AP Statistics Unit 8: Inference for Categorical Data: Chi-Square

Chi-square procedures handle categorical variables with more than two categories. A goodness-of-fit test compares one variable's observed counts with a claimed distribution. Tests for homogeneity and independence use a two-way table: homogeneity compares several populations, while independence looks at two variables in one population.

The statistic is $\chi^2 = \sum \frac{(O - E)^2}{E}$, which is large when observed counts differ a lot from expected counts. For two-way tables, $E = \frac{\text{row total} \times \text{column total}}{\text{table total}}$. Conditions are random samples and all expected counts at least 5; degrees of freedom are categories minus one, or $(r-1)(c-1)$ for tables.