Here - Tilburg University

Author and presenter
Kampen, Jarl; Wageningen University and Research Centre
Title
Ferguson's and Hankin's delta revisited: Towards a renewed interest in the
discriminating power of tests
Abstract
Discriminating power is a characteristic of health indices, tests and
questionnaires that is crucial for use of test scores in practice. Recently, renewed
attention has been paid to Ferguson's Coefficient of Test Discrimination (delta)
for test scores based on dichotomous items, and an extension thereof that
quantifies discrimination for test scores based on polytomous ordinal items. In
this article, four potential problems relating to Ferguson's delta and Hankins'
recent generalization are discussed. Alternative methods of analysis that test for
certain aspects of discriminative power are proposed.
The properties of Ferguson's delta and its generalization are illustrated by
mathematical argument, numerical examples, and the analysis of a real data set
consisting of ordinal scaled items (WHOQOL-BREF Domain 2).
It is shown that 1) Ferguson's delta in practical applications its maximal
value cannot be attained which obfuscates interpretation, 2) its statistical
significance cannot be computed reliably, 3) it is insensitive to the fineness of
test scores and 4) it is insensitive to variation in discriminating power over the
range of possible test scores.
It is concluded that the renewed attention for discriminative power can
help improve measurement in health. However, Ferguson's delta is not the most
effective coefficient for this purpose. The proposed alternative methods are
promising but require further assessment.