## Test Selection for Continuous Data — Two Independent Groups ### Data Characteristics **Key Point:** The outcome variable is continuous (systolic blood pressure reduction in mmHg), and we are comparing two independent groups (Drug X vs. Drug Y). ### Why Unpaired t-Test is Correct | Feature | Unpaired t-test | Paired t-test | Chi-square | Mann-Whitney U | |---------|-----------------|---------------|-----------|----------------| | **Data Type** | Continuous | Continuous | Categorical | Continuous | | **Group Structure** | Independent groups | Matched/repeated measures | Categorical | Independent groups | | **Current Study** | ✓ Two separate drug groups | ✗ Not before-after | ✗ Not proportions | Possible but less powerful | | **Sample Size** | n=40 per group (adequate) | — | — | Used if normality violated | **High-Yield:** Unpaired (independent samples) t-test is the standard parametric test for comparing means of a continuous variable between two independent groups. It assumes: 1. Data are approximately normally distributed (reasonable with n=40 per group by Central Limit Theorem) 2. Variances are roughly equal (can be checked via Levene's test; SDs of 5 and 6 are similar) 3. Observations are independent (different patients in each group) ### Assumptions Assessment - **Normality:** With n=40 per group, the Central Limit Theorem supports approximate normality even if the underlying distribution is not perfectly normal. - **Equal variances:** SD₁ = 5, SD₂ = 6 → ratio ≈ 1.2, well within acceptable range (< 2). - **Independence:** Different patients randomized to different drugs → independent observations. **Clinical Pearl:** The t-test will determine if the 3 mmHg difference in mean SBP reduction (18 vs. 15) is statistically significant or likely due to random variation. **Mnemonic:** **COCO** — COntinuous outcome, COmpare two independent groups = unpaired t-test.
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