Daniel M. Ennis
Philip Morris Research Center and Department of Physiology
Medical College of Virginia
Department of Mathematics and Statistics
University of Guelph
From a mathematical modeling viewpoint, there are very close parallels between triad discrimination, preferential choice, and two-alternative identification under certain assumptions concerning the decision rules employed. The purpose of this chapter is to introduce a very general probabilistic model in a computationally simple form that can be used to model results obtained from several different types of psychological tasks. Chapter 11 contains a discussion of a number of probabilistic models of identification. One of these models, based on ordinal decision rules, will be covered in this chapter.
It might be useful to begin by providing a general overview of tasks involving three alternatives. First consider the situation in which all three alternatives are stimuli. Depending on the instructions, these tasks are variants of the Method of Triads. Two methods have been commonly discussed in the literature. Torgerson ( 1958) refers to one of them as the "complete method of triads," which we call Torgerson's Method of Triads, and the other as "Richardson's method of triadic combinations" ( 1938), which we call Richardson's Method of Triads. In Torgerson's Method of Triads, the three stimuli are presented to the subject in each of three independent trials. On each trial, one stimulus is designated as the standard. The subject's task is to select from the remaining two stimuli, the stimulus most similar to the standard. Each stimulus serves as the standard for one of the three trials. For instance, in the first trial, the subject's task might be to select which of Sj or Sk is most similar to Si. The symbol iPjk is the probability that Si is more similar to Sj than Sk. The three trials are independent and may give rise to different psychological magnitudes from trial to trial for the same stimulus. Richardson's Method of Triads involves a single presentation of the three stimuli and the subject's task is to judge which two objects are most alike perceptually