content has been archived, and is no longer maintained by Indiana University. Microsoft Excel 2010 and later (Student's T Test)ĭefault output from proc ttest (labeled "Satterthwaite") Microsoft Excel pre 2010 (Student's T Test) Ttest2(data1, data2, 'Vartype', 'unequal') Software implementations Language/Program For unequal variances, Welch's t-test gave p-values close to simulated p-values. So with actual data, the two tests will almost always give somewhat different results.įor unequal variances, Student's t-test gave a low p-value when the smaller sample had a larger variance (Example 2) and a high p-value when the larger sample had a larger variance (Example 3). But note that if you sample data from populations with identical variances, the sample variances will differ, as will the results of the two t-tests. Welch's t-test and Student's t-test gave identical results when the two samples have identical 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 hypothesis that two populations have equal means. ( August 2022) ( Learn how and when to remove this template message) Several templates and tools are available to assist in formatting, such as Reflinks ( documentation), reFill ( documentation) and Citation bot ( documentation). Please consider converting them to full citations to ensure the article remains verifiable and maintains a consistent citation style. This article uses bare URLs, which are uninformative and vulnerable to link rot.
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