Which test of significance is used to compare the means of two independent groups when the data are normally distributed and variances are equal?

Explanation

## Test Selection for Comparing Two Independent Group Means **Key Point:** The unpaired (independent samples) t-test is the parametric test of choice for comparing means between two independent groups when assumptions of normality and equal variance are met. ### Conditions for Unpaired t-test - Two independent groups (no pairing or matching) - Continuous outcome variable - Data approximately normally distributed - Equal variances between groups (Levene's test can verify) - Sample sizes typically ≥30 or normality confirmed by Q-Q plot ### Why Unpaired t-test Here Since the stem specifies: 1. **Two independent groups** (not paired/matched) 2. **Normal distribution** (parametric assumption met) 3. **Equal variances** (homogeneity assumption met) The unpaired t-test is the most powerful and appropriate choice. **High-Yield:** The t-test assumes independent observations. If the same subjects are measured twice (before-after), use the **paired t-test** instead. ### Formula $$t = \frac{\bar{x}_1 - \bar{x}_2}{SE_{difference}}$$ where $SE_{difference} = s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}$ and $s_p$ is the pooled standard deviation.