hypothesis-test

# 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 variable