When comparing the distribution of a categorical variable across two independent groups, which test is most appropriate?

Explanation

## Chi-Square Test of Independence **Key Point:** The chi-square test is used to determine whether there is a statistically significant association between two categorical variables. ### When to Use Chi-Square The chi-square test of independence is appropriate when: 1. Both variables are categorical (nominal or ordinal) 2. Data are arranged in a contingency table (rows × columns) 3. You want to test the null hypothesis that the two variables are independent 4. Expected frequency in each cell is ≥ 5 (or ≥ 1 in <20% of cells) ### Test Statistic $$\chi^2 = \sum \frac{(O - E)^2}{E}$$ where O = observed frequency and E = expected frequency. ### Contingency Table Example | | Disease Present | Disease Absent | Total | |---|---|---|---| | **Exposed** | a | b | a+b | | **Not Exposed** | c | d | c+d | | **Total** | a+c | b+d | n | **High-Yield:** The chi-square test produces a p-value; if p < 0.05, reject the null hypothesis of independence. ### Why Other Options Are Wrong | Option | Why Incorrect | |--------|---------------| | Paired t-test | Requires continuous data and paired/matched observations | | One-way ANOVA | Compares means of 3+ groups with continuous outcome | | Pearson correlation | Measures linear relationship between two continuous variables | **Mnemonic:** **CAT** = **C**ategorical × **A**nother **T**hing (categorical) → **Chi-square** **Clinical Pearl:** If expected frequencies are too low (<5), use Fisher's exact test (for 2×2 tables) instead of chi-square.