statistical-analysis

Test selection depends on your research question, number of groups, and data distribution. The included test selection guide maps scenarios to tests: independent t-test or Mann-Whitney for two groups, ANOVA or Kruskal-Wallis for three or more, and Pearson or Spearman for correlations.

Use the provided assumption_checks.py module, which runs Shapiro-Wilk tests for normality and Levene's test for homogeneity of variance. It also generates Q-Q plots, box plots, and outlier detection with IQR and z-score methods, plus recommendations when assumptions fail.

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. Matplotlib and seaborn handle diagnostic visualizations.

For violated normality, use non-parametric alternatives like Mann-Whitney or Kruskal-Wallis, or transform the data. For unequal variances, use Welch's t-test or Welch's ANOVA. For regression non-linearity, add polynomial terms or use generalized additive models.

Bayesian methods are preferable when you have prior information, want direct probability statements about hypotheses, have small samples, or need to quantify evidence for the null hypothesis. They provide credible intervals and Bayes Factors rather than p-values.

Post-hoc power analysis is generally not recommended because observed power is a direct function of the p-value and adds no information. Instead, conduct a sensitivity analysis to determine the minimum detectable effect size given your sample, or report confidence intervals.