A public health researcher in Mumbai conducted a study to compare the effectiveness of two different health education interventions on reducing smoking prevalence among 40-year-old males in two urban slums. Group A (n=150) received intensive counselling, while Group B (n=150) received standard pamphlets. After 6 months, 45 subjects in Group A and 30 subjects in Group B had quit smoking. The researcher wants to test whether the difference in quit rates between the two groups is statistically significant. Which test of significance is most appropriate for this analysis?

Explanation

## Test Selection for Categorical Data **Key Point:** The choice of statistical test depends on the type of data (categorical vs. continuous) and study design. ### Data Type Analysis - **Outcome variable:** Smoking status (quit vs. not quit) — **categorical/binary** - **Groups:** Two independent groups (Group A vs. Group B) - **Sample size:** n₁ = 150, n₂ = 150 (both > 30, large samples) ### Why Chi-Square Test? The chi-square test is used to compare **proportions/frequencies** across two or more independent groups when: 1. Data is categorical (nominal or ordinal) 2. Groups are independent 3. Expected frequencies in each cell ≥ 5 **Contingency Table:** | Outcome | Group A | Group B | Total | |---------|---------|---------|-------| | Quit smoking | 45 | 30 | 75 | | Did not quit | 105 | 120 | 225 | | Total | 150 | 150 | 300 | **High-Yield:** Chi-square (χ²) compares **observed frequencies** with **expected frequencies** under the null hypothesis of no association. ### Formula Context $$\chi^2 = \sum \frac{(O - E)^2}{E}$$ where O = observed frequency, E = expected frequency ### Test Assumptions Met - ✓ Categorical outcome - ✓ Independent groups - ✓ Large sample size (n > 30 each) - ✓ Expected frequencies > 5 in all cells **Clinical Pearl:** In epidemiological and public health studies, comparing intervention success rates (binary outcomes) between two groups almost always requires chi-square, not t-test.