Which of the following statements about the independent samples t-test is correct?

Explanation

## Independent Samples t-Test: Key Concepts **Key Point:** The independent samples t-test is designed to compare the means of two independent groups and assumes homogeneity of variance (equal variances across groups). ### Correct Answer Explanation The independent samples t-test uses a pooled standard deviation when variances are assumed equal. This pooled estimate combines information from both samples to estimate the common population variance, making the test more powerful when the assumption holds. $$t = \frac{\bar{X}_1 - \bar{X}_2}{S_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$$ where $S_p$ is the pooled standard deviation. ### Why Other Options Are Wrong | Option | Why Incorrect | |--------|---------------| | Compares 3+ groups | This describes ANOVA (Analysis of Variance), not t-test | | Paired/matched data | This describes paired t-test, a different variant | | Categorical dependent variable | t-test requires continuous (interval/ratio) data; categorical data use chi-square | **High-Yield:** Remember the distinction: - **t-test**: compares 2 groups, continuous outcome - **ANOVA**: compares 3+ groups, continuous outcome - **Chi-square**: categorical outcome, any number of groups **Clinical Pearl:** Levene's test is used to check the assumption of equal variances. If variances are unequal, use Welch's t-test instead of the standard independent samples t-test.