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Open Access Research article

Questionnaire discrimination: (re)-introducing coefficient δ

Matthew Hankins

Author Affiliations

King's College London, Department of Psychology (at Guy's), Institute of Psychiatry, London, UK

Department of Primary Care & Public Health, Brighton & Sussex Medical School, Brighton, UK

Brighton & Sussex University Hospitals NHS Trust, Royal Sussex County Hospital, Brighton, UK

BMC Medical Research Methodology 2007, 7:19  doi:10.1186/1471-2288-7-19

Published: 18 May 2007



Questionnaires are used routinely in clinical research to measure health status and quality of life. Questionnaire measurements are traditionally formally assessed by indices of reliability (the degree of measurement error) and validity (the extent to which the questionnaire measures what it is supposed to measure). Neither of these indices assesses the degree to which the questionnaire is able to discriminate between individuals, an important aspect of measurement. This paper introduces and extends an existing index of a questionnaire's ability to distinguish between individuals, that is, the questionnaire's discrimination.


Ferguson (1949) [1] derived an index of test discrimination, coefficient δ, for psychometric tests with dichotomous (correct/incorrect) items. In this paper a general form of the formula, δG, is derived for the more general class of questionnaires allowing for several response choices. The calculation and characteristics of δG are then demonstrated using questionnaire data (GHQ-12) from 2003–2004 British Household Panel Survey (N = 14761). Coefficients for reliability (α) and discrimination (δG) are computed for two commonly-used GHQ-12 coding methods: dichotomous coding and four-point Likert-type coding.


Both scoring methods were reliable (α > 0.88). However, δG was substantially lower (0.73) for the dichotomous coding of the GHQ-12 than for the Likert-type method (δG = 0.96), indicating that the dichotomous coding, although reliable, failed to discriminate between individuals.


Coefficient δG was shown to have decisive utility in distinguishing between the cross-sectional discrimination of two equally reliable scoring methods. Ferguson's δ has been neglected in discussions of questionnaire design and performance, perhaps because it has not been implemented in software and was restricted to questionnaires with dichotomous items, which are rare in health care research. It is suggested that the more general formula introduced here is reported as δG, to avoid the implication that items are dichotomously coded.