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 fo...

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Bibliographic Details
Published in:Journal of educational statistics 1978-07, Vol.3 (2), p.121-143
Main Authors: Betz, M. Austin, Gabriel, K. Ruben
Format: Article
Language:English
Subjects:
Academic achievement
Confidence interval
Critical values
Degrees of freedom
Educational research
Error rates
Factorial design
Sample size
Teaching methods
Teaching styles
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Summary: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.
ISSN:0362-9791
DOI:10.2307/1164881