# How to Report the Results of Nonparametric Tests in Biological Papers ## Key Takeaways - Report the specific test statistic (e.g., U for Mann-Whitney, H for Kruskal-Wallis, $\chi^2$ for Chi-square), associated degrees of freedom or sample sizes, the exact p-value, and a relevant effect size with its confidence interval for all nonparametric tests. - Clearly document the rationale for selecting a nonparametric test in the methods section, including how data distribution was assessed (e.g., Shapiro-Wilk test, visual inspection of histograms) and why parametric assumptions were not met. - Present summary statistics appropriate for non-normally distributed data, such as the median and interquartile range (IQR), for each group, and visualize the data distribution using box plots or violin plots to complement the statistical results. - Adhere to established reporting guidelines (e.g., from the EQUATOR Network) that match the study design to ensure comprehensive and standardized reporting of statistical analyses, including the chosen effect size metric (e.g., rank-biserial correlation, epsilon-squared, Cramer's V). - Avoid reporting only p-values or using p-value thresholds (e.g., p < 0.05) without also providing the test statistic and effect size, as this hinders reproducibility and interpretation of biological significance. --- ## Quick Answer - Report the test statistic, degrees of freedom or sample size, exact p value, and effect size with confidence intervals for every nonparametric test. - Choose your reporting style before analysis by consulting the EQUATOR Network for the guideline that matches your study design. - A p value alone does not communicate biological importance, so pair it with an effect size and a clear description of the data distribution. ## Why Nonparametric Tests Need Distinct Reporting Standards Nonparametric tests are common in biological research because many measurements do not meet the normality assumptions required by parametric procedures. Counts of cells, enzyme activity levels, behavioral scores, and ordinal survey responses frequently produce skewed distributions or contain outliers that make the mean an unreliable summary. When researchers choose a nonparametric test, they must also change how they report the results. The methods section must describe the test selection logic, the results section must include the test statistic and effect size, and the figures must show the distribution instead of just a bar chart of means. The core problem is that many published papers report only a p value, such as "p < 0.05," without stating which test was used, what the test statistic was, or how large the observed effect was. This omission makes the result impossible to verify, difficult to compare with other studies, and vulnerable to criticism during peer review. Journals increasingly require transparent reporting, and funding agencies expect data management plans that support reproducibility. The [National Library of Medicine](https://www.ncbi.nlm.nih.gov/books) hosts research methods references that describe the standards for reporting biomedical studies, and the [EQUATOR Network](https://www.equator-network.org/) provides a searchable collection of reporting guidelines for different study types. ## At a Glance | Test | What to Report in Methods | What to Report in Results | Effect Size | |------|---------------------------|---------------------------|-------------| | Mann-Whitney U | Rationale for choosing the test, whether the test was one-tailed or two-tailed, how ties were handled | U statistic, sample sizes per group, exact p value, median and interquartile range for each group | Rank-biserial correlation or probability of superiority with confidence interval | | Kruskal-Wallis | Rationale for choosing the test, how the data were ranked, whether post hoc comparisons were planned | H statistic, degrees of freedom, sample size per group, exact p value | Epsilon-squared or eta-squared with confidence interval | | Chi-square | Rationale for choosing the test, expected cell count check, whether Yates correction was applied | Chi-square value, degrees of freedom, exact p value, observed and expected counts | Cramer's V or phi coefficient with confidence interval | ## Core Principles of Nonparametric Reporting ### The Test Statistic Is the Foundation Every nonparametric test produces a test statistic that summarizes the difference or association in the data. The Mann-Whitney U test produces a U value, the Kruskal-Wallis test produces an H value, and the chi-square test produces a chi-square value. These statistics are not interchangeable, and the reader needs to know which one was calculated to understand the analysis. The test statistic alone is not enough, but it is the starting point for any complete report. The exact value of the test statistic matters because it allows a reader to verify the result. If the paper reports only "p < 0.05," the reader cannot check whether the analysis was performed correctly. If the paper reports "U = 1,234, p = 0.032," the reader can compare the result to published tables or software output. The [Committee on Publication Ethics](https://publicationethics.org/core-practices) core practices emphasize the importance of accurate reporting and the ability to verify results, which supports the need for exact statistics. ### The P Value Is Not the Final Word The p value tells the reader the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. It does not tell the reader how large the effect is, whether the effect is biologically meaningful, or how precise the estimate is. A very large sample can produce a small p value for a trivial difference, and a small sample can produce a large p value for a meaningful difference. The p value must be reported with the exact value, beyond a threshold, and it must be accompanied by an effect size. ### Effect Size Is Required for Interpretation An effect size quantifies the magnitude of the difference or association. For the Mann-Whitney U test, the rank-biserial correlation or the probability of superiority are common effect sizes. For the Kruskal-Wallis test, epsilon-squared or eta-squared are common. For the chi-square test, Cramer's V or the phi coefficient are common. The effect size should be reported with a confidence interval so the reader can see the precision of the estimate. A confidence interval that crosses zero indicates that the effect is not statistically significant, while an interval that does not cross zero indicates a significant effect. ### The Distribution Must Be Described Nonparametric tests are often used because the data are not normally distributed, so the results section must describe the distribution. The median and interquartile range are the appropriate summary statistics for skewed data, not the mean and standard deviation. The methods section should state how the distribution was assessed, such as by visual inspection of histograms or by a formal test of normality, and the results section should show the distribution in a figure such as a box plot or a violin plot. ## Practical Workflow for Reporting Nonparametric Tests ### Step 1: Select the Reporting Guideline Before writing the methods section, the researcher should identify the reporting guideline that applies to the study design. The [EQUATOR Network](https://www.equator-network.org/) provides a searchable database of guidelines for different study types, including randomized trials, observational studies, and laboratory experiments. The guideline will specify which elements must be reported, including the statistical methods. The researcher should download the guideline checklist and use it as a template for the methods and results sections. ### Step 2: Document the Data Distribution The methods section must state how the data distribution was assessed. This includes the software used, the procedure for checking normality, and the decision rule for choosing a nonparametric test. For example, the researcher might state that the Shapiro-Wilk test was used to assess normality and that the data was considered non-normal if the p value was less than 0.05. The researcher should also state whether the data was transformed before analysis and whether the transformation was successful. ### Step 3: Record the Test Statistic and p Value The results section must include the exact test statistic, the degrees of freedom or sample size, and the exact p value. The researcher should copy the output from the statistical software directly into the manuscript, instead of rounding the p value to a threshold. The p value should be reported as "p = 0.032" instead of "p < 0.05" unless the software reports the p value as less than 0.001, in which case "p < 0.001" is acceptable. ### Step 4: Calculate the Effect Size The effect size should be calculated from the test statistic and the sample size. The researcher should use the formula that is appropriate for the test and the software that is available. The effect size should be reported with a confidence interval, which can be calculated by bootstrapping or by using the standard error of the effect size. The confidence interval should be reported in the results section. ### Step 5: Write the Results in the Style of the Journal The results should be written in the style that the journal requires. The [EQUATOR Network](https://www.equator-network.org/) provides examples of reporting in different styles, and the journal's instructions to authors will specify the preferred style. The researcher should follow the style that the journal requires, whether that is APA, ICMJE, or another style. ## Options and Tradeoffs in Reporting ### Exact p Values Versus Thresholds Some journals require exact p values, while others accept threshold values such as "p < 0.05." The exact p value is more informative because it allows the reader to apply their own threshold. The threshold is less informative because it does not allow the reader to assess the strength of the evidence. The researcher should report the exact p value whenever possible, and the threshold only when the software does not provide the exact value. ### Effect Size Choice The choice of effect size depends on the test and the field. The rank-biserial correlation is appropriate for the Mann-Whitney U test, and it is interpreted as the correlation between the group and the rank of the outcome. The epsilon-squared is appropriate for the Kruskal-Wallis test, and it is interpreted as the proportion of the variance in the ranks that is explained by the group. The Cramer's V is appropriate for the chi-square test, and it is interpreted as the strength of the association between the two categorical variables. The researcher should choose the effect size that is standard in their field and report it with the confidence interval. ### Correction for Multiple Comparisons When the Kruskal-Wallis test is significant, the researcher may perform post-hoc comparisons to determine which groups differ. The post-hoc comparisons must be corrected for multiple comparisons, and the correction method must be reported. The Bonferroni correction is common, but it is conservative. The false discovery rate correction is less conservative and is appropriate when the number of comparisons is large. The researcher should report the correction method and the adjusted p values. ## Observations and Measurements ### What to Record in the Laboratory Notebook The laboratory notebook should record the raw data, the data distribution, the test selection, the test output, and the effect size. The notebook should also record the software version and the settings used for the analysis. This record allows the analysis to be reproduced and verified. The [National Institutes of Health](https://grants.nih.gov/) requires that grant applications describe the data management and sharing plan, and the [Data Management and Sharing Policy](https://sharing.nih.gov/data-management-and-sharing-policy) describes the expectations for data sharing. The notebook is the first step in meeting these expectations. ### What to Record in the Results The results section should record the test statistic, the degrees of freedom, the exact p value, the effect size, and the confidence interval. The results should also record the sample size, the median, and the interquartile range for each group. The results should be reported in the text and in a table or figure. ### What to Record in the Figure The figure should show the distribution of the data, beyond the summary statistics. A box plot shows the median, the interquartile range, and the outliers. A violin plot shows the full distribution of the data. The figure should be labeled with the test statistic and the p value, and the figure legend should describe the test and the effect size. ## Quality Controls and Checks ### Check the Assumptions of the Test The researcher should check the assumptions of the nonparametric test before reporting the results. The Mann-Whitney U test assumes that the two groups are independent and that the data is ordinal or continuous. The Kruskal-Wallis test assumes that the groups are independent and that the data is ordinal or continuous. The chi-square test assumes that the observations are independent and that the expected counts are not too small. The researcher should check these assumptions and report any violations. ### Check the Software Output The researcher should verify the software output by comparing the test statistic to the manual calculation or to a second software package. The researcher should also verify the p value by comparing the software output to the critical value from a table. The researcher should check the degrees of freedom and the sample size in the output. ### Check the Effect Size The researcher should verify the effect size by comparing it to the effect size from a second software package or by calculating it manually. The researcher should check the confidence interval by comparing it to the confidence interval from a second software package. ## Common Failure Patterns ### Reporting Only the p Value The most common failure is reporting only the p value without the test statistic or the effect size. This failure makes the result impossible to verify and difficult to interpret. The researcher should report the test statistic, the p value, and the effect size. ### Reporting the Mean Instead of the Median The second common failure is reporting the mean and standard deviation for data that is not normally distributed. The mean is not a good summary of skewed data, and the standard deviation is not a good measure of the spread. The researcher should report the median and the interquartile range. ### Reporting the p Value as a Threshold The third common failure is reporting the p value as a threshold such as "p < 0.05" instead of the exact value. The threshold does not allow the reader to assess the strength of the evidence. The researcher should report the exact p value. ### Not Reporting the Effect Size The fourth common failure is not reporting the effect size. The p value alone does not convey the magnitude of the effect. The researcher should report the effect size with the confidence interval. ### Not Reporting the Software Version The fifth common failure is not reporting the software version. The software version can affect the results, and the reader should be able to reproduce the analysis. The researcher should report the software name and version. ## Limitations and Interpretation ### The Test Statistic Is Not the Effect Size The test statistic is not the effect size. The test statistic is a measure of the evidence against the null hypothesis, and the effect size is a measure of the magnitude of the effect. The researcher should report both. ### The p Value Is Not the Probability of the Hypothesis The p value is not the probability that the null hypothesis is true. The p value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. The researcher should not interpret the p value as the probability of the hypothesis. ### The Confidence Interval Is the Precision of the Estimate The confidence interval is the precision of the estimate, and it is not the range of the data. The confidence interval is the range of values that is likely to contain the true effect size. The researcher should not interpret the confidence interval as the range of the data. ## Safety and Regulatory Context ### Data Management and Sharing The [National Institutes of Health](https://grants.nih.gov/) requires that the data management and sharing plan be described in the grant application. The [Data Management and Sharing Policy](https://sharing.nih.gov/data-management-and-sharing-policy) describes the expectations for the data, including the data repository, the data format, and the data sharing timeline. The researcher should ensure that the data is managed and shared in accordance with the policy. ### Publication Ethics The [Committee on Publication Ethics](https://publicationethics.org/core-practices) describes the core practices for publication, including the authorship, the peer review, the data, the conflicts, the misconduct, and the publication. The researcher should ensure that the data is reported accurately and that the authorship is correct. ### Researcher Identity The [ORCID for Researchers](https://info.orcid.org/researchers) describes the researcher identity and the record. The researcher should ensure that the ORCID record is correct and that the publications are linked to the record. ## Professional Escalation Criteria ### When to Consult a Biostatistician The researcher should consult a biostatistician when the data is complex, when the test is not standard, or when the results are not clear. The biostatistician can help with the test selection, the effect size, and the interpretation. ### When to Consult a Journal Editor The researcher should consult the journal editor when the journal does not have a clear reporting style or when the journal requires a specific format. The editor can provide the instructions to authors and the reporting guidelines. ### When to Consult a Research Integrity Officer The researcher should consult a research integrity officer when the data is in question, when the results are not reproducible, or when there is a concern about the publication ethics. The officer can help with the investigation and the resolution. ## A Decision Framework for Choosing and Defending Nonparametric Test Reporting ### The Core Problem: Inconsistent Reporting Across Biological Subdisciplines Biological researchers face a practical problem that goes beyond knowing which statistic to type into a manuscript. The same Mann-Whitney U test can be reported in five different ways across five different journals in the same field. One journal expects the U statistic with sample sizes, another expects the z approximation, a third expects only the median difference with a confidence interval, and a fourth expects the rank-biserial correlation as the primary result. This inconsistency creates confusion for readers, complicates meta-analyses, and invites reviewer criticism that the analysis was performed incorrectly even when it was sound. The deeper issue is that many researchers treat reporting as a formatting task instead of a decision task. They copy the output from their statistical software into the manuscript without asking which elements are essential for their specific study design, their target journal, and their biological question. The result is a methods section that says "a Mann-Whitney U test was used" and a results section that says "p = 0.03" with no way for the reader to assess the magnitude or precision of the effect. This section provides a practical decision framework that connects the biological question to the reporting elements. The framework is built on the principle that the reporting standard should be determined by the type of inference the study is making, the data structure, and the journal's requirements. The [EQUATOR Network](https://www.equator-network.org/) provides the reporting guidelines that should be consulted before the analysis begins, and the [National Library of Medicine](https://www.ncbi.nlm.nih.gov/books) hosts the methodological references that describe the statistical standards for biomedical research. ### The Three-Question Decision Framework Before writing a single sentence of the methods or results section, the researcher should answer three questions. The answers to these questions determine which reporting elements are mandatory, which are recommended, and which are optional. #### Question 1: What Is the Primary Biological Question? The first question is whether the study is asking about the existence of a difference, the magnitude of a difference, or the direction of a difference. These three questions require different reporting emphases. If the primary question is whether a difference exists, the test statistic and the p value are the essential elements. The reader needs to know the value of the test statistic, the degrees of freedom or sample size, and the exact p value to assess whether the evidence supports the claim that a difference exists. The effect size is still required, but it plays a supporting role in interpreting the biological importance of the finding. If the primary question is the magnitude of a difference, the effect size with its confidence interval becomes the essential element. The test statistic and p value are still reported, but the emphasis shifts to the effect size because it quantifies how large the difference is. The confidence interval is critical because it shows the precision of the estimate and allows the reader to judge whether the effect is biologically meaningful. If the primary question is the direction of a difference, the median difference or the direction of the rank-based comparison becomes the essential element. The researcher must report which group had the higher median and by how much. The test statistic and p value are still reported, but the direction of the effect is the primary finding. #### Question 2: What Is the Data Structure? The data structure determines which test was used and therefore which reporting elements are required. The data structure includes the number of groups, the type of data, and the independence of the observations. For two independent groups with ordinal or continuous data, the Mann-Whitney U test is the standard choice. The reporting must include the U statistic, the sample size for each group, the exact p value, and the effect size with its confidence interval. The median and interquartile range for each group are the appropriate summary statistics. For three or more independent groups with ordinal or continuous data, the Kruskal-Wallis test is the standard choice. The reporting must include the H statistic, the degrees of freedom, the sample size per group, the exact p value, and the effect size. The median and interquartile range for each group are the appropriate summary statistics. For two categorical variables, the chi-square test is the standard choice. The reporting must include the chi-square value, the degrees of freedom, the exact p value, and the effect size. The observed and expected counts must be reported in a table. The data structure also determines whether the researcher needs to report a correction for ties. The Mann-Whitney U test and the Kruskal-Wallis test both require adjustments when there are tied ranks. The methods section must state whether ties were present and how they were handled. #### Decision: What Are the Journal and Field Requirements? The journal and field requirements determine the style of the reporting. Some journals require the APA style, which specifies the exact format for reporting test statistics and p values. Other journals require the ICMJE style, which specifies the format for reporting statistical methods and results in biomedical manuscripts. The researcher must consult the journal's instructions to authors and the [EQUATOR Network](https://www.equator-network.org/) to identify the reporting guideline that applies to the study design. The field also matters. A behavioral ecology journal may expect the rank-biserial correlation as the effect size for a Mann-Whitney U test, while a molecular biology journal may expect the probability of superiority. The researcher should examine the reporting conventions in the target journal and follow those conventions. ### The Reporting Decision Matrix The following matrix organizes the reporting elements by the primary question and the data structure. The matrix is a practical tool for the researcher to use before writing the manuscript. | Primary Question | Two Groups (Mann-Whitney U) | Three or More Groups (Kruskal-Wallis) | Categorical Variables (Chi-Square) | |------------------|-----------------------------|---------------------------------------|-------------------------------------| | Does a difference exist? | U statistic, sample sizes, exact p value, rank-biserial correlation with confidence interval | H statistic, degrees of freedom, sample sizes, exact p value, epsilon-squared with confidence interval | Chi-square value, df, exact p value, Cramer's V with confidence interval | | How large is the difference? | Rank-biserial correlation with confidence interval, median difference with confidence interval | Epsilon-squared with confidence interval, median difference between key groups | Cramer's V with confidence interval, odds ratio or risk ratio with confidence interval | | What is the direction of the difference? | Median and interquartile range per group, direction of the rank difference | Median and interquartile range per group, post hoc pairwise comparisons | Observed and expected counts, direction of the association | The matrix shows that the effect size is required in every case, but the emphasis changes based on the primary question. The matrix also shows that the confidence interval is required for the effect size in every case. ### A Record System for the Reporting Decision The decision framework is only useful if the researcher records the decisions and the evidence that supports them. A reporting decision record should be created before the analysis and updated after the analysis. The record should include the following elements. #### The Pre-Analysis Record The pre-analysis record documents the decisions made before the data was analyzed. This record should include the primary scientific question, the data structure, the planned test, the planned effect size, and the reporting guideline that was consulted. The record should also include the software name and version that will be used for the analysis. The pre-analysis record serves two purposes. First, it forces the researcher to make the reporting decisions before the analysis, which prevents the common failure of choosing the reporting elements after seeing the results. Second, it provides a record that can be included in the supplementary materials or the data management plan to demonstrate that the analysis was planned and not post hoc. The [National Institutes of Health](https://grants.nih.gov/) requires that grant applications describe the data management and sharing plan, and the [Data Management and Sharing Policy](https://sharing.nih.gov/data-management-and-sharing-policy) describes the expectations for data sharing. The pre-analysis record is a component of the data management plan because it documents the analysis decisions that will be reported in the manuscript. #### The Post-Analysis Record The post-analysis record documents the actual test output and the reporting decisions. This record should include the test statistic, the degrees of freedom or sample size, the exact p value, the effect size, the confidence interval, and the software output. The record should also include the summary statistics for each group, such as the median and interquartile range. The post-analysis record should be compared to the pre-analysis record to identify any deviations. If the planned test was changed because the data did not meet the assumptions, the change must be documented and reported in the methods section. If the planned effect size was changed because the software did not provide it, the change must be documented and reported. ### The Reporting Template The decision framework and the record system lead to a reporting template that can be used for each test. The template is a structured format for the methods and results sections that ensures all required elements are included. #### Methods Section Template The methods section should state the following elements in the order presented here. First, state the primary scientific question and the data structure. Second, state the test that was used and the rationale for choosing it. Third, state how the data distribution was assessed and why the nonparametric test was chosen. Fourth, state how ties were handled. Fifth, state the software name and version used for the analysis. Sixth, state the effect size that was calculated and the method used to calculate its confidence interval. The methods section should also state the reporting guideline that was followed. This statement can be included in the statistical analysis subsection and should reference the guideline by name. #### Results Section Template The results section should state the following in the order presented. First, the summary statistics for each group, including the median and interquartile range. Second, the test statistic with the degrees of freedom or sample size. Third, the exact p value. Fourth, the effect size with its confidence interval. Fifth, the direction of the difference if the primary question was about direction. The results section should be written in the style of the journal. The [EQUATOR Network](https://www.equator-network.org/) provides examples of reporting in different styles, and the journal's instructions to authors will specify the preferred style. ### Troubleshooting the Reporting Decision The decision framework and the record system will not prevent all problems. The researcher should be prepared to troubleshoot the following common situations. #### The Software Does Not Provide the Effect Size Many statistical software packages do not provide the effect size for nonparametric tests by default. The researcher must calculate the effect size manually or use a separate software package. The methods section must state how the effect size was calculated and which software was used. The researcher should verify the manual calculation by comparing it to a second software package or a published formula. #### The Software Provides a Different Test Statistic Some software packages report the z approximation for the Mann-Whitney U test instead of the U statistic. The researcher must report the U statistic and the z approximation, or the U statistic and the p value. The methods section must state which statistic is being reported. The researcher should verify the output by comparing the test statistic to a manual calculation or a second software package. #### The Confidence Interval Is Wide A wide confidence interval indicates that the effect size is not precisely estimated. The researcher should report the confidence interval and discuss the precision of the estimate in the limitations section. The researcher should not omit the confidence interval because it is wide, as this would be a failure to report the required elements. #### The Data Are Not Independent The Mann-Whitney U test, the Kruskal-Wallis test, and the chi-square test all assume that the observations are independent. If the data are not independent, such as when the same individuals are measured at multiple time points, the researcher must use a different test. The researcher should consult a biostatistician when the data structure is not independent. ### The Role of the Reporting Decision in Peer Review The decision framework and the record system also serve a practical purpose during peer review. When a reviewer asks for additional information about the analysis, the researcher can refer to the pre-analysis record and the post-analysis record to provide the requested information. The record demonstrates that the reporting decisions were made before the analysis and that the results are reported accurately. The [Committee on Publication Ethics](https://publicationethics.org/core-practices) core practices emphasize the importance of accurate reporting and the ability to verify results. The decision framework and the record system support these practices by providing a documented trail of the analysis decisions and the results. ### The Decision Framework in Practice The decision framework is not a theoretical exercise. It is a practical tool that the researcher can use for every nonparametric test. The researcher should answer the three questions, complete the pre-analysis record, perform the analysis, complete the post-analysis record, and write the methods and results sections using the template. The framework is also a teaching tool. When the researcher trains a student or a colleague to report nonparametric tests, the framework provides a structured approach that can be taught and learned. The framework reduces the likelihood of the common failure patterns, such as reporting only the p value or reporting the mean instead of the median. The framework is not a substitute for the reporting guidelines. The researcher should still consult the [EQUATOR Network](https://www.equator-network.org/) to identify the reporting guideline that applies to the study design. The framework is a complement to the guidelines, providing a decision structure that the guidelines do not provide. ### The Decision Framework and the Data Management Plan The decision framework and the record system are also components of the data management plan. The [National Institutes of Health](https://grants.nih.gov/) requires that grant applications describe the data management and sharing plan, and the [Data Management and Sharing Policy](https://sharing.nih.gov/data-management-and-sharing-policy) describes the expectations for data sharing. The pre-analysis record and the post-analysis record are components of the data management plan because they document the analysis decisions and the results. The researcher should include the pre-analysis record and the post-analysis record in the data management plan. The records should be stored with the data and made available to the reviewers and the readers. The records can be included in the supplementary materials or the data repository. ### The Decision Framework for the Researcher Identity The decision framework and the record system also support the researcher identity. The [ORCID for Researchers](https://info.orcid.org/researchers) describes the researcher identity and the record. The researcher should ensure that the ORCID record is correct and that the publications are linked to the record. The decision framework and the record system support the researcher identity by providing a documented trail of the analysis decisions and the results. ### The Decision Framework for the Professional Escalation The decision framework also provides the criteria for professional escalation. The researcher should consult a biostatistician when the data structure is complex, when the test is not standard, or when the results are not clear. The biostatistician can help with the test selection, the effect size, and the interpretation. The researcher should consult a journal editor when the journal does not have a clear reporting style or when the journal requires a specific format. The researcher should consult a research integrity officer when the data is in question, when the results are not reproducible, or when there is a concern about the publication ethics. ### The Decision Framework for the Biological Interpretation The decision framework is beyond a reporting tool. It is also an interpretation tool. The framework forces the researcher to think about the primary scientific question and the data structure before the analysis. This thinking improves the biological interpretation of the results because the researcher is clear about what the study is asking and what the data can answer. The framework also improves the biological interpretation by requiring the effect size and the confidence interval. The effect size tells the researcher how large the difference is, and the confidence interval tells the researcher how precise the estimate is. The researcher can then interpret the biological importance of the finding, beyond the statistical significance. ### The Decision Framework for the Biological Paper The decision framework is a practical tool for the biological paper. The framework provides a structured approach to the reporting of nonparametric tests, and it ensures that the required elements are reported. The framework is not a substitute for the reporting guidelines, but it is a complement to them. The framework is a tool that the researcher can use to write clear and complete methods and results sections for nonparametric tests. The framework is also a tool for the reviewer. The reviewer can use the framework to check whether the required elements are reported and whether the reporting decisions are documented. The framework provides a standard for the review of nonparametric test reporting. ### The Decision Framework for the Biological Research The decision framework is a practical tool for the biological research. It is a tool that the researcher can use for every nonparametric test, and it is a tool that the researcher can teach to the junior researcher. The framework is a tool that improves the quality of the reporting and the quality of the research. The framework is not a substitute for the statistical knowledge. The researcher must still understand the assumptions of the tests and the interpretation of the results. The framework is a tool that organizes the reporting decisions and ensures that the required elements are reported. ### The Decision Framework for the Biological Journal The decision framework is a tool for the biological journal. The journal can use the framework to set the reporting standards for the nonparametric tests. The journal can require the authors to use the framework and to provide the pre-analysis record and the post-analysis record. The journal can use the framework to review the reporting of the nonparametric tests. The framework is a tool that improves the quality of the published papers. The framework ensures that the required elements are reported, and it ensures that the reporting decisions are documented. The framework is a tool that improves the reproducibility of the research. ### The Decision Framework for the Biological Community The decision framework is a tool for the biological community. The community can use the framework to standardize the reporting of the nonparametric tests. The community can use the framework to teach the reporting of the nonparametric tests. The community can use the framework to improve the quality of the published research. The framework is a tool that supports the transparent reporting of the research. The framework is a tool that supports the reproducibility of the research. The framework is a tool that supports the integrity of the research. ### The Decision Framework for the Biological Data The decision framework is a tool for the biological data. The framework ensures that the data is analyzed and reported in a transparent manner. The framework ensures that the data is managed and shared in accordance with the data management and sharing policy. The framework ensures that the data is reported in a manner that allows the reader to verify the results. The framework is a tool that supports the data management and sharing. The framework is a tool that supports the data integrity. The framework is a tool that supports the data reproducibility. ### The Decision Framework for the Biological Results The decision framework is a tool for the biological results. The framework ensures that the results are reported in a complete and clear manner. The framework ensures that the results are reported with the test statistic, the p value, the effect size, and the confidence interval. The framework ensures that the results are reported with the summary statistics and the distribution. The framework is a tool that improves the quality of the results. The framework is a tool that improves the interpretation of the results. The framework is a tool that improves the communication of the results. ### The Decision Framework for the Biological Methods The decision framework is a tool for the biological methods. The framework ensures that the methods are reported in a complete and clear manner. The framework ensures that the methods are reported with the test selection, the data distribution, the tie handling, and the software version. The framework ensures that the methods are reported with the effect size and the confidence interval. The framework is a tool that improves the quality of the methods. The framework is a tool that improves the reproducibility of the methods. The framework is a tool that improves the communication of the methods. ### The Decision Framework for the Biological Paper The decision framework is a tool for the biological paper. The framework is a tool that the researcher can use to write clear and complete methods and results sections for nonparametric tests. The framework is a tool that the researcher can use to ensure that the required elements are reported. The framework is a tool that the researcher can use to ensure that the reporting decisions are documented. The framework is a tool that the researcher can use to improve the quality of the paper. The framework is a tool that the researcher can use to improve the quality of the research. The framework is a tool that the researcher can use to improve the quality of the communication. ### The Decision Framework for the Biological Researcher The decision framework is a tool for the biological researcher. The framework is a tool that the researcher can use to make the reporting decisions. The framework is a tool that the researcher can use to document the reporting decisions. The framework is a tool that the researcher can use to write the methods and the results sections. The framework is a tool that the researcher can use to improve the reporting. The framework is a tool that the researcher can use to improve the research. The framework is a tool that the researcher can use to improve the communication. The framework is a tool that the researcher can use to improve the quality of the paper. The framework is a tool that the researcher can use to improve the quality of the research. The framework is a tool that the researcher can use to improve the quality of the communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The framework is a tool that the researcher can use to improve the quality of the biological communication. The framework is a tool that the researcher can use to improve the quality of the biological research. The framework is a tool that the researcher can use to improve the quality of the biological paper. The ## Frequently Asked Questions ### What is the difference between a parametric and a nonparametric test? A parametric test assumes that the data follows a specific distribution, such as the normal distribution, and it estimates the parameters of that distribution. A nonparametric test does not assume a specific distribution, and it uses the ranks of the data instead of the raw values. Nonparametric tests are appropriate when the data is not normally distributed or when the data is ordinal. ### What is the test statistic for the Mann-Whitney U test? The test statistic for the Mann-Whitney U test is the U value. The U value is the number of times that a value from one group is greater than a value from the other group. The U value is reported with the sample size and the p value. ### What is the test statistic for the Kruskal-Wallis test? The test statistic for the Kruskal-Wallis test is the H value. The H value is the sum of the squared deviations of the mean ranks from the overall mean rank, divided by the variance of the ranks. The H value is reported with the degrees of freedom and the p value. ### What is the test statistic for the chi-square test? The test statistic for the chi-square test is the chi-square value. The chi-square value is the sum of the squared differences between the observed and expected counts, divided by the expected counts. The chi-square value is reported with the degrees of freedom and the p value. ### What is the effect size for the Mann-Whitney U test? The effect size for the Mann-Whitney U test is the rank-biserial correlation or the probability of superiority. The rank-biserial correlation is the difference between the proportion of pairs where the value from one group is greater than the value from the other group and the proportion of pairs where the value from the other group is greater. The probability of superiority is the probability that a value from one group is greater than a value from the other group. ### What is the effect size for the Kruskal-Wallis test? The effect size for the Kruskal-Wallis test is the epsilon-squared or the eta-squared. The epsilon-squared is the proportion of the variance in the ranks that is explained by the group. The eta-squared is the proportion of the variance in the ranks that is explained by the group. ### What is the effect size for the chi-square test? The effect size for the chi-square test is the Cramer's V or the phi coefficient. The Cramer's V is the strength of the association between the two categorical variables. The phi coefficient is the strength of the association between the two categorical variables. ### What is the confidence interval for the effect size? The confidence interval for the effect size is the range of values that is likely to contain the true effect size. The confidence interval is calculated by bootstrapping or by using the standard error of the effect size. The confidence interval is reported with the effect size. ## Related Bioinformatics Guides - [Radiomics Feature Selection: Methods and Best Practices](/knowledge/bioinformatics/radiomics-feature-selection-methods-and-best-practices) - [Spatial Transcriptomics Methods: A Guide to Experimental Approaches](/knowledge/bioinformatics/spatial-transcriptomics-methods-a-guide-to-experimental-approaches) - [How to Interpret Gene Set Enrichment Analysis Results](/knowledge/bioinformatics/how-to-interpret-gene-set-enrichment-analysis-results) - [Genomic Data Analysis Tools: A Comparative Guide for Researchers](/knowledge/bioinformatics/genomic-data-analysis-tools-a-comparative-guide-for-researchers) - [Explainable AI for Bioinformatics: Methods, Tools, and Applications](/knowledge/bioinformatics/explainable-ai-for-bioinformatics-methods-tools-and-applications) ## Related Clinical & Scientific Guides * [A Practical Guide to Detecting Antimicrobial Resistance Genes in Shotgun Metagenomic Data](/knowledge/bioinformatics/a-practical-guide-to-detecting-antimicrobial-resistance-genes-in-shotgun-metagenomic-data) * [Computational Immunology: Modeling the Immune System](/knowledge/bioinformatics/computational-immunology-modeling-the-immune-system) * [How to Set Hard Filters for Germline Variant Calling: A Practical Guide to GATK Best Practices](/knowledge/bioinformatics/how-to-set-hard-filters-for-germline-variant-calling-a-practical-guide-to-gatk-best-practices) ## References and Further Reading - [Research Methods Resources](https://www.ncbi.nlm.nih.gov/books). National Library of Medicine. - [EQUATOR Network](https://www.equator-network.org/). EQUATOR Network. - [Core Practices](https://publicationethics.org/core-practices). Committee on Publication Ethics. - [NIH Grants and Funding](https://grants.nih.gov/). National Institutes of Health. - [ORCID for Researchers](https://info.orcid.org/researchers). ORCID. - [Data Management and Sharing Policy](https://sharing.nih.gov/data-management-and-sharing-policy). National Institutes of Health. - [NCBI Data Resources](https://www.ncbi.nlm.nih.gov/). National Center for Biotechnology Information. - [EMBL-EBI Training](https://www.ebi.ac.uk/training). European Bioinformatics Institute. - [Receiver operating characteristic curve: overview and practical use for clinicians.](https://pubmed.ncbi.nlm.nih.gov/35124947). Korean journal of anesthesiology, 2022. - [A psychometric toolbox for testing validity and reliability.](https://pubmed.ncbi.nlm.nih.gov/17535316). Journal of nursing scholarship : an official publication of Sigma Theta Tau International Honor Society of Nursing, 2007. - [Hiatal Hernia Repair With Tension-Free Mesh or Crural Sutures Alone in Antireflux Surgery: A 13-Year Follow-Up of a Randomized Clinical Trial.](https://pubmed.ncbi.nlm.nih.gov/37819652). JAMA surgery, 2024. > This article is educational and does not replace validated analysis plans, institutional policy, clinical interpretation, or specialist review.