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Hypothesis testing and the error of the third kind

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Author(s): Dieter Rasch

Journal: Psychological Test and Assessment Modeling
ISSN 2190-0493

Volume: 54;
Issue: 1;
Start page: 90;
Date: 2012;
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Keywords: Hypothesis testing | more-decision-problems | Neyman-Pearson Theory | power of a test

ABSTRACT
In this note it is shown that the concept of an error of the third kind (type-III-error) stems from a wrong understanding of the concept of hypothesis testing in mathematical statistics. If the alterna-tive hypothesis in a statistical testing problem states that the null hypothesis is wrong, then an error of the third kind cannot occur. This error can only be defined in more-decision-problems, i.e. prob-lems where we have to decide for one of more than two possibilities. Further the problem of the power of tests between a null and an alternative hypothesis is discussed. The notation of set theory is used because it allows for a concise notation of this type of statistical testing problems. The notation is explained in an appendix.

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