An Alternative Approach to the Anova Problem

Abstract

When the hypothesis of equality of means of several univariate homoscedastic normal populations from which independent samples are available, is rejected on the basis of the ANOV A F-test, the populations have to be divided into disjoint groups such that within each group the populations are all same. For any such division a natural index of correctness of the grouping is defined and a procedure is proposed such that it leads to the choice of a division for which the true index does not fall below a stipulated threshold at a given level of confidence. The procedure is illustrated through some numerical examples.