reporting-effect-sizes

Reporting hypothesis-test results with effect sizes requires selecting the correct metric by test family, computing a 95% confidence interval using closed-form or bootstrap methods, and producing a direction sentence naming the test, sample size, statistic, p-value, and effect size. This prevents misleading statistical reporting by refusing significance claims from p-values alone.

For paired t-tests and Wilcoxon tests, you must use matched-pair effect size metrics rather than unpaired versions to avoid mismatched data reporting. The correct approach computes the appropriate effect size for paired comparisons and pairs it with a 95% confidence interval, ensuring your statistical report accurately reflects the paired nature of your hypothesis test.

Writing a publication-ready statistical results sentence involves combining the test name, sample size, test statistic, exact p-value, correct effect size, and a clear direction statement indicating which group was higher or lower. This comprehensive reporting format produces defensible results sentences suitable for papers, homework submissions, dashboards, and presentations.

You cannot claim statistical significance from a p-value alone in rigorous data reporting because this approach lacks supporting effect-size evidence. Proper statistical reporting requires guardrails against misuse by demanding an accompanying effect size, a 95% confidence interval, and a clear direction statement before labeling any hypothesis test result as significant.

This statistical reporting approach works for ANOVA, regression, and categorical tests including chi-squared and McNemar tests by applying test-aware logic. It automatically selects the appropriate effect size metric for each test family, computes the relevant 95% confidence interval, and formats the output into a defensible publication-ready statement across diverse hypothesis testing scenarios.