statistical-analysis

Match the test to your design and data type: independent t-test or Mann-Whitney U for two groups, ANOVA or Kruskal-Wallis for three or more groups, Pearson or Spearman for correlations, and regression for prediction. The included test selection guide walks through each decision based on normality and pairing.

Use the Shapiro-Wilk test from scipy for normality and Levene's test for homogeneity of variance, combined with Q-Q plots and box plots. The assumption_checks.py script automates both checks and recommends remedies such as Welch's correction or non-parametric alternatives.

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 diagnostics.

Use Bayesian methods when you have prior information to incorporate, want direct probability statements about hypotheses, have small samples, or need to quantify evidence for the null hypothesis. Frequentist tests remain sufficient for standard analyses with large samples.

For violated normality, use non-parametric alternatives or transformations; for unequal variances, use Welch's t-test or Welch's ANOVA; for regression non-linearity, add polynomial terms or transform variables. Mild violations are tolerable with more than 30 observations per group.

Post-hoc power is a direct function of the observed p-value and adds no information beyond it. Instead, conduct a sensitivity analysis to determine the minimum detectable effect size given your sample, or report confidence intervals for effect sizes.