Sample variances are always pooled when computing independent samples t-tests.

Question

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Pooled sample variance is used in the computation of an independent samples t-test only when the assumption of equal variances (homogeneity of variance) between the two groups being compared is met. If this assumption is violated, a different version of the t-test (such as Welch's t-test) that does not assume equal variances should be used, and variances are not pooled.

Sample Variances Are Always Pooled When Computing Independent Samples T-Tests