Welch statistic

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A statistic used in a test for the equality of the means of m normal populations that cannot be assumed to have the same variance. The test statistic, W, is given by where j is the mean of the nj observations in the jth sample, sj2 is the variance (using the (n − 1) divisor) of the jth sample, , and . Under the null hypothesis that the samples come from populations with the same mean, W has an approximate F-distribution with (m − 1) and ν degrees of freedom, where ν is the nearest integer to The special case m = 2 corresponds to the Behrens–Fisher problem.

Subjects: Probability and Statistics.

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