A clinical trial enrolls 150 hypertensive patients to compare the effect of two antihypertensive drugs on blood pressure reduction. After 12 weeks, mean systolic BP reduction in Drug A group (n=75) is 18 mmHg (SD=6) and in Drug B group (n=75) is 15 mmHg (SD=5). Which test would be most appropriate to determine if this difference in mean BP reduction is statistically significant?

## Selecting the Appropriate Test for Continuous Outcome Data ### Data Characteristics **Key Point:** The choice hinges on: 1. **Outcome variable type:** Blood pressure reduction (continuous, measured in mmHg) 2. **Group structure:** Two independent groups (Drug A vs. Drug B) 3. **Sample information provided:** Means, standard deviations, and sample sizes — classic t-test inputs ### Why Unpaired t-Test? **High-Yield:** The unpaired (independent samples) t-test is designed to compare **means of a continuous outcome between two independent groups**. It tests whether the difference between group means is statistically significant, accounting for within-group variability. ### Test Selection Flowchart ```mermaid flowchart TD A[Outcome Variable Type?]:::decision A -->|Categorical| B[Chi-square test]:::action A -->|Continuous| C{Groups Paired?}:::decision C -->|Yes, Paired| D[Paired t-test]:::action C -->|No, Independent| E[Unpaired t-test]:::action E --> F[Check normality & equal variance]:::outcome F -->|Violated| G[Mann-Whitney U]:::action F -->|Satisfied| H[Report t-statistic & p-value]:::outcome ``` ### Unpaired t-Test Formula $$t = \frac{\bar{X}_1 - \bar{X}_2}{SE_{diff}}$$ where $SE_{diff} = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$ **Clinical Pearl:** With large equal sample sizes (n=75 each) and reasonable SDs, the t-test is robust even if normality is slightly violated. ### Comparison Table: When to Use Which Test | Test | Outcome Type | Groups | Independence | Example | |------|--------------|--------|--------------|----------| | **Unpaired t-test** | Continuous | 2 | Independent | BP reduction: Drug A vs. Drug B | | Paired t-test | Continuous | 2 | Paired (same subjects) | BP: pre-treatment vs. post-treatment | | Chi-square | Categorical | 2+ | Independent | Cure rate: Drug A vs. Drug B | | Mann-Whitney U | Continuous (non-normal) | 2 | Independent | Non-parametric alternative | | Spearman's | Ordinal/Rank | 2 variables | Correlation | Association between two ranks | **Mnemonic:** **CON** = **C**ontinuous outcome, **O**ne comparison, **N**ormal distribution → t-test