Linear and nonlinear cue utilization in the identification of individual members of two bivariate normal populations

Abstract

An attempt was made to investigate the decision processes of subjects in a bivariate decision making task, similar to that facing a medical specialist who is required to classify a patient as belonging to one of a number of possible disease populations on the basis of the patient's scores of two predictor cues. It was felt that such tasks had been largely neglected in experimental psychology, where the tendency has been towards requiring subjects to learn relationships between continuous predictor variables and a continuous criterion, rather than between continuous predictor variables and a categorical criterion. When the relationship between the predictor variables is the same in both the populations to be discriminated, the best decision function is based on a linear combination of the cues (Fisher’s Linear Discriminant Function). It was found that the decisions of those subjects who learned to use the cues in a way which was at all valid in such situations, could be well approximated by a model which weighted the two cues equally in a linear combination and based it’s decisions on the result. When the relationship between the predictor variables differs from one population to the other, however, the best decision function becomes more complex, including terms in the squares and cross-products of the cues. It was felt that such situations are particularly relevant to medical decision making where clinicians have frequently claimed that the "pattern" of scores of a patient is important, not Just the individual scores on each cue. It was found that if differences in cue intercorrelation were large, then subjects seemed to inolude in their iii decision processes, some nonlinear term to take account of this fact. If, however, differences in cue intercorrelation were only moderate, or if the correlations involved were large hut negative, this seemed to go unnoticed by the subjects and did not lead to any reliance on nonlinear terms. The results show that previous findings in "real life" tasks, that decision making processes could be adequately represented as linear combinations of cues, may be due more to the linear nature of the tasks than to any predisposition towards linear processes on the part of human decision makers, and that the statistical properties of "real life" tasks must be more thoroughly investigated before it is assumed that they require nonlinear decision processes.