On Dependent Tests from a Non-Orthogonal Design

Abstract

This paper illustrates, through a special case, an effect of non-independent numerators on F -test's in an analysis of variance. Symmetrical balanced incomplete block designs are considered with “blocks” a random effect and no interaction. The joint density of the adjusted sums of squares is determined under the null hypothesis of no treatment effect. Given the result of testing for the block effect, the conditional probability of a Type I error when testing the null hypothesis concerning the treatment effect is evaluated for a number of designs.