The estimation of residual variance in quadratically balanced least-squares problems and the robustness of the F -test

Abstract

In the first part of the paper a new simple proof is given of a special case of a result due to Hsu (1938) concerning the estimation of residual variance in a linear least-squares model. In the second part of the paper similar methods are applied to examine the effect of non-normality in the standard analysis of variance F -test. A condition is found for the test to be insensitive to non-normality; the condition is satisfied in the standard set-ups, such as balanced two-or more-way arrangements, Latin squares, balanced incomplete block designs and equi-replicated nested designs. It is shown that non-normality has little effect on inference made by intrablock analysis in a wider class of incomplete block designs with a particular property. Expressions for judging the effect of non-normality in other practical situations are given.