statistical-analysis

Statistical Analysis

Overview

Conduct hypothesis tests (t-tests, ANOVA, chi-square), regression, correlation, and Bayesian analyses with systematic assumption checking, effect sizes, and APA-style reporting. The goal is an analysis a reviewer could not tear apart: the right test, verified assumptions, honest effect sizes, and a complete write-up.

When to Use This Skill

Use this skill when:

• Conducting statistical hypothesis tests (t-tests, ANOVA, chi-square, non-parametric)
• Performing regression or correlation analyses
• Running Bayesian statistical analyses
• Checking statistical assumptions and diagnostics
• Calculating effect sizes and conducting power analyses
• Reporting statistical results in APA format
• Analyzing experimental or observational data for research

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Installation

Use uv to install the libraries used in this skill. Pin versions in production; unpinned installs are fine for exploration.

# Core frequentist stack (Python 3.10+; 3.12+ recommended for latest SciPy/ArviZ)
uv pip install "pingouin>=0.6" "scipy>=1.11" "statsmodels>=0.14.6" pandas matplotlib seaborn

# Bayesian modeling (PyMC 5 + ArviZ)
uv pip install "pymc>=5.0" "arviz>=1.0"

Compatibility notes (verified against pingouin 0.6.1, statsmodels 0.14.6, arviz 1.2, 2026):

• Pingouin 0.6.0 renamed output columns to remove special characters: p_val, cohen_d, CI95, p_unc (previously p-val, cohen-d, CI95%, p-unc in 0.5.x). Examples below use the current names; if stuck on 0.5.x, use the hyphenated forms.
• statsmodels + SciPy: use statsmodels>=0.14.6 with scipy>=1.11 to avoid _lazywhere import errors on SciPy 1.16+.
• ArviZ 1.x: az.summary() now defaults to 89% intervals (eti89 columns) and the width parameter is ci_prob (not hdi_prob). To report a conventional 95% credible interval, pass az.summary(trace, ci_prob=0.95).
• One-sided Bayes Factors are gone from Pingouin: pg.ttest(..., alternative='greater') silently drops the BF10 column, and pg.bayesfactor_ttest raises on one-sided alternatives. For one-sided Bayesian tests, use PyMC directly (compute the posterior probability of the directional hypothesis) or JASP/R's BayesFactor.