## Quick Reference

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*

*observations in the*

_{j}*j*th sample, s

_{j}

^{2}is the variance (using the (

*n*− 1) divisor) of the

*j*th 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.