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

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:

```python
from scripts.assumption_checks import comprehensive_assumption_check

# Comprehensive check with visualizations

From foryourhealth111-pixel/Vibe-Skills, Apache-2.0.

More from foryourhealth111-pixel/Vibe-Skills