Type IV Errors and Analysis of Simple Effects

M. Austin Betz and K. Ruben Gabriel

Journal of Educational and Behavioral Statistics, 1978, vol. 3, issue 2, 121-143

Abstract: 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.

Keywords: Type IV Error; Simple Effect; Composite Hypothesis; Alpha Level; Power; Effect Size; Apriori Approach; Simultaneous Test Procedure; Multiple Comparisons; Simultaneous Inference (search for similar items in EconPapers)
Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:3:y:1978:i:2:p:121-143

DOI: 10.3102/10769986003002121

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