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Error Probabilities in Educational and Psychological Research

Author

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  • Rainer Westermann
  • Willi Hager

Abstract

The well-known problem of cumulating error probabilities is reconsidered from a general epistemological perspective, namely, the concepts of severity (Popper) and of fairness of tests. Applying these concepts to hypothesis-testing research leads to a reevaluation of the relative importance of the probabilities of Type 1 and Type 2 errors connected with those statistical hypotheses that have been derived from the substantive ones. It is shown that not only Type 1 but also Type 2 errors can cumulate. This cumulation is discussed for various basic types of empirical situations in which substantive hypotheses are examined by means of statistical ones. A new adjustment strategy based on the Dunn-Bonferroni inequality for planned tests is proposed and applied to some empirical examples.

Suggested Citation

  • Rainer Westermann & Willi Hager, 1986. "Error Probabilities in Educational and Psychological Research," Journal of Educational and Behavioral Statistics, , vol. 11(2), pages 117-146, June.
    • Handle: RePEc:sae:jedbes:v:11:y:1986:i:2:p:117-146
    DOI: 10.3102/10769986011002117
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