## Test Selection for Categorical Data Comparison ### Study Design Analysis The researcher is comparing two independent groups (two intervention groups) on a categorical outcome (tobacco use: yes/no). This is a classic scenario for the chi-square test of independence. ### Why Chi-Square Test? **Key Point:** The chi-square test is the most commonly used test for comparing categorical variables between two or more independent groups. It tests whether there is a significant association between two categorical variables. **High-Yield:** Chi-square test requirements: - Both variables must be categorical (nominal or ordinal) - Data arranged in a contingency table (2×2, 2×3, etc.) - Expected frequency in each cell ≥ 5 (if not, use Fisher's exact test) - Independent observations ### Contingency Table Structure | Intervention | Tobacco Users | Non-Users | Total | | --- | --- | --- | --- | | Group A | a | b | a+b | | Group B | c | d | c+d | | Total | a+c | b+d | n | **Formula:** $$\chi^2 = \sum \frac{(O - E)^2}{E}$$ where O = observed frequency, E = expected frequency ### When to Use Chi-Square vs. Other Tests | Test | Data Type | Use Case | | --- | --- | --- | | **Chi-square** | Categorical × Categorical | Association between two categorical variables | | **t-test** | Continuous × Categorical (2 groups) | Compare means between two independent/paired groups | | **ANOVA** | Continuous × Categorical (3+ groups) | Compare means across multiple groups | | **Pearson r** | Continuous × Continuous | Correlation between two continuous variables | **Clinical Pearl:** In epidemiological and public health studies, chi-square is the workhorse test for comparing proportions and frequencies between groups — it is by far the most commonly used test in such scenarios. **Tip:** Always ask: "Are my variables categorical or continuous?" If both are categorical → chi-square.
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