statistical-analysis

Test selection depends on the number of groups, whether data is paired or independent, and whether distributions are normal. The included test_selection_guide.md provides a decision tree covering t-tests, ANOVA, chi-square, correlations, and their non-parametric alternatives.

Use the assumption_checks.py script, which runs Shapiro-Wilk normality tests, Levene's homogeneity of variance test, and outlier detection with Q-Q plots and box plots. It returns interpretations and recommendations when assumptions are violated.

The workflow uses scipy.stats for core tests, statsmodels for regression and power analysis, pingouin for tests with built-in effect sizes, and pymc with arviz for Bayesian modeling and posterior diagnostics.

Bayesian methods are appropriate when you have prior information, want direct probability statements about hypotheses, need to quantify evidence for the null, or work with small samples and hierarchical models. The bayesian_statistics.md reference covers priors, Bayes Factors, and credible intervals.

For mild violations with n over 30 per group, parametric tests remain robust. For moderate violations, switch to non-parametric alternatives like Mann-Whitney U or Kruskal-Wallis. Severe violations call for data transformation or non-parametric methods.

Post-hoc power calculated from observed effects adds no information beyond the p-value and is often misleading. The skill recommends sensitivity analysis instead, which determines the minimum detectable effect size given your sample and alpha level.