Reporting Statistics in a Research Paper Correctly

A results section can be correct and still fail review because the numbers are reported badly. Reviewers want to see what was measured, which test was used, how large the effect was and how uncertain the estimate is, in a form they can check. This guide shows how to report descriptives, test statistics with degrees of freedom, exact p-values, confidence intervals and effect sizes, with APA-style examples, table advice and the wording habits that make editors suspicious.

What reviewers check in your statistics

Statistical reviewers rarely re-run your analysis. They check whether the numbers are complete, consistent and matched to the question: Is the sample size stated for every analysis? Does the test suit the data? Is there an estimate of the effect, not just a verdict of “significant”? How precise is it?

“The groups differed significantly (p < 0.05)” answers none of these. It hides the direction, size, test and number of participants. Compare:

The second version lets any reader judge the finding, and a careful reviewer can confirm that the t value follows from the means and SDs. Many of the problems behind common rejection reasons start with a results section that states conclusions instead of evidence.

Follow the analysis plan, not the software output

Report analyses in the order you planned them: primary outcome first, then secondary outcomes, then sensitivity and exploratory analyses labelled as such. If you registered a protocol or analysis plan, report every deviation and why.

State the analysis set for each result, such as intention-to-treat, per-protocol or complete cases. Readers need to know why one table has n = 412 and another n = 387.

Explain how the sample size was reached. A power calculation names the expected effect, alpha, power and resulting number: “To detect a standardised difference of 0.5 with 80% power at a two-sided alpha of .05, 64 participants per group were required.” If the sample was fixed by availability, say so and focus on precision rather than claiming adequate power.

Every test in Results should be named in the statistical analysis paragraph of Methods; see our guide to writing a reproducible methods section.

Reporting descriptive statistics

Descriptive statistics tell readers who or what was studied. Choose the summary that fits each variable:

• Roughly symmetric continuous data: mean and standard deviation, written as M = 24.6, SD = 3.1 in text or 24.6 (3.1) in a table.
• Skewed data and ordinal scales: median and interquartile range, e.g. median 7 days (IQR 4–12). Give the IQR as two limits, not a single width.
• Categorical data: count and percentage with the denominator, e.g. 58 of 140 (41.4%). A percentage without its n cannot be checked.

Use the standard deviation for spread. The standard error describes the precision of a mean, so “mean ± SE” in a descriptive table makes data look tidier than they are. Keep decimals sensible (usually one more than the raw data), give counts rather than percentages for very small groups, and report missing values per variable so totals reconcile.

Test statistics with degrees of freedom

Each inferential result should give the test statistic, its degrees of freedom where the test has them, the exact p-value and an effect size. In APA style, statistical symbols are italicised, degrees of freedom go in parentheses and there are spaces around the equals sign (see our APA 7th edition format guide).

APA style drops the leading zero for values that cannot exceed 1, such as p, r and η²; many medical styles keep it (P = 0.016). Follow the target journal’s author guidelines and stay consistent. With non-parametric tests, also report the group medians, because a U value alone describes nothing readers can picture.

Exact p-values and what they do not show

Report exact p-values to two or three decimals (p = .032, p = .27) rather than thresholds such as p < .05 or “NS”. The exception is very small values: write p < .001, never p = .000. Exact values show how close a borderline result was and let others include your study in a meta-analysis.

Be precise about meaning. A p-value is the probability of data at least as extreme as yours if the null hypothesis and every model assumption were true. It is not the probability that your hypothesis is true, not the chance that the result is a fluke, and not a measure of importance. The American Statistical Association’s 2016 statement on p-values makes these points and warns against drawing conclusions only from whether p crosses .05.

Two consequences follow. A non-significant result is not proof of no effect, so report the estimate, its interval and the effect size the study could not rule out. And when you run many tests, explain how you handled multiplicity: a Bonferroni or Holm correction, a false discovery rate procedure, or a plain statement that secondary analyses are exploratory.

Confidence intervals show precision

A confidence interval shows the range of effects compatible with your data under the model. A difference of 4.1 points with a 95% CI of 0.3 to 7.9 tells a different story from the same difference with a CI of 3.6 to 4.6, even though both are “significant”. The ICMJE recommendations ask authors to present findings with indicators of uncertainty such as confidence intervals rather than relying on p-values alone.

• State the level the first time: 95% CI [2.15, 6.04] in APA style, or (95% CI 2.15 to 6.04) in many medical styles; “to” avoids confusion with minus signs.
• Use the same units and decimals as the estimate.
• For odds, risk and hazard ratios the interval is asymmetric around the estimate; that is correct, not a typo.
• Give the interval for the difference between groups, not only for each group mean. Overlapping group intervals do not prove that the difference is non-significant.

When interpreting, discuss both ends: “the data are compatible with a negligible benefit of 0.3 points or a moderate benefit of 7.9 points”.

Effect sizes readers can interpret

An effect size answers the question reviewers care about most: how big is it? Report it in original units first where possible. “Students in the flipped classroom scored 6.2 marks higher out of 100” means more than d = 0.42 alone; giving both is best.

• Mean differences: the raw difference with its CI, plus Cohen’s d or Hedges’ g (g corrects small-sample bias).
• ANOVA: η², partial η² or the less biased ω². Say which one, because partial η² is usually larger.
• Associations: Pearson’s r or Spearman’s ρ, with a CI.
• Binary outcomes: risk difference, risk ratio or odds ratio, plus the absolute risk in each group so relative measures do not mislead.
• Regression: unstandardised coefficients (B) with CIs, and standardised β if predictors are compared.

Cohen’s labels of small (0.2), medium (0.5) and large (0.8) were meant as a fallback. Interpret effects against what matters in your field, such as a minimal clinically important difference or effects in earlier studies.

Reporting regression and multivariable models

Model-based results need more context than a single test. For each model, report:

1. the model type (linear, logistic, Poisson, Cox, mixed-effects) and why it suits the outcome;
2. the outcome, every predictor and covariate, and how covariates were chosen (theory or prior evidence, not unexplained stepwise selection);
3. the number of observations used and how missing data were handled (e.g. complete cases or multiple imputation);
4. coefficients with 95% CIs and p-values, set out in a table;
5. model fit, such as adjusted R² for linear models or the C statistic and calibration for prediction models;
6. assumption checks: residuals, multicollinearity (for example variance inflation factors), proportional hazards and influential points.

Show unadjusted and adjusted estimates side by side when confounding matters. For structural equation models, give fit indices and cut-offs (for example CFI, RMSEA with its CI and SRMR) instead of simply declaring a “good fit”.

Statistical tables and figures

Tables are the natural home for detailed statistics. The text should highlight key numbers and point to the table, not repeat every cell. A good statistical table:

• has a title naming the variables, sample and statistic, e.g. “Adjusted odds ratios for exam failure (N = 1,204)”;
• labels each column’s summary, such as mean (SD) or n (%);
• keeps decimal places consistent within a column;
• defines every abbreviation and symbol in a note;
• names the test behind each p-value when tests differ by row.

Do not add significance tests to the baseline table of a randomised trial: differences between randomised groups arise by chance, and CONSORT advises against testing them. In figures, show the data where you can, using individual points, box plots or violin plots instead of bar charts of means, and state whether error bars show SD, SE or 95% CI. Our guide to preparing figures and tables for journals covers layout and resolution.

Common errors and p-hacking language

Some phrases signal that an analysis was steered towards significance. Replace them with neutral, complete reporting:

Other frequent problems include reporting only the analyses that “worked”, switching the primary outcome and testing many subgroups without correction. If decisions were data-driven, say so and label those analyses exploratory.

Software, versions and reproducibility

Name the software and version for each analysis and cite key packages, for example “Analyses were run in R version 4.4.1 using lme4 version 1.1-35” or “IBM SPSS Statistics version 29”. Defaults change between versions and can alter mixed-model, imputation and bootstrap results. Give random seeds, the significance level, and whether tests were one- or two-sided.

Share analysis code and data where you can, or explain the restrictions. If you submit to JMVRA, a Data Availability Statement is expected before the reference list; our page on data availability statements has templates.

Before submission, recompute a few test statistics from the reported means and SDs, and confirm that degrees of freedom match sample sizes and percentages match counts. Tools such as statcheck flag APA-formatted results whose p-values do not match their test statistics, and the SAMPL guidelines listed by the EQUATOR Network give a fuller checklist.

Quick Checklist

1. Order by planPrimary outcome first, exploratory analyses last
2. n everywhereEvery analysis states its sample size
3. Full resultStatistic, df, exact p, effect size and 95% CI
4. Spread vs precisionSD for spread, CI for precision, never mean ± SE
5. Neutral wordingNo “trend towards significance” phrases
6. Tools and codeSoftware versions, seeds and shared scripts

Practical tips for a cleaner results section

These habits save a round of revisions and make your numbers easier to trust.

• Draft tables first. Build the main tables before the text. Writing then becomes a matter of pointing readers to the key cells.
• Export, do not retype. Move results from your software or script straight into tables to avoid transcription slips, then format them consistently.
• Ask someone to recompute. Give a colleague two or three results and ask them to check the df, p-value and effect size against your summary data.
• Match the house style. Check whether the journal follows APA, AMA or its own rules for leading zeros, italics and CI brackets before you format.
• Report the dull results too. Include every outcome your plan promised, including null ones. Missing outcomes look like selective reporting.

Report each key result as an estimate, an interval and an exact p-value from a named test, and readers can judge it for themselves.

Questions Researchers Often Ask

In Summary

Good statistical reporting is mostly about completeness and honesty. For every key result, describe the sample, name the test, give the statistic with its degrees of freedom and an exact p-value, and add an effect size with a confidence interval. Keep descriptive spread and estimate precision separate, label exploratory analyses, avoid wording that inflates borderline results, and cite your software versions and code. Check the numbers against your output once more before you submit, whether to JMVRA through its free online submission or elsewhere, and read the journal’s publication guidelines for its preferred style. A reviewer who can verify your numbers quickly is far more likely to trust your conclusions.

References and Sources

• American Statistical Association — Statement on statistical significance and p-values (2016)
• APA Style — official APA 7th edition guidance
• ICMJE — Recommendations for the conduct and reporting of scholarly work
• EQUATOR Network — reporting guidelines library (including SAMPL)