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

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.

For model-specific APIs (OLS, GLM, ARIMA), see the statsmodels skill. For PyMC workflows, see the pymc skill.

Analysis Workflow

Use the following workflow, documenting prespecified decisions and exploratory departures.

1. Frame the question before touching the data. State the hypothesis, the outcome and predictor variables, and the design (independent vs. paired, number of groups). Specify the target effect, sampling unit, dependence, contrasts and multiplicity family before outcome-driven selection. Label adaptive exploration explicitly.
2. Inspect the data. Per group: n, mean, SD, median, missing values. Plot the raw data (histograms or box plots) before any test. Unequal group sizes, missingness, floor/ceiling effects, and outliers all change what test is appropriate — surface them to the user rather than silently working around them.
3. Select the test using the quick reference below, or references/test_selection_guide.md for designs beyond the basics (counts, time-to-event, reliability, factorial).
4. Check assumptions with scripts/assumption_checks.py. Interpret plots and screens alongside the design and estimand; do not switch tests automatically at a diagnostic p-value threshold. Report justified sensitivity analyses and any departures from the plan.
5. Run the test and always compute the effect size alongside it — a p-value assesses incompatibility with the null model; the effect estimate and its uncertainty support judgments about practical importance.
6. Report using the APA templates below, including descriptives, exact statistics, effect sizes with CIs, and the assumption checks performed.

If the user only needs one step (e.g., "how many participants do I need?"), jump straight to that section — but still confirm the design assumptions the calculation rests on.

Test Selection Guide

Quick Reference: Choosing the Right Test

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