Parsimony in the construction of diagnostic scales
P. A. P. Moran · British Journal of Mathematical and Statistical Psychology · 1985
Diagnostic scales are used for a variety of purposes. A widely used example is Goldberg's General Health Questionnaire (GHQ). Consider a scale consisting of n items, scored 0 or 1, and such that the total score is taken as a measure of some psychological attitude. It is natural to suppose that the more items are used, the more effective the scale. It is shown by simple examples that if a series of items is used in which the discriminating power of each is decreasing in order, and if the first n of these items are used to form the scale, the discriminating power of the sum, as measured by its correlation with an unobserved underlying variable, may increase and decrease as n increases in an almost arbitrary manner. This helps to explain why the 30‐item GHQ scale performs equally well with the 60‐item GHQ scale in practice. It also points to the need to use scales in which the items are weighted. If the weights are chosen in an optimal manner the efficiency of the scale will not decrease as the number of items increases.