A clinical trial in Mumbai compares the mean systolic blood pressure (mmHg) between two treatment groups: Group A (n=45, receiving Drug X) and Group B (n=48, receiving Drug Y). Both groups are normally distributed with similar variances. The investigator wishes to test whether the mean SBP differs significantly between the two groups. Which test should be used?

## Selection of Appropriate Significance Test **Key Point:** When comparing the means of a continuous variable between two independent groups with normal distribution and equal variances, the unpaired (independent samples) t-test is the parametric test of choice. ### Study Design Characteristics | Feature | Observation | |---|---| | **Dependent variable** | Systolic blood pressure (continuous, measured in mmHg) | | **Independent variable** | Treatment group (categorical: Drug X vs. Drug Y) | | **Group structure** | Two independent, non-paired groups | | **Sample sizes** | n₁ = 45, n₂ = 48 (both > 30, adequate for CLT) | | **Distribution** | Normal in both groups | | **Variance** | Similar (homogeneous) | ### Unpaired t-Test Formula $$t = \frac{\bar{X}_1 - \bar{X}_2}{SE_{diff}} = \frac{\bar{X}_1 - \bar{X}_2}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$$ where $s_p$ is the pooled standard deviation and df = n₁ + n₂ − 2 = 91. ### Assumptions of Unpaired t-Test 1. **Independence:** Observations within and between groups are independent ✓ 2. **Normality:** Both groups are normally distributed ✓ 3. **Homogeneity of variance:** Variances are approximately equal ✓ (can verify with Levene's test) 4. **Continuous outcome:** SBP is continuous ✓ **High-Yield:** The unpaired t-test is robust to minor violations of normality when n > 30 due to the Central Limit Theorem. ### When to Use Alternatives ```mermaid flowchart TD A[Comparing means between 2 groups]:::outcome --> B{Independent or paired?}:::decision B -->|Independent| C{Normal distribution?}:::decision B -->|Paired| D[Paired t-test]:::action C -->|Yes| E{Equal variances?}:::decision C -->|No| F[Mann-Whitney U test]:::action E -->|Yes| G[Unpaired t-test]:::action E -->|No| H[Welch's t-test]:::action ``` **Clinical Pearl:** In clinical trials comparing continuous outcomes (BP, cholesterol, weight) between treatment arms, the unpaired t-test is the standard analysis when assumptions are met.