## Chi-Square Test: Scope, Assumptions, and Applications ### Purpose and Scope of χ² Test **Key Point:** The chi-square test is a non-parametric test designed exclusively for **categorical data**. It tests associations and goodness-of-fit, NOT differences in means of continuous variables. ### Valid Applications of χ² Test | Application | Data Type | Example | |---|---|---| | **Test of Independence** | Two categorical variables | Association between smoking status and lung cancer (2×2 table) | | **Goodness-of-Fit** | One categorical variable | Do observed genotype frequencies match Hardy-Weinberg expectations? | | **Homogeneity** | Categorical across groups | Is disease prevalence equal across three geographic regions? | ### Why Each Option Is Correct or Incorrect **Option 1 (Correct):** Goodness-of-fit is a classic χ² application. Example: testing whether observed disease cases match expected Poisson distribution. **Option 2 (Correct):** The assumption of minimum expected frequency ≥ 5 in each cell is essential. If violated, use Fisher's exact test (2×2) or combine categories. This is a well-established validity criterion. **Option 3 (INCORRECT — The Answer):** This is fundamentally wrong. The χ² test: - Works with **categorical** data (frequencies, counts) - Does NOT work with **continuous** data (means, measurements) - Cannot compare means across groups For comparing means of continuous variables across multiple groups, use **ANOVA** (parametric) or **Kruskal-Wallis** (non-parametric), NOT χ². **Option 4 (Correct):** The 2×2 contingency table is the most common χ² application in epidemiology, testing association between exposure and disease. ### High-Yield Distinction: χ² vs. ANOVA **High-Yield:** - **χ² test:** Categorical × Categorical → association/independence - **ANOVA:** Continuous × Categorical → compare means across groups - **Pearson correlation / linear regression:** Continuous × Continuous → association **Mnemonic:** **"CHI-square for CATegories"** — if your data are counts/frequencies/proportions, use χ². If your data are measurements (height, weight, BP, glucose), use ANOVA or t-test. ### Common Exam Trap **Warning:** A question may present a scenario like "comparing mean hemoglobin levels across three treatment groups" and offer χ² as an option. This is a distractor — the correct test is ANOVA or Kruskal-Wallis, not χ².
Sign up free to access AI-powered MCQ practice with detailed explanations and adaptive learning.