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Type IV Errors and Analysis of Simple Effects

Author

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  • M. Austin Betz
  • K. Ruben Gabriel

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.

Suggested Citation

  • M. Austin Betz & K. Ruben Gabriel, 1978. "Type IV Errors and Analysis of Simple Effects," Journal of Educational and Behavioral Statistics, , vol. 3(2), pages 121-143, June.
    • Handle: RePEc:sae:jedbes:v:3:y:1978:i:2:p:121-143
    DOI: 10.3102/10769986003002121
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