In a study comparing the association between smoking status (smoker/non-smoker) and lung cancer (present/absent) in 500 subjects, which test of significance is most appropriate?

Explanation

## Test Selection for Categorical Association **Key Point:** The chi-square (χ²) test of independence is used to test the association between two categorical variables arranged in a contingency table. ### Why Chi-Square Test Here Both variables are **categorical**: - **Smoking status:** categorical (smoker vs. non-smoker) - **Lung cancer:** categorical (present vs. absent) - **Data structure:** 2×2 contingency table (500 subjects) ### Chi-Square Test Assumptions 1. Both variables are categorical (nominal or ordinal) 2. Observations are independent 3. Expected frequency in each cell ≥5 (if violated, use Fisher's exact test) 4. Data presented in contingency table format ### Contingency Table Layout | | Lung Cancer Present | Lung Cancer Absent | Total | | --- | --- | --- | --- | | Smoker | a | b | a+b | | Non-smoker | c | d | c+d | | Total | a+c | b+d | n | ### Chi-Square Formula $$\chi^2 = \sum \frac{(O - E)^2}{E}$$ where O = observed frequency, E = expected frequency **High-Yield:** Chi-square tests association (independence), not causation. It tells you whether two categorical variables are related, not which causes which. **Mnemonic:** **CAT-CAT** = **CAT**egorical data → **CAT**egory test (chi-square)