Type IV Errors and Analysis of Simple Effects

Games (1973) , Levin and Marascuilo (1973) and Marascuilo and Levin (1970 , 1976) have raised a number of issues pertaining to the analysis of simple effects in designs with two factors. This paper presents procedures for analyzing interactions and simple effects in two-way designs with suggestions for implementation in aptitude-treatment interaction studies. It is shown how to choose a composite hypothesis so as to avoid type IV errors, control the experimentwise error rate for the family implied by the composite hypothesis and determine type I and type II error rates for hypotheses based on fewer degrees of freedom implied by a composite hypothesis. A numerical example is used to illustrate the concepts. Apriori approaches are also considered and compared.