![]() ![]() Welch's t-test and Student's t-test gave identical results when the two samples have similar variances and sample sizes (Example 1). Welch's t-test defines the statistic t by the following formula: Welch's t-test is an approximate solution to the Behrens–Fisher problem. Welch's t-test is designed for unequal population variances, but the assumption of normality is maintained. Student's t-test assumes that the sample means being compared for two populations are normally distributed, and that the populations have equal variances. Given that Welch's t-test has been less popular than Student's t-test and may be less familiar to readers, a more informative name is "Welch's unequal variances t-test" - or "unequal variances t-test" for brevity. ![]() These tests are often referred to as "unpaired" or "independent samples" t-tests, as they are typically applied when the statistical units underlying the two samples being compared are non-overlapping. It is named for its creator, Bernard Lewis Welch, is an adaptation of Student's t-test, and is more reliable when the two samples have unequal variances and possibly unequal sample sizes. In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the (null) hypothesis that two populations have equal means. Statistical test of whether two populations have equal means ![]()
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