Welch's t-test

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. It is named for its creator, Bernard Lewis Welch, and is an adaptation of Student's t-test,[1] and is more reliable when the two samples have unequal variances and possibly unequal sample sizes.[2][3] 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. Given that Welch's t-test has been less popular than Student's t-test[2] 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.[3]

  1. ^ Welch, B. L. (1947). "The generalization of "Student's" problem when several different population variances are involved". Biometrika. 34 (1–2): 28–35. doi:10.1093/biomet/34.1-2.28. MR 0019277. PMID 20287819.
  2. ^ a b Ruxton, G. D. (2006). "The unequal variance t-test is an underused alternative to Student's t-test and the Mann–Whitney U test". Behavioral Ecology. 17 (4): 688–690. doi:10.1093/beheco/ark016.
  3. ^ a b Derrick, B; Toher, D; White, P (2016). "Why Welchs test is Type I error robust" (PDF). The Quantitative Methods for Psychology. 12 (1): 30–38. doi:10.20982/tqmp.12.1.p030.