statistical-analysis

Files (7)

• SKILL.md
• assumptions_and_diagnostics.md · references/
• bayesian_statistics.md · references/
• effect_sizes_and_power.md · references/
• reporting_standards.md · references/
• test_selection_guide.md · references/
• assumption_checks.py · scripts/

SKILL.md (first lines)

# 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.

```bash
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](https://pingouin-stats.org/changelog.html).
- 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](references/bayesian_statistics.md).
- 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

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

**Group comparisons:** Independent continuous means usually use prespecified Welch's t-test or Welch's ANOVA. Pooled Student/ANOVA inference needs justified equal variance. Paired means use a paired t-test on aligned within-person differences. Repeated or clustered observations require a model of that dependence.

**Rank questions:** Mann-Whitney or Kruskal-Wallis can address distribution/rank contrasts; they are not automatic tests of medians. Wilcoxon signed-rank requires meaningful, symmetrically distributed paired differences. Friedman addresses blocked/repeated rank contrasts. See the reference for ties, small samples, and exact/permutation choices.

**Relationships:** Pearson measures linear association; Spearman measures monotone rank association. Choose by the scientific question, not a normality pretest. Use a suitable regression likelihood for continuous, binary, count or time-to-event outcomes.

**Bayesian alternatives:** Specify the likelihood, prior and comparison explicitly. Posterior estimation does not automatically yield a Bayes factor for a point null.

---

## 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. Add the skill’s `scripts/` directory to `PYTHONPATH` (the skill root alone is insufficient):

```python
from assumption_checks import comprehensive_assumption_check

# Within-group outlier screens, normality and variance diagnostics; with plots
results = comprehensive_assumption_check(
    data=df,
    value_col='score',
    group_col='group',  # Independent groups; paired tests use difference scores
    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,  # Levene's test + box plots
    check_linearity,                # scatter + residual plot for simple regression
    check_regression_diagnostics,   # full OLS diagnostics (see Regression below)
    detect_outliers                 # IQR or z-score methods
)

result = check_normality(data=df['score'], name='Test Score', alpha=0.05, plot=True)
print(result['interpretation'])
print(result['recommendation'])
```

### What to Do When Assumptions Are Violated

- A non-significant Shapiro/Levene result does not verify normality/equal variance. There is no universal n=30 robustness rule; tails, skewness, imbalance, dependence and the target estimator matter.
- For paired t-tests diagnose differences; for regression inspect residuals. Rank tests change the question and retain assumptions.
- Prespecify Welch for independent mean comparisons; use Games-Howell pairwise comparisons when appropriate to a heteroscedastic one-way design. Regression HC3 addresses heteroscedasticity, not clustering, confounding or a wrong mean model.
- The helper rejects infinities, undersized or degenerate samples, reports omitted NaNs, retains original outlier positions, and rejects missing group labels. No binary Shapiro verdict is returned above 5000 observations, where its p-value may be inaccurate.
- Grouped output uses `outliers_per_group`; legacy `is_normal`/`is_homogeneous` and the `Normal` table label mean only non-rejection. Independence is established through design review, never this helper. Pass `ordered=True` to regression diagnostics only for meaningful row order; Durbin-Watson is descriptive without a universal cutoff.

See [assumptions and diagnostics](references/assumptions_and_diagnostics.md).

---

From K-Dense-AI/scientific-agent-skills, MIT.

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