Power of Tukey's Test for Non-Additivity

SUMMARY The problem of testing for non-additivity in a two-way classification has been considered in this paper where the mean μii can be expressed as μ+αi+βi where αi and βi are 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 form μii = μ+αi+βi+cαi βi and numerical calculations made for the case of p = q = 6. For the sake of comparison the special case of α2i–1 = α2i, β2j–1 = β2j has also been considered, when an F-test is available with d.f. (4, 27). It is seen that the power of Tukey's statistic is slightly less than that of the F-test for smaller values of C 2 σ2 and ∑αi2σ2=∑βj2σ2, but for a wide range of values of these parameters, the performance of Tukey's statistic is better.