Use Chi‑Square to test categorical relationships or fit to a theoretical distribution. Always pair significance with effect size.
Independence Test
Cross‑tabulate two categorical variables; compute expected counts; report χ², df, p‑value, and Cramér’s V/Phi. Inspect standardized residuals to see which cells drive the signal.
Goodness‑of‑Fit
Compare observed category frequencies to expected proportions. Useful for distribution checks in survey responses or event categories.
Assumptions
- Expected counts per cell are sufficiently large (≈ ≥ 5)
- Independent observations
Alternatives
- Fisher’s exact test for small/sparse tables
- G‑test as a likelihood‑ratio alternative