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Journal Article

Error Probabilities in Educational and Psychological Research

Rainer Westermann and Willi Hager
Journal of Educational Statistics
Vol. 11, No. 2 (Summer, 1986), pp. 117-146
DOI: 10.2307/1164973
Stable URL: http://www.jstor.org/stable/1164973
Page Count: 30
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Error Probabilities in Educational and Psychological Research
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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.

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