| 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:
- Independence of observations
- Normality (especially for small N)
- 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:
- Independence
- Normality
- Homogeneity of variance
- No outliers
Violations?
- Non-normal → Kruskal-Wallis test
- Unequal variance → Welch's ANOVA
- Outliers → Robust methods or transformation
Step 3: Interpret results
Always report:
- Test statistic (t, F, χ²)
- Degrees of freedom
- p-value
- Effect size with CI
- 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
