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6 Steps to Write an Excellent Discussion in Your Manuscript

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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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How to Write a Discussion Section for a Research Paper

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

What is the Discussion section of a research paper?

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

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

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

What should I include in the Discussion section?

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

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

How to Write the Discussion Section

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

Technical writing elements

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

Discussion section organization

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

Discussion Part 1: Summarizing Key Findings

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

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

Phrase examples: Summarizing the results

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

Discussion Part 2: Interpreting the Findings

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

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

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

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

Discussion Part 3: Discussing the Implications

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

Questions to ask yourself when dealing with potential implications:

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

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

Phrase examples: Discussing the implications of the research

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

Step 4: Acknowledging the limitations

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

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

Possible types of study limitations:

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

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

Phrase examples: Limitations sentence beginners

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

Discussion Part 5: Giving Recommendations for Further Research

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

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

Phrase examples: Recommendation sentence beginners

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

Consider Receiving Professional Language Editing

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

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

Wordvice Writing Resources

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

Additional Academic Resources

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

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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• 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

• How to Write a Great Title
• How to Write an Abstract
• How to Write Your Methods
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Systematic Review Discussion Example

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What should be included in the discussion section of a systematic review.

There are a number of key elements that are included in a discussion section of a systematic review. Remember to use all these elements to ensure the quality of your review remains high, that your review is deemed useful to your peers, and that the validity of your systematic review cannot be questioned.

The first thing to do in your discussion is to summarize your most important findings. This can simply be identifying your key results. Be careful not to just repeat all the results you have outlined in your previous sections. Instead, once you have briefly mentioned them, go on to interpret them. The results from included studies are presented in a summary. The results are then compared among different studies, and the consistent themes, agreements, and contradictions among studies are identified. The consistencies are reported and reasons for contradictions are given. The themes and agreement among the studies are used to answer the research question. Your interpretations need to be backed up by evidence so that they make the intended impact. Interpretations can be based on your critical thinking. Your interpretations of study findings can be compared to the interpretation of another review on the same topic.

Another way to ensure that your review is as persuasive as possible is to discuss any strengths and weaknesses at this point, in your discussion. It is advisable to first talk about the most notable strengths and limitations of included studies. Afterward, you can show how the characteristics of individual included studies have affected the strengths and limitations of the review. Identifying weaknesses may not be immediately obvious for some writers of reviews. However, they are essential to include, especially in the discussion section, as it means you can explain them and examine why your findings are still valid, despite such weaknesses. Discussing strengths will support your view even further. By highlighting both strengths and weaknesses together, you can dismiss any negative criticism before it even begins.

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How Long Should A Discussion Be In A Systematic Review?

When it comes to the length of a discussion section, there is never really a right or wrong answer. The length of the discussion section is a systematic review is usually determined by the number of included studies, the scope of the research question, and the ability of the author to analyze and synthesize data from the included studies. That being said, given the breadth and number of areas to be covered as mentioned above, it will never be just one paragraph. Examining the strengths and weaknesses of your review alone will often call for a couple of paragraphs of discussion. Then you assert your findings that will answer your research question and support your initial hypothesis. This will likely demand another paragraph or two at least.

The Importance of Systematic Review Discussion

Remember that the discussion section of your review is, arguably, the most important part of your work. It is where you can put your label on all previous studies conducted, and highlight why your research into the area has been a worthwhile process. It is an opportunity for you to set yourself apart, and have your paper be seen as evidence for the subject matter in question. Therefore, the importance of a systematic review discussion cannot be overstated. The discussion section of a review is your chance to present the results of your analysis, which takes into account all previous studies or research in the area.

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

Michael höfler, sebastian trautmann, robert miller.

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Received 2017 Oct 27; Accepted 2018 Apr 1; Collection date 2018.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/ ) applies to the data made available in this article, unless otherwise stated.

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.

Keywords: Discussion, Conclusion, Writing, Bias, Causality, Mechanism, Assumptions, Statistician, Substantive researcher, Bayes

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. 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.

Start the discussion with the conclusion your design and results unambiguously allow

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.

Mention the conclusion(s) that researchers would like to draw

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.

Specify all assumptions to interprete the observed result in the desired (causal) way

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.

Otherwise avoid causal language

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).

Reflect critically on how deviations from the assumptions would have influenced the results

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. 2 ).

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. 3 ).

Comment on all main types of bias and the inferential consequences they putatively have

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. 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).

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.

Propose a specific study design that requires less and weaker assumptions for a conclusion

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.

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

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")

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

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.

Don’t mistake the absence of evidence as evidence for absence

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.

Strictly distinguish between discussing pre-specified hypotheses and newly proposed hypotheses from post-hoc analyses

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 ].

Do not over-interpret small findings. Statistical significance should not be mis-interpreted as practical significance

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.

Avoid claims that are not statistically well-founded

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

Not applicable.

Abbreviations

health behavior

lung cancer

randomized clinical trial

factor variable

outcome variable

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.

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