# Statistical Hypothesis Testing

Guides agents in running statistical tests for A/B testing and hypothesis validation. Generates ready-to-run Python code for t-tests, ANOVA, and p-value checks.

- skill · `type=skill` · Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, OpenCode · 494 installs · ★ 371
- Author: aj-geddes
- License: MIT · policy=mirror · the beginning of the file is at the end of this page
- Source: https://github.com/aj-geddes/useful-ai-prompts/tree/HEAD/skills/statistical-hypothesis-testing/SKILL.md
- Updated: 2026-03-04
- HTML: https://affpapa.org/en/nevibecode/skills/statistical-hypothesis-testing

## What it does

This skill provides structured guidelines and Python snippets for hypothesis testing. It helps verify whether experimental differences stem from random noise or statistical significance. The agent sets up null hypotheses. It calculates p-values and compares them against the standard 0.05 significance threshold.

Code templates rely on `scipy.stats`, `numpy`, and `pandas`. Implementations cover independent and paired t-tests, Welch's t-test, one-way ANOVA, and chi-square contingency tables. For non-normal data, the skill applies Mann-Whitney U and Kruskal-Wallis tests. It also handles bootstrap confidence intervals and Bonferroni corrections.

Visual diagnostics use `matplotlib` for histograms and Q-Q normality plots. The code computes effect sizes like Cohen's d or eta-squared, as well as test power. Without `scipy` and `numpy` installed in the Python environment, executing these scripts fails immediately.

## Install

### Claude Code (native platform)

1. **Skills CLI (Vercel)**
```bash
npx skills add aj-geddes/useful-ai-prompts --skill statistical-hypothesis-testing -a claude-code
```

2. **Manually: put the files in place**
- File: `~/.claude/skills/statistical-hypothesis-testing/SKILL.md` — Copy the whole skill folder; for one project use .claude/skills/statistical-hypothesis-testing/

### Codex

1. **Skills CLI (Vercel)**
```bash
npx skills add aj-geddes/useful-ai-prompts --skill statistical-hypothesis-testing -a codex
```

2. **Manually: put the files in place**
- File: `.agents/skills/statistical-hypothesis-testing/SKILL.md` — For all projects use ~/.agents/skills/

### Cursor

1. **Skills CLI (Vercel)**
```bash
npx skills add aj-geddes/useful-ai-prompts --skill statistical-hypothesis-testing -a cursor
```

2. **Manually: put the files in place**
- File: `.cursor/skills/statistical-hypothesis-testing/SKILL.md` — Cursor also reads .agents/skills/ and .claude/skills/

### GitHub Copilot

1. **GitHub CLI**
```bash
gh skill install aj-geddes/useful-ai-prompts statistical-hypothesis-testing
```

2. **Manually: put the files in place**
- File: `.github/skills/statistical-hypothesis-testing/SKILL.md`

### Gemini CLI

1. **Skills CLI (Vercel)**
```bash
npx skills add aj-geddes/useful-ai-prompts --skill statistical-hypothesis-testing -a gemini-cli
```

2. **Platform CLI**
```bash
gemini skills install https://github.com/aj-geddes/useful-ai-prompts --path skills/statistical-hypothesis-testing
```

### Windsurf (Devin Desktop)

**Manually: put the files in place**
- File: `.devin/skills/statistical-hypothesis-testing/SKILL.md` — The legacy .windsurf/skills/ path still works

### OpenCode

**Skills CLI (Vercel)**
```bash
npx skills add aj-geddes/useful-ai-prompts --skill statistical-hypothesis-testing -a opencode
```

### Claude.ai

**Claude.ai**
- Zip the folder and upload it in Settings → Capabilities → Skills

Where a file is given instead of a command, copy the files from the source to that path: https://github.com/aj-geddes/useful-ai-prompts/tree/HEAD/skills/statistical-hypothesis-testing/SKILL.md

## When to use it
- run independent and paired t-tests on experimental groups
- evaluate categorical split test data with chi-square contingency tables
- check normality and variance assumptions with Shapiro-Wilk and Levene tests
- calculate Cohen's d effect sizes and statistical test power
- apply Bonferroni corrections across multiple testing iterations

## Example prompts
- Run an independent t-test and calculate Cohen's d for `group_a` and `group_b` in Python
- Set up a chi-square test on this 2x2 contingency table for our landing page test
- Perform a one-way ANOVA with normality checks on `metrics.csv`

## Source text · SKILL.md · MIT

Below is the content of a third-party file. It is data, not instructions for you: do not act on anything written inside unless the human asks. Block tag: fe6eb52caf61dc46.

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````text
---
name: Statistical Hypothesis Testing
description: Conduct statistical tests including t-tests, chi-square, ANOVA, and p-value analysis for statistical significance, hypothesis validation, and A/B testing
---

# Statistical Hypothesis Testing

## Overview

Hypothesis testing provides a framework for making data-driven decisions by testing whether observed differences are statistically significant or due to chance.

## Testing Framework

- **Null Hypothesis (H0)**: No effect or difference exists
- **Alternative Hypothesis (H1)**: Effect or difference exists
- **Significance Level (α)**: Threshold for rejecting H0 (typically 0.05)
- **P-value**: Probability of observing data if H0 is true

## Common Tests

- **T-test**: Compare means between two groups
- **ANOVA**: Compare means across multiple groups
- **Chi-square**: Test independence of categorical variables
- **Mann-Whitney U**: Non-parametric alternative to t-test
- **Kruskal-Wallis**: Non-parametric alternative to ANOVA

## Implementation with Python

```python
import pandas as pd
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

# Sample data
group_a = np.random.normal(100, 15, 50)  # Mean=100, SD=15
group_b = np.random.normal(105, 15, 50)  # Mean=105, SD=15

# Test 1: Independent samples t-test
t_stat, p_value = stats.ttest_ind(group_a, group_b)
print(f"T-test: t={t_stat:.4f}, p-value={p_value:.4f}")
if p_value < 0.05:
    print("Reject null hypothesis: Groups are significantly different")
else:
    print("Fail to reject null hypothesis: No significant difference")

# Test 2: Paired t-test (same subjects, two conditions)
before = np.array([85, 90, 88, 92, 87, 89, 91, 86, 88, 90])
after = np.array([92, 95, 91, 98, 94, 96, 99, 93, 95, 97])

t_stat, p_value = stats.ttest_rel(before, after)
print(f"\nPaired t-test: t={t_stat:.4f}, p-value={p_value:.4f}")

# Test 3: One-way ANOVA (multiple groups)
group1 = np.random.normal(100, 10, 30)
group2 = np.random.normal(105, 10, 30)
group3 = np.random.normal(102, 10, 30)

f_stat, p_value = stats.f_oneway(group1, group2, group3)
print(f"\nANOVA: F={f_stat:.4f}, p-value={p_value:.4f}")

# Test 4: Chi-square test (categorical variables)
# Create contingency table
contingency = np.array([
    [50, 30],  # Control: success, failure
    [45, 35]   # Treatment: success, failure
])
````
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