gh-astoreyai-ai-scientist/skills/hypothesis-test/SKILL.md

name, description, allowed-tools, version

name	description	allowed-tools	version
hypothesis-test	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.	Read, Write	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.

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Version: 1.0.0