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ERIC Number: ED309182
Record Type: Non-Journal
Publication Date: 1977-Jun
Pages: 35
Abstractor: N/A
ISBN: N/A
ISSN: N/A
EISSN: N/A
Available Date: N/A
Coefficients for Tests from a Decision Theoretic Point of View. Research Report No. 1.
van der Linden, Wim J.; Mellenbergh, Gideon J.
From a decision theoretic viewpoint, a general coefficient (delta) for tests is derived. The coefficient is applied to three kinds of decision situations. The first situation involves a true score estimated by a function of the observed score of a subject on a test (point estimation). Using the squared error loss function and Kelley's formula for estimating the true score, it is shown that delta equals the reliability coefficient from classical test theory. The second situation involves the observed scores split into more than two categories after which different decisions are made for the categories (multiple decision). The general form of the coefficient is derived, and two loss functions suited to multiple decision situations are described. It is shown that, for the loss function specifying constant losses for the various combinations of categories on the true and observed scores, the coefficient can be computed under the assumptions of the beta-binomial model. The third situation involves splitting of the observed scores into only two categories and making different decisions for the categories (dichotomous decisions). Finally, it is shown that for a linear loss function and Kelley's formula for the regression of the true score on the observed score, the coefficient equals the reliability coefficient of classical test theory. (TJH)
Publication Type: Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: Twente Univ. of Technology, Enschede (Netherlands).
Grant or Contract Numbers: N/A
Author Affiliations: N/A