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statistical-conventions

Chooses and reports statistical tests the way a careful referee expects, deciding paired versus unpaired and parametric versus rank-based from the design, using ordered-trend tests such as Jonckheere-Terpstra and Cochran-Armitage for dose or grade levels, correcting for multiple comparisons with Bonferroni, Holm or Benjamini-Hochberg and showing raw and adjusted p-values side by side, giving effect sizes such as Cohen's d, Cliff's delta and odds ratios with confidence intervals, bootstrapping intervals when no formula applies, and stating checked assumptions, exact p-values and degrees of freedom. Use whenever an analysis will report a p-value, a group difference, a trend across ordered categories or a correlation; use statistical-power for sample-size planning and experimental-design for laying out the study.

backend/cli/skills/core/statistical-conventions/SKILL.md

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# Statistical conventions

The design and the measurement scale choose the test, not the size of the p-value it
yields. Every reported number travels with the quantity it estimates, its uncertainty, the
assumption it rests on, and the software that computed it.

## Choosing the test

1. **Design first.** The same units measured twice (before and after, matched pairs, two
   methods on the same samples) are paired: `scipy.stats.ttest_rel`, `wilcoxon`.
   Independent groups: `ttest_ind(a, b, equal_var=False)` (Welch; use Student's only when
   equal variances are a design fact, and say so), `mannwhitneyu`. Three or more groups:
   `f_oneway` or `kruskal`; repeated measures across blocks: `friedmanchisquare`. Name
   the unit of analysis before choosing: observations nested in a unit (cells within a