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 x̄_j is the mean of the n_j observations in the sample from the jth population, s_j² is the corresponding sample 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 toThe special case m=2 corresponds to the Behrens–Fisher problem.