Playing safe with misweighted means

Abstract This article concludes that Student's t statistic is a forgiving or safe statistic in the presence of unequal variances. More generally, for every weighted mean , there is a corresponding weighted sum of deviations squared S w,0 2, which together with the mean defines a safe Student-like test statistic. These results imply that the choice of weights in need not be all that precise, provided a compensation is made via S w,0. Such is the case in the example considered.