Some Comments Concerning the Use of Monotonic Transformations To Remove the Interaction in Two-Factor Anova's

Abstract

In his discussion of two-factor experiments, Winer (1971) points out that it may be desirable to remove the interaction (and thus obtain additivity of effects) through a monotonic data transformation. The present authors extend Lubin's (1961) discussion of ordinal and disordinal interactions by introducing the concept of "dual-ordinal." This concept is important since a transformation cannot bring about additivity of effects unless the interaction is "dual-ordinal" in nature. For the applied researcher, a simple rule-of-thumb is set forth which allows one to determine, through visual inspection of a single interaction graph, whether or not an interaction is dual-ordinal.