# Lecture 15: Two-sample testing under heteroscedasticity

November 3rd, 2022 (8th week of classes)**Two-sample testing the issues of samples differing in their variances**

When samples vary in the variances we can’t use the standard t-test for comparing two sample means. We introduce here the F-ratio test to test whether two sample variances differ significantly. If they don’t, then we assume that the samples are homoscedastic (i.e., their statistical populations have the same variance). If they do vary significantly, then we use the Welch’s modified t test.

**Lecture**

Slides:

Download lecture: 3 slides per page and outline

Download lecture: 1 slide per page

Videos:

**part 1**

The issues involved when treatments or groups vary in their variances.

**part 2**

The modified Welch’s t-test for comparing two independent samples when we cannot assume that they come from populations that have equal variances; i.e., we can’t assume homoscedasticity.