Testing for interactions of unbalanced case using analysis of means

Abstract

An ANOM procedure is presented for testing the significance of two-factor interactions for unbalanced case. When at least one factor is at only two levels, the technique is the same as that of Ott (1967) and P.R. Nelson (1988) except that we have used the critical value by using the Sidak``s multiplicative inequality. This technique can be extended to the case in which both factors are at more than two levels. Tables of the necessary critical values $g(\alpha;(p,q);\nu)$ are given for $\alpha = 0.05$ and 0.01 ; (p,q) combinations satisfying $3\le p \le q \le 5$; and various degrees of freedom $\nu$. We present and prove the formula of the variance of the interactions for the n-way model.