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

---

## Installation

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

```bash
# 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.

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

---

## Analysis Workflow

Every sound analysis follows the same arc. Skipping steps is how analyses end up retracted, so work through them in order and say what you did at each one.

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). Commit to a planned test now — choosing the test after peeking at results is p-hacking, even when done innocently.
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`. If an assumption fails, switch to the remedial test (table below) and report both the plan and the change.
5. **Run the test** and always compute the effect size alongside it — a p-value says an effect exists; the effect size says whether anyone should care.
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

Use `references/test_selection_guide.md` for comprehensive guidance (counts, survival, reliability, factorial designs). Quick reference:

**Comparing Two Groups:**
- Independent, continuous, normal → Independent t-test
- Independent, continuous, non-normal → Mann-Whitney U test
- Paired, continuous, normal → Paired t-test
- Paired, continuous, non-normal → Wilcoxon signed-rank test
- Binary outcome → Chi-square or Fisher's exact test

**Comparing 3+ Groups:**
- Independent, continuous, normal → One-way ANOVA
- Independent, continuous, non-normal → Kruskal-Wallis test
- Paired, continuous, normal → Repeated measures ANOVA
- Paired, continuous, non-normal → Friedman test

**Relationships:**
- Two continuous variables → Pearson (normal) or Spearman correlation (non-normal)
- Continuous outcome with predictor(s) → Linear regression
- Binary outcome with predictor(s) → Logistic regression

**Bayesian Alternatives:**
All tests have Bayesian versions providing direct probability statements about hypotheses, Bayes Factors quantifying evidence, and the ability to support the null. See `references/bayesian_statistics.md`.

---

## Assumption Checking

**Always check assumptions before interpreting test results**, and report the checks — reviewers look for them.

Use the bundled `scripts/assumption_checks.py` module. Run Python from the skill directory (`skills/statistical-analysis/`) or add `scripts/` to `sys.path`:

```python
from assumption_checks import comprehensive_assumption_check

# Outliers + normality (per group) + homogeneity of variance, with plots
results = comprehensive_assumption_check(
    data=df,
    value_col='score',
    group_col='group',  # Optional: for group comparisons
    alpha=0.05
)
```

For targeted checks, import individual functions:

```python
from assumption_checks import (
    check_normality,                # Shapiro-Wilk + Q-Q plot + histogram
    check_normality_per_group,
    check_homogeneity_of_variance