Power of Tukey's Test for Non-Additivity

Abstract

The problem of testing for non-additivity in a two-way classification has been considered in this paper where the meanμiican be expressed asμ+αi+βiwhere αiandβiare the effects of the two ways of classification (i= 1, …,p;j= 1, …,q). Tukey (1949) has suggested a test for non-additivity. The power function of this test has been found in this paper for alternatives of the formμii=μ+αi+βi+cαiβiand numerical calculations made for the case ofp=q= 6. For the sake of comparison the special case of α2i–1= α2i, β2j–1= β2jhas also been considered, when anF-test is available with d.f. (4, 27). It is seen that the power of Tukey's statistic is slightly less than that of theF-test for smaller values ofC2σ2and, but for a wide range of values of these parameters, the performance of Tukey's statistic is better.