/statistical-analysis

name: statistical-analysis
description: "統計検定の選択・仮定チェック・検出力分析・APA形式レポートを支援するスキル。 「統計分析をして」「t検定を実行」「適切な検定を選んで」等のリクエストで発動。"
triggers:
  - 統計分析をして
  - t検定を実行
  - 適切な検定を選んで
  - 検出力分析
  - APA形式でレポート
  - statistical-analysis
  - hypothesis test
license: MIT license
metadata:
    skill-author: K-Dense Inc.
source: github.com/K-Dense-AI/claude-scientific-skills@main

Statistical Analysis

Overview

Statistical analysis is a systematic process for testing hypotheses and quantifying relationships. Conduct hypothesis tests (t-test, ANOVA, chi-square), regression, correlation, and Bayesian analyses with assumption checks and APA reporting. Apply this skill for academic research.

When to Use This Skill

This skill should be used when:

• Conducting statistical hypothesis tests (t-tests, ANOVA, chi-square)
• 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

---

Core Capabilities

1. Test Selection and Planning

• Choose appropriate statistical tests based on research questions and data characteristics
• Conduct a priori power analyses to determine required sample sizes
• Plan analysis strategies including multiple comparison corrections

2. Assumption Checking

• Automatically verify all relevant assumptions before running tests
• Provide diagnostic visualizations (Q-Q plots, residual plots, box plots)
• Recommend remedial actions when assumptions are violated

3. Statistical Testing

• Hypothesis testing: t-tests, ANOVA, chi-square, non-parametric alternatives
• Regression: linear, multiple, logistic, with diagnostics
• Correlations: Pearson, Spearman, with confidence intervals
• Bayesian alternatives: Bayesian t-tests, ANOVA, regression with Bayes Factors

4. Effect Sizes and Interpretation

• Calculate and interpret appropriate effect sizes for all analyses
• Provide confidence intervals for effect estimates
• Distinguish statistical from practical significance

5. Professional Reporting

• Generate APA-style statistical reports
• Create publication-ready figures and tables
• Provide complete interpretation with all required statistics

---

Workflow Decision Tree

Use this decision tree to determine your analysis path:

START
│
├─ Need to SELECT a statistical test?
│  └─ YES → See "Test Selection Guide"
│  └─ NO → Continue
│
├─ Ready to check ASSUMPTIONS?
│  └─ YES → See "Assumption Checking"
│  └─ NO → Continue
│
├─ Ready to run ANALYSIS?
│  └─ YES → See "Running Statistical Tests"
│  └─ NO → Continue
│
└─ Need to REPORT results?
   └─ YES → See "Reporting Results"

---

Test Selection Guide

Quick Reference: Choosing the Right Test

Use `references/test_selection_guide.md` for comprehensive guidance. 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 that provide:

• Direct probability statements about hypotheses
• Bayes Factors quantifying evidence
• Ability to support null hypothesis
• See `references/bayesian_statistics.md`

---

Assumption Checking

Systematic Assumption Verification

**ALWAYS check assumptions before interpreting test results.**

Use the provided `scripts/assumption_checks.py` module for automated checking:

from scripts.assumption_checks import comprehensive_assumption_check

# Comprehensive check with visualizations
results = comprehensive_assumption_check(
    data=df,
    value_col='score',
    group_col='group',  # Optional: for group comparisons
    alpha=0.05
)

This performs: 1. **Outlier detection** (IQR and z-score methods) 2. **Normality testing** (Shapiro-Wilk test + Q-Q plots) 3. **Homogeneity of variance** (Levene's test + box plots) 4. **Interpretation and recommendations**

Individual Assumption Checks

For targeted checks, use individual functions:

from scripts.assumption_checks import (
    check_normality,
    check_normality_per_group,
    check_homogeneity_of_variance,
    check_linearity,
    detect_outliers
)

# Example: Check normality with visualization
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

**Normality violated:**

• Mild violation + n > 30 per group → Proceed with parametric test (robust)
• Moderate violation → Use non-parametric alternative
• Severe violation → Transform data or use non-parametric test

**Homogeneity of variance violated:**

• For t-test → Use Welch's t-test
• For ANOVA → Use Welch's ANOVA or Brown-Forsythe ANOVA
• For regression → Use robust standard errors or weighted least squares

**Linearity violated (regression):**

• Add polynomial terms
• Transform variables
• Use non-linear models or GAM

See `references/assumptions_and_diagnostics.md` for comprehensive guidance.

---

Running Statistical Tests

Python Libraries

Primary libraries for statistical analysis:

• **scipy.stats**: Core statistical tests
• **statsmodels**: Advanced regression a