Abstract
A critique of Hankins, M: 'How discriminating are discriminative instruments?' Health and Quality of Life Outcomes 2008, 6:36.
Highlights
Hankinsintroduced Ferguson's coefficient δ as an index of discrimination, to be distinguished from the well-known measurement properties validity and reliability [1,2]
Scrutinizing Hankins' examples and adding one of his own, Norman illustrated his main point that Ferguson's δ fails to distinguish between true differences and measurement error [4]
Hankins remarked that both Norman and Wyrwich made too much of his examples, and seemed to have missed his point, which is that Ferguson's δ is an additional index of an instruments' measurement properties, beside reliability, validity and interpretability, and that Ferguson's δ can only be computed on the assumption that the measurement is valid and reliable [6]
Summary
Hankins (re-)introduced Ferguson's coefficient δ as an index of discrimination, to be distinguished from the well-known measurement properties validity and reliability [1,2]. It should be noted that Ferguson's δ treats the score categories as the scores of a nominal (or categorical) scale: all differences (if present) between all subjects are valued . The subjects are uniformly distributed over the 10 score categories and we assume no measurement errors (Figure 2). 3x3 a GFirgauprheica2l representation of how Ferguson's δ 'works' Graphical representation of how Ferguson's δ 'works' In this sample 30 subjects are uniformly distributed over a scale with 10 score categories (i), so that the frequency (fi) for all i scores is 3. Graphical representation of the same 30 subjects, and their mutual comparisons, as, but with a little measurement error added to their scores, resulting in different frequencies (fi) per score category. This has nothing to do with the discrimination of the instrument
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