analysis, enzymatic analysis, Near-Infrared (NIR) analysis, as described in the sections below. The mean values of biological duplicates are reported for each compound.

HS-GC-FID/FPD

HS-GC-FID/FPD (Shimadzu GC 2010 Plus) was used to measure higher alcohols, acetaldehyde, esters, 4-vinyl guaicol, and sulfur compounds. Each measurement comprised 5 ml of sample pipetted into a 20 ml glass vial containing 1.75 g NaCl (VWR, 27810.295). 100 µl of 2-heptanol (Sigma-Aldrich, H3003) (internal standard) solution in ethanol (Fisher Chemical, E/0650DF/C17) was added for a final concentration of 2.44 mg/L. Samples were flushed with nitrogen for 10 s, sealed with a silicone septum, stored at −80 °C and analyzed in batches of 20.

The GC was equipped with a DB-WAXetr column (length, 30 m; internal diameter, 0.32 mm; layer thickness, 0.50 µm; Agilent Technologies, Santa Clara, CA, USA) to the FID and an HP-5 column (length, 30 m; internal diameter, 0.25 mm; layer thickness, 0.25 µm; Agilent Technologies, Santa Clara, CA, USA) to the FPD. N 2 was used as the carrier gas. Samples were incubated for 20 min at 70 °C in the headspace autosampler (Flow rate, 35 cm/s; Injection volume, 1000 µL; Injection mode, split; Combi PAL autosampler, CTC analytics, Switzerland). The injector, FID and FPD temperatures were kept at 250 °C. The GC oven temperature was first held at 50 °C for 5 min and then allowed to rise to 80 °C at a rate of 5 °C/min, followed by a second ramp of 4 °C/min until 200 °C kept for 3 min and a final ramp of (4 °C/min) until 230 °C for 1 min. Results were analyzed with the GCSolution software version 2.4 (Shimadzu, Kyoto, Japan). The GC was calibrated with a 5% EtOH solution (VWR International) containing the volatiles under study (Supplementary Table  S7 ).

HS-SPME-GC-MS

HS-SPME-GC-MS (Shimadzu GCMS-QP-2010 Ultra) was used to measure additional volatile compounds, mainly comprising terpenoids and esters. Samples were analyzed by HS-SPME using a triphase DVB/Carboxen/PDMS 50/30 μm SPME fiber (Supelco Co., Bellefonte, PA, USA) followed by gas chromatography (Thermo Fisher Scientific Trace 1300 series, USA) coupled to a mass spectrometer (Thermo Fisher Scientific ISQ series MS) equipped with a TriPlus RSH autosampler. 5 ml of degassed beer sample was placed in 20 ml vials containing 1.75 g NaCl (VWR, 27810.295). 5 µl internal standard mix was added, containing 2-heptanol (1 g/L) (Sigma-Aldrich, H3003), 4-fluorobenzaldehyde (1 g/L) (Sigma-Aldrich, 128376), 2,3-hexanedione (1 g/L) (Sigma-Aldrich, 144169) and guaiacol (1 g/L) (Sigma-Aldrich, W253200) in ethanol (Fisher Chemical, E/0650DF/C17). Each sample was incubated at 60 °C in the autosampler oven with constant agitation. After 5 min equilibration, the SPME fiber was exposed to the sample headspace for 30 min. The compounds trapped on the fiber were thermally desorbed in the injection port of the chromatograph by heating the fiber for 15 min at 270 °C.

The GC-MS was equipped with a low polarity RXi-5Sil MS column (length, 20 m; internal diameter, 0.18 mm; layer thickness, 0.18 µm; Restek, Bellefonte, PA, USA). Injection was performed in splitless mode at 320 °C, a split flow of 9 ml/min, a purge flow of 5 ml/min and an open valve time of 3 min. To obtain a pulsed injection, a programmed gas flow was used whereby the helium gas flow was set at 2.7 mL/min for 0.1 min, followed by a decrease in flow of 20 ml/min to the normal 0.9 mL/min. The temperature was first held at 30 °C for 3 min and then allowed to rise to 80 °C at a rate of 7 °C/min, followed by a second ramp of 2 °C/min till 125 °C and a final ramp of 8 °C/min with a final temperature of 270 °C.

Mass acquisition range was 33 to 550 amu at a scan rate of 5 scans/s. Electron impact ionization energy was 70 eV. The interface and ion source were kept at 275 °C and 250 °C, respectively. A mix of linear n-alkanes (from C7 to C40, Supelco Co.) was injected into the GC-MS under identical conditions to serve as external retention index markers. Identification and quantification of the compounds were performed using an in-house developed R script as described in Goelen et al. and Reher et al. 87 , 88 (for package information, see Supplementary Table  S8 ). Briefly, chromatograms were analyzed using AMDIS (v2.71) 89 to separate overlapping peaks and obtain pure compound spectra. The NIST MS Search software (v2.0 g) in combination with the NIST2017, FFNSC3 and Adams4 libraries were used to manually identify the empirical spectra, taking into account the expected retention time. After background subtraction and correcting for retention time shifts between samples run on different days based on alkane ladders, compound elution profiles were extracted and integrated using a file with 284 target compounds of interest, which were either recovered in our identified AMDIS list of spectra or were known to occur in beer. Compound elution profiles were estimated for every peak in every chromatogram over a time-restricted window using weighted non-negative least square analysis after which peak areas were integrated 87 , 88 . Batch effect correction was performed by normalizing against the most stable internal standard compound, 4-fluorobenzaldehyde. Out of all 284 target compounds that were analyzed, 167 were visually judged to have reliable elution profiles and were used for final analysis.

Discrete photometric and enzymatic analysis

Discrete photometric and enzymatic analysis (Thermo Scientific TM Gallery TM Plus Beermaster Discrete Analyzer) was used to measure acetic acid, ammonia, beta-glucan, iso-alpha acids, color, sugars, glycerol, iron, pH, protein, and sulfite. 2 ml of sample volume was used for the analyses. Information regarding the reagents and standard solutions used for analyses and calibrations is included in Supplementary Table  S7 and Supplementary Table  S9 .

NIR analyses

NIR analysis (Anton Paar Alcolyzer Beer ME System) was used to measure ethanol. Measurements comprised 50 ml of sample, and a 10% EtOH solution was used for calibration.

Correlation calculations

Pairwise Spearman Rank correlations were calculated between all chemical properties.

Sensory dataset

Trained panel.

Our trained tasting panel consisted of volunteers who gave prior verbal informed consent. All compounds used for the validation experiment were of food-grade quality. The tasting sessions were approved by the Social and Societal Ethics Committee of the KU Leuven (G-2022-5677-R2(MAR)). All online reviewers agreed to the Terms and Conditions of the RateBeer website.

Sensory analysis was performed according to the American Society of Brewing Chemists (ASBC) Sensory Analysis Methods 90 . 30 volunteers were screened through a series of triangle tests. The sixteen most sensitive and consistent tasters were retained as taste panel members. The resulting panel was diverse in age [22–42, mean: 29], sex [56% male] and nationality [7 different countries]. The panel developed a consensus vocabulary to describe beer aroma, taste and mouthfeel. Panelists were trained to identify and score 50 different attributes, using a 7-point scale to rate attributes’ intensity. The scoring sheet is included as Supplementary Data  3 . Sensory assessments took place between 10–12 a.m. The beers were served in black-colored glasses. Per session, between 5 and 12 beers of the same style were tasted at 12 °C to 16 °C. Two reference beers were added to each set and indicated as ‘Reference 1 & 2’, allowing panel members to calibrate their ratings. Not all panelists were present at every tasting. Scores were scaled by standard deviation and mean-centered per taster. Values are represented as z-scores and clustered by Euclidean distance. Pairwise Spearman correlations were calculated between taste and aroma sensory attributes. Panel consistency was evaluated by repeating samples on different sessions and performing ANOVA to identify differences, using the ‘stats’ package (v4.2.2) in R (for package information, see Supplementary Table  S8 ).

Online reviews from a public database

The ‘scrapy’ package in Python (v3.6) (for package information, see Supplementary Table  S8 ). was used to collect 232,288 online reviews (mean=922, min=6, max=5343) from RateBeer, an online beer review database. Each review entry comprised 5 numerical scores (appearance, aroma, taste, palate and overall quality) and an optional review text. The total number of reviews per reviewer was collected separately. Numerical scores were scaled and centered per rater, and mean scores were calculated per beer.

For the review texts, the language was estimated using the packages ‘langdetect’ and ‘langid’ in Python. Reviews that were classified as English by both packages were kept. Reviewers with fewer than 100 entries overall were discarded. 181,025 reviews from >6000 reviewers from >40 countries remained. Text processing was done using the ‘nltk’ package in Python. Texts were corrected for slang and misspellings; proper nouns and rare words that are relevant to the beer context were specified and kept as-is (‘Chimay’,’Lambic’, etc.). A dictionary of semantically similar sensorial terms, for example ‘floral’ and ‘flower’, was created and collapsed together into one term. Words were stemmed and lemmatized to avoid identifying words such as ‘acid’ and ‘acidity’ as separate terms. Numbers and punctuation were removed.

Sentences from up to 50 randomly chosen reviews per beer were manually categorized according to the aspect of beer they describe (appearance, aroma, taste, palate, overall quality—not to be confused with the 5 numerical scores described above) or flagged as irrelevant if they contained no useful information. If a beer contained fewer than 50 reviews, all reviews were manually classified. This labeled data set was used to train a model that classified the rest of the sentences for all beers 91 . Sentences describing taste and aroma were extracted, and term frequency–inverse document frequency (TFIDF) was implemented to calculate enrichment scores for sensorial words per beer.

The sex of the tasting subject was not considered when building our sensory database. Instead, results from different panelists were averaged, both for our trained panel (56% male, 44% female) and the RateBeer reviews (70% male, 30% female for RateBeer as a whole).

Beer price collection and processing

Beer prices were collected from the following stores: Colruyt, Delhaize, Total Wine, BeerHawk, The Belgian Beer Shop, The Belgian Shop, and Beer of Belgium. Where applicable, prices were converted to Euros and normalized per liter. Spearman correlations were calculated between these prices and mean overall appreciation scores from RateBeer and the taste panel, respectively.

Pairwise Spearman Rank correlations were calculated between all sensory properties.

Machine learning models

Predictive modeling of sensory profiles from chemical data.

Regression models were constructed to predict (a) trained panel scores for beer flavors and quality from beer chemical profiles and (b) public reviews’ appreciation scores from beer chemical profiles. Z-scores were used to represent sensory attributes in both data sets. Chemical properties with log-normal distributions (Shapiro-Wilk test, p  <  0.05 ) were log-transformed. Missing chemical measurements (0.1% of all data) were replaced with mean values per attribute. Observations from 250 beers were randomly separated into a training set (70%, 175 beers) and a test set (30%, 75 beers), stratified per beer style. Chemical measurements (p = 231) were normalized based on the training set average and standard deviation. In total, three linear regression-based models: linear regression with first-order interaction terms (LR), lasso regression with first-order interaction terms (Lasso) and partial least squares regression (PLSR); five decision tree models, Adaboost regressor (ABR), Extra Trees (ET), Gradient Boosting regressor (GBR), Random Forest (RF) and XGBoost regressor (XGBR); one support vector machine model (SVR) and one artificial neural network model (ANN) were trained. The models were implemented using the ‘scikit-learn’ package (v1.2.2) and ‘xgboost’ package (v1.7.3) in Python (v3.9.16). Models were trained, and hyperparameters optimized, using five-fold cross-validated grid search with the coefficient of determination (R 2 ) as the evaluation metric. The ANN (scikit-learn’s MLPRegressor) was optimized using Bayesian Tree-Structured Parzen Estimator optimization with the ‘Optuna’ Python package (v3.2.0). Individual models were trained per attribute, and a multi-output model was trained on all attributes simultaneously.

Model dissection

GBR was found to outperform other methods, resulting in models with the highest average R 2 values in both trained panel and public review data sets. Impurity-based rankings of the most important predictors for each predicted sensorial trait were obtained using the ‘scikit-learn’ package. To observe the relationships between these chemical properties and their predicted targets, partial dependence plots (PDP) were constructed for the six most important predictors of consumer appreciation 74 , 75 .

The ‘SHAP’ package in Python (v0.41.0) was implemented to provide an alternative ranking of predictor importance and to visualize the predictors’ effects as a function of their concentration 68 .

Validation of causal chemical properties

To validate the effects of the most important model features on predicted sensory attributes, beers were spiked with the chemical compounds identified by the models and descriptive sensory analyses were carried out according to the American Society of Brewing Chemists (ASBC) protocol 90 .

Compound spiking was done 30 min before tasting. Compounds were spiked into fresh beer bottles, that were immediately resealed and inverted three times. Fresh bottles of beer were opened for the same duration, resealed, and inverted thrice, to serve as controls. Pairs of spiked samples and controls were served simultaneously, chilled and in dark glasses as outlined in the Trained panel section above. Tasters were instructed to select the glass with the higher flavor intensity for each attribute (directional difference test 92 ) and to select the glass they prefer.

The final concentration after spiking was equal to the within-style average, after normalizing by ethanol concentration. This was done to ensure balanced flavor profiles in the final spiked beer. The same methods were applied to improve a non-alcoholic beer. Compounds were the following: ethyl acetate (Merck KGaA, W241415), ethyl hexanoate (Merck KGaA, W243906), isoamyl acetate (Merck KGaA, W205508), phenethyl acetate (Merck KGaA, W285706), ethanol (96%, Colruyt), glycerol (Merck KGaA, W252506), lactic acid (Merck KGaA, 261106).

Significant differences in preference or perceived intensity were determined by performing the two-sided binomial test on each attribute.

Reporting summary

Further information on research design is available in the  Nature Portfolio Reporting Summary linked to this article.

Data availability

The data that support the findings of this work are available in the Supplementary Data files and have been deposited to Zenodo under accession code 10653704 93 . The RateBeer scores data are under restricted access, they are not publicly available as they are property of RateBeer (ZX Ventures, USA). Access can be obtained from the authors upon reasonable request and with permission of RateBeer (ZX Ventures, USA).  Source data are provided with this paper.

Code availability

The code for training the machine learning models, analyzing the models, and generating the figures has been deposited to Zenodo under accession code 10653704 93 .

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Acknowledgements

We thank all lab members for their discussions and thank all tasting panel members for their contributions. Special thanks go out to Dr. Karin Voordeckers for her tremendous help in proofreading and improving the manuscript. M.S. was supported by a Baillet-Latour fellowship, L.C. acknowledges financial support from KU Leuven (C16/17/006), F.A.T. was supported by a PhD fellowship from FWO (1S08821N). Research in the lab of K.J.V. is supported by KU Leuven, FWO, VIB, VLAIO and the Brewing Science Serves Health Fund. Research in the lab of T.W. is supported by FWO (G.0A51.15) and KU Leuven (C16/17/006).

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These authors contributed equally: Michiel Schreurs, Supinya Piampongsant, Miguel Roncoroni.

Authors and Affiliations

VIB—KU Leuven Center for Microbiology, Gaston Geenslaan 1, B-3001, Leuven, Belgium

Michiel Schreurs, Supinya Piampongsant, Miguel Roncoroni, Lloyd Cool, Beatriz Herrera-Malaver, Florian A. Theßeling & Kevin J. Verstrepen

CMPG Laboratory of Genetics and Genomics, KU Leuven, Gaston Geenslaan 1, B-3001, Leuven, Belgium

Leuven Institute for Beer Research (LIBR), Gaston Geenslaan 1, B-3001, Leuven, Belgium

Laboratory of Socioecology and Social Evolution, KU Leuven, Naamsestraat 59, B-3000, Leuven, Belgium

Lloyd Cool, Christophe Vanderaa & Tom Wenseleers

VIB Bioinformatics Core, VIB, Rijvisschestraat 120, B-9052, Ghent, Belgium

Łukasz Kreft & Alexander Botzki

AB InBev SA/NV, Brouwerijplein 1, B-3000, Leuven, Belgium

Philippe Malcorps & Luk Daenen

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Contributions

S.P., M.S. and K.J.V. conceived the experiments. S.P., M.S. and K.J.V. designed the experiments. S.P., M.S., M.R., B.H. and F.A.T. performed the experiments. S.P., M.S., L.C., C.V., L.K., A.B., P.M., L.D., T.W. and K.J.V. contributed analysis ideas. S.P., M.S., L.C., C.V., T.W. and K.J.V. analyzed the data. All authors contributed to writing the manuscript.

Corresponding author

Correspondence to Kevin J. Verstrepen .

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Competing interests.

K.J.V. is affiliated with bar.on. The other authors declare no competing interests.

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Schreurs, M., Piampongsant, S., Roncoroni, M. et al. Predicting and improving complex beer flavor through machine learning. Nat Commun 15 , 2368 (2024). https://doi.org/10.1038/s41467-024-46346-0

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Received : 30 October 2023

Accepted : 21 February 2024

Published : 26 March 2024

DOI : https://doi.org/10.1038/s41467-024-46346-0

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