Discrimination and reliability: Equal partners?
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Open Access
Letter to the Editor
Discrimination and reliability: Equal partners? Geoffrey R Norman Address: McMaster University, Hamilton, Canada Email: Geoffrey R Norman - [email protected]
Published: 16 October 2008 Health and Quality of Life Outcomes 2008, 6:81
doi:10.1186/1477-7525-6-81
Received: 6 August 2008 Accepted: 16 October 2008
This article is available from: http://www.hqlo.com/content/6/1/81 © 2008 Norman; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract A critique of Hankins, M article: How discriminating are discriminative instruments?" Health and Quality of Life Outcomes 2008, 6:36
Letter to the editor There are several definitions of discrimination. Two, from the Webster dictionary, are: 1) the process by which two stimuli differing in some aspect are responded to differently, and 2) the quality or power of finely distinguishing. It seems to me that the manuscript by Hankins [1], in attempting to elaborate on 1), shows considerable absence of 2). To begin with, a small disclaimer: The “McMaster Framework” is hardly endorsed by all at McMaster. In fact, my co-author Dave Streiner and I, both of us originally from McMaster, in our textbook [2] specifically challenge the Kirshner and Guyatt [3] notion of different kinds of instruments for different purposes. And now to the matter at hand. Hankins [1] attempts to show that reliability is not a good measure of discrimination, and that instruments can be reliable but not discriminating, and vice versa. But, while he refers to formulas for both reliability and discrimination (more on this in a moment), he does not actually define either. This is not just pedantry; in my view, reliability is, by definition, an index of the ability of an instrument to discriminate among individuals. To quote an authority on the subject, me [1]:
viduals, since the magnitude of the coefficient is directly related to the variability between subjects”. An almost perfect paraphrase of the Webster definition above. Fundamentally all reliability coefficients are intraclass coefficients, and mathematically reflect the proportion of the variance in the observations that relate to real differences among subjects. The formula is:
Reliability =
Variance ( Subjects ) Variance ( Subjects ) + Variance ( error )
The numerator expresses variability due to different responses among individuals. The denominator expresses all variability. So reliability is a measure of the extent to which people differ, expressed as a number between 0 and 1. QED – reliability is discrimination. This is also precisely consistent with Hawkins' “test discrimination”. However there is a very important concept buried in the formula. Discrimination and reliability is a matter of true differences between subjects, in contrast to differences arisi
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