A researcher wants to test the association between smoking status (smoker/non-smoker) and the presence of chronic obstructive pulmonary disease (COPD) (yes/no) in a cross-sectional study of 500 Indian adults. Which statistical test is most appropriate?

Explanation

## Choosing the Correct Test: Chi-Square vs. t-Test **Key Point:** The chi-square test is used to test the association between **two categorical variables**, while the t-test compares **means of continuous variables** between groups. ### Test Selection Algorithm ```mermaid flowchart TD A[What type of variables?]:::decision A -->|Both categorical| B[Chi-square test]:::action A -->|One continuous, one categorical| C[t-test or ANOVA]:::action A -->|Both continuous| D[Correlation or Regression]:::action B --> E[2×2 or larger contingency table]:::outcome C --> F[Compare means between groups]:::outcome D --> G[Measure linear relationship]:::outcome ``` ### Data Classification in This Question | Variable | Type | Categories | |---|---|---| | **Smoking Status** | Categorical | Smoker / Non-smoker | | **COPD Presence** | Categorical | Yes / No | | **Study Design** | Cross-sectional | Observational | **High-Yield:** Both variables are **categorical** (nominal scale). The chi-square test of independence is the standard parametric test for this scenario. ### Chi-Square Test Essentials **Mnemonic: CATS** — **C**ategorical variables, **A**ssociation testing, **T**wo or more groups, **S**quared differences from expected. **Clinical Pearl:** The chi-square test produces a contingency table (2×2 in this case) and tests whether the observed cell frequencies differ significantly from expected frequencies under the null hypothesis of independence. ### Why Other Tests Are Incorrect - **Independent t-test:** Requires a continuous dependent variable (e.g., FEV₁ score); smoking status and COPD presence are both categorical - **Paired t-test:** Used for matched/repeated measurements in the same subjects; no pairing here - **Pearson correlation:** Measures linear relationship between two **continuous** variables; both variables here are categorical **Warning:** A common mistake is using t-test when both variables are categorical. This violates the assumption that the dependent variable is continuous and normally distributed. [cite:Park 26e Ch 10]