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skills/hypothesis-test/SKILL.md

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+---
+name: hypothesis-test
+description: "Guide selection and interpretation of statistical hypothesis tests. Use when: (1) Choosing appropriate test for research data, (2) Checking assumptions before analysis, (3) Interpreting test results correctly, (4) Reporting statistical findings, (5) Troubleshooting assumption violations."
+allowed-tools: Read, Write
+version: 1.0.0
+---
+
+# Hypothesis Testing Skill
+
+## Purpose
+
+Guide appropriate selection and interpretation of statistical hypothesis tests for research data analysis.
+
+## Test Selection Decision Tree
+
+### Step 1: How many variables?
+
+**One variable:**
+- Categorical → Chi-square goodness of fit
+- Continuous → One-sample t-test
+
+**Two variables:**
+- Both categorical → Chi-square test of independence
+- One categorical, one continuous → T-test or ANOVA
+- Both continuous → Correlation or regression
+
+**Three+ variables:**
+- Multiple predictors → Multiple regression or ANOVA
+- Complex designs → Mixed models or advanced methods
+
+### Step 2: Check assumptions
+
+**For t-tests:**
+1. Independence of observations
+2. Normality (especially for small N)
+3. Homogeneity of variance
+
+**Violations?**
+- Non-normal → Mann-Whitney U (non-parametric)
+- Unequal variance → Welch's t-test
+- Dependent observations → Paired t-test or mixed models
+
+**For ANOVA:**
+1. Independence
+2. Normality
+3. Homogeneity of variance
+4. No outliers
+
+**Violations?**
+- Non-normal → Kruskal-Wallis test
+- Unequal variance → Welch's ANOVA
+- Outliers → Robust methods or transformation
+
+### Step 3: Interpret results
+
+Always report:
+1. **Test statistic** (t, F, χ²)
+2. **Degrees of freedom**
+3. **p-value**
+4. **Effect size with CI**
+5. **Descriptive statistics**
+
+**Example:**
+```
+Independent samples t-test showed a significant difference between 
+groups, t(98) = 3.45, p < .001, d = 0.69, 95% CI [0.29, 1.09]. 
+The experimental group (M = 45.2, SD = 8.3) scored higher than 
+control (M = 37.8, SD = 9.1).
+```
+
+## Common Tests Reference
+
+| Research Question | Test | Assumptions |
+|------------------|------|-------------|
+| 2 groups, continuous outcome | Independent t-test | Normality, equal variance |
+| 2 measurements, same people | Paired t-test | Normality of differences |
+| 3+ groups, one factor | One-way ANOVA | Normality, homogeneity |
+| 3+ groups, multiple factors | Factorial ANOVA | Normality, homogeneity |
+| Relationship between variables | Pearson correlation | Linearity, normality |
+| Predict continuous outcome | Linear regression | Linearity, normality of residuals |
+| 2 categorical variables | Chi-square test | Expected frequencies ≥5 |
+| Ordinal data, 2 groups | Mann-Whitney U | None (non-parametric) |
+| Ordinal data, paired | Wilcoxon signed-rank | None (non-parametric) |
+
+## Assumption Checking
+
+### Normality
+```
+Visual: Q-Q plot, histogram
+Statistical: Shapiro-Wilk test (N < 50), Kolmogorov-Smirnov (N ≥ 50)
+Guideline: Robust to moderate violations if N ≥ 30
+```
+
+### Homogeneity of Variance
+```
+Visual: Box plots, residual plots
+Statistical: Levene's test, Bartlett's test
+Guideline: Ratio of largest/smallest variance < 4
+```
+
+### Independence
+```
+Check: Research design, data collection
+Red flags: Time series, clustered data, repeated measures
+Solution: Use appropriate model (mixed effects, GEE)
+```
+
+## Integration
+
+Use with data-analyst agent for complete statistical analysis workflow and experiment-designer agent for planning appropriate analyses.
+
+---
+
+**Version:** 1.0.0