A public health researcher in Delhi conducted a study comparing the effectiveness of two different health education interventions on reducing tobacco use among 200 factory workers. Group A (n=100) received intensive counseling, while Group B (n=100) received standard written material. After 6 months, 65 workers in Group A and 45 workers in Group B had quit tobacco use. The researcher wants to determine if the difference in quit rates between the two groups is statistically significant. Which test of significance should be used, and what is the most appropriate null hypothesis?

Explanation

## Test Selection for Categorical Data Comparison **Key Point:** When comparing categorical outcomes (quit/not quit) between two independent groups, the chi-square test is the appropriate test of significance. ### Why Chi-Square Test? 1. **Data Type:** Both variables are categorical (binary outcome: quit vs. did not quit; group: intervention A vs. intervention B) 2. **Sample Size:** With n=100 in each group and expected frequencies >5 in all cells, chi-square assumptions are met 3. **Independence:** The two groups are independent (different workers in each group) ### Null Hypothesis Formulation **High-Yield:** The null hypothesis for chi-square test states that there is **no association** between the categorical variables (intervention type and cessation outcome). ### Contingency Table Structure | Intervention | Quit | Did Not Quit | Total | |---|---|---|---| | Group A (Counseling) | 65 | 35 | 100 | | Group B (Written) | 45 | 55 | 100 | | Total | 110 | 90 | 200 | ### Chi-Square Test Formula $$\chi^2 = \sum \frac{(O - E)^2}{E}$$ where O = observed frequency, E = expected frequency **Clinical Pearl:** In public health intervention studies, chi-square is the standard test for comparing binary outcomes (success/failure, disease/no disease, intervention effect/no effect) across independent groups. ### When to Use Alternative Tests - **Fisher's exact test:** Used when expected frequencies are <5 in any cell (small sample sizes) - **t-test (unpaired):** Used for continuous data (e.g., comparing mean blood pressure, mean weight loss) - **t-test (paired):** Used for before-after measurements in the same subjects **Mnemonic:** **CATS** — **C**ategorical data → chi-square; **A**lternative test (Fisher's) when frequencies are small; **T**-test for continuous data; **S**ame subjects (paired) vs. different subjects (unpaired)