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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 ...
If data are ordinal, a non-parametric alternative to this test should be used such as Kruskal–Wallis one-way analysis of variance. If the variances are not known to be equal, a generalization of 2-sample Welch's t-test can be used. [2]
Behrens–Fisher problem: Yuri Linnik showed in 1966 that there is no uniformly most powerful test for the difference of two means when the variances are unknown and possibly unequal. That is, there is no exact test (meaning that, if the means are in fact equal, one that rejects the null hypothesis with probability exactly α) that is also the ...
If the sample sizes in the two groups being compared are equal, Student's original t-test is highly robust to the presence of unequal variances. [20] Welch's t-test is insensitive to equality of the variances regardless of whether the sample sizes are similar.
There are some alternatives to conventional one-way analysis of variance, e.g.: Welch's heteroscedastic F test, Welch's heteroscedastic F test with trimmed means and Winsorized variances, Brown-Forsythe test, Alexander-Govern test, James second order test and Kruskal-Wallis test, available in onewaytests R
In statistical hypothesis testing, a two-sample test is a test performed on the data of two random samples, each independently obtained from a different given population. The purpose of the test is to determine whether the difference between these two populations is statistically significant .
The result can be used to perform approximate statistical inference tests. The simplest application of this equation is in performing Welch's t-test. An improved equation was derived to reduce underestimating the effective degrees of freedom if the pooled sample variances have small degrees of freedom.
Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference between the variances in the population. Levene's test has been used in the past before a comparison of means to inform the decision on whether to use a pooled t-test or the Welch's t-test for two sample tests or analysis of variance or Welch ...