A public health researcher is comparing the effectiveness of two different health education interventions on smoking cessation rates in a cohort of 200 smokers (100 per group). After 6 months, Group A shows 45% quit rate and Group B shows 38% quit rate. Which statistical test would be most appropriate to determine if this difference is statistically significant?

Explanation

## Choosing the Right Test of Significance ### Data Type Analysis **Key Point:** The choice of statistical test depends on: 1. Nature of the outcome variable (categorical vs. continuous) 2. Number of groups being compared 3. Whether data are paired or unpaired In this scenario: - **Outcome variable:** Smoking cessation (quit vs. not quit) — **categorical/dichotomous** - **Groups:** 2 independent groups (Group A vs. Group B) - **Sample size:** Large (n=100 per group) ### Why Chi-Square Test? **High-Yield:** Chi-square test is the test of choice for comparing **categorical outcomes between two or more independent groups**. It tests whether observed frequencies differ significantly from expected frequencies under the null hypothesis of no association. ### Test Comparison Table | Test | Data Type | Groups | Pairing | Use Case | |------|-----------|--------|---------|----------| | **Chi-square** | Categorical | 2+ | Independent | Quit rates, disease prevalence, proportions | | Unpaired t-test | Continuous | 2 | Independent | Blood pressure, weight, lab values | | Paired t-test | Continuous | 2 | Paired | Pre-post measurements in same subjects | | Mann-Whitney U | Ordinal/non-normal | 2 | Independent | Non-parametric alternative to t-test | ### Calculation Framework **Key Point:** For a 2×2 contingency table: ``` Quit Not Quit Total Group A 45 55 100 Group B 38 62 100 Total 83 117 200 ``` Chi-square formula: $$\chi^2 = \sum \frac{(O - E)^2}{E}$$ where O = observed frequency, E = expected frequency. **Clinical Pearl:** The chi-square test assumes expected frequencies ≥5 in each cell — satisfied here (all cells >>5). **Mnemonic:** **CAT** = **C**ategorical data, **A**ssociation test, **T**wo or more groups → Chi-square