Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview
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SIAM-AMS Proceedings Volume 13 1981

Optimal Decision Rules for Some Common Psychophysical Paradigms


Abstract. A decision rule specifies how information from a presented stimulus situation may be used to determine a course of action, or response. This paper discusses decision rules that are optimal from the standpoint of both a minimal-error criterion and a maximized-expected-value objective. In the first three sections of the paper, the basic decision problem is outlined and well-known results from the yes-no and two-alternative forced-choice paradigms are reviewed. In subsequent sections, the same basic techniques of analysis used in the earlier sections are applied to the "same-different" and "ABX" discrimination tasks to obtain new results. For important special cases of these two discrimination tasks, the optimal decision strategy involves an implicit classification or "categorization" process on the part of the observer. While such a decision strategy differs in a fundamental way from one in which the observer compares differences in sensations ("Sensory Difference Theory"), the predictions of averaged percentage correct scores by the optimal decision strategy and by Sensory Difference Theory are nevertheless often quite similar -- for example, for data from a task involving the discrimination of tones differing in frequency, the two sets of predictions are within several percentage points of each other, and each set provides at least a first-order approximation to the obtained performance. The discussion section of the paper considers implications of these results and shows how the optimal decision rule analysis can be applied to a variety of other psychophysical paradigms.

1. Introduction. An experimenter can use a variety of different methods to investigate how an observer discriminates between two classes of stimuli. For instance, on any given trial he can select a single stimulus from one of the two classes, present it to the observer, and ask him to identify which class it represents (the "yes-no" or "two-stimulus complete identification" paradigm). Alternatively, he can present an instance of each of the two classes and ask the observer to specify which of the two possible presentation orders was used (the "two-alternative forced-choice" paradigm).

© 1981 American Mathematical Society

1980 Mathematics Subject Classification. Primary 92A27.
The author wishes to thank Dirk Vorberg for helpful suggestions, Stephen Coffin and John Holmgren for comments on an earlier version of the manuscript, and Beverly Heravi for assisance with the production of the manuscript.


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