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The Scaling Constant D in Item Response Theory

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Document pages: 6 pages

Abstract: In item response theory(IRT), the scaling constant D = 1.7is used to scale a discrimination coefficient a estimated with the logistic model tothe normal metric. Empirical verification is provided that Savalei’s [1] proposed a scaling constant of D = 1.749 based on Kullback-Leibler divergence appears to give the bestempirical approximation. However, the understanding of this issue as one of theaccuracy of the approximation is incorrect for two reasons. First, scaling doesnot affect the fit of the logistic model to the data. Second, the best scalingconstant to the normal metric varies with item difficulty, and the constant D = 1.749 is best thought of as theaverage of scaling transformations across items. The reason why the traditionalscaling with D = 1.7 is used issimply because it preserves historical interpretation of the metric of item discriminationparameters.

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