On Testing for Non‐Additivity in Factorial Experiments

Abstract

In analysis of variance the assumption of non-additivity has more serious consequences on the interpretation of results than the assumptions of non-normality or non-homogeneity of variances.TUKEY (1949, 1955) suggested a procedure for separating out a single degree of freedom for non-additivity ror two factor and multi-factor experiments, respectively. In multifactor experiments Tukey's procedure does not indicate which combinations of the factors contribute to non-additivity. In this paper a procedure is proposed which separates out a sum of squares with a single degree of freedom from each of the 2'-P-1 interactions in a P-factor experiment.Key words: Non-additivity ; Tukey's one degree of freedom. WILK, M. B. and KEMPTHORNE, O., 1957: Non-additivity in the latin square design. J.A.S.A. 52, 218. YATES. F. A., 1972: A Monte-Carlo trial on the behaviour of non-additivity test with non-normal ZAFAR-YAB, M.. 1974: Non-additivity in analysis of variance. M. Sc.