Understanding Chi-Square Tests

Chi-square tests assess whether there is a significant association between categorical variables.

When to Use:

• Independence Test: Testing if two categorical variables are related (e.g., treatment vs. outcome)
• Goodness of Fit: Testing if observed frequencies match expected theoretical distribution

Interpreting χ²:

Larger χ² values indicate greater deviation from expected frequencies. P-value < 0.05 suggests significant association.

Effect Size (Cramér's V):

• Small: 0.1
• Medium: 0.3
• Large: 0.5+

Assumptions:

• Independent observations
• Expected frequency ≥ 5 in most cells (80%+)
• Random sampling