Open Journal of Statistics

Volume 7, Issue 5 (October 2017)

ISSN Print: 2161-718X   ISSN Online: 2161-7198

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The Scaling Constant D in Item Response Theory

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DOI: 10.4236/ojs.2017.75055    1,325 Downloads   1,951 Views   Citations


In item response theory (IRT), the scaling constant D = 1.7 is used to scale a discrimination coefficient a estimated with the logistic model to the 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 best empirical approximation. However, the understanding of this issue as one of the accuracy of the approximation is incorrect for two reasons. First, scaling does not affect the fit of the logistic model to the data. Second, the best scaling constant to the normal metric varies with item difficulty, and the constant D = 1.749 is best thought of as the average of scaling transformations across items. The reason why the traditional scaling with D = 1.7 is used is simply because it preserves historical interpretation of the metric of item discrimination parameters.

Cite this paper

Camilli, G. (2017) The Scaling Constant D in Item Response Theory. Open Journal of Statistics, 7, 780-785. doi: 10.4236/ojs.2017.75055.

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