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. Define the estimand and sampling units, diagnose model limitations, and report effect estimates with uncertainty. Numerical screens cannot certify assumptions or scientific validity.

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

Targets Pingouin 0.7.0, SciPy 1.18.1, statsmodels 0.15.0, PyMC 6.3.2 and ArviZ 1.3.0 (reviewed 2026-10-01). Create a separate environment; do not add mutually incompatible scientific stacks to a shared project environment.

uv venv --python 3.12 .venv-statistics
uv pip install --python .venv-statistics/bin/python "pingouin==0.7.0" "scipy==1.18.1" "statsmodels==0.15.0" pandas matplotlib seaborn
# Optional Bayesian examples:
uv pip install --python .venv-statistics/bin/python "pymc==6.3.2" "arviz==1.3.0"

On Windows use .venv-statistics/Scripts/python.exe. Lock the resolved environment for reproduction.

• Pingouin 0.7 fixes erroneous mixed/repeated-measures corrections, categorical ANOVA, and other results; do not reproduce an old analysis by merely changing its reported version. See the official changelog.
• Pingouin 0.6+ names are p_val, cohen_d, CI95, p_unc. ttest reports absolute Cohen's d; calculate a signed estimate explicitly. Its power column is observed power and should not be used to interpret a null result.
• correction='auto' chooses Welch by unequal sample sizes, not by variance evidence. Set correction=True for prespecified Welch inference.
• PyMC 6 returns an xarray DataTree. ArviZ 1 uses ci_prob in summary/plot_dist and prob in hdi; specify 95% intervals explicitly. See Bayesian guidance.
• Pingouin omits BF10 for one-sided t-tests; posterior directional probabilities are not Bayes factors. A two-sided BF10 uses its own model/prior and is not the Bayesian counterpart of a Welch unequal-variance model.