SIAM-AMS Proceedings
Volume 13
1981

DAVID L. NOREEN ¹

Abstract. A decision rule specifies how information from a presented stimulus situa-
tion 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 impor-
tant 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 deci-
sion 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 per-
formance. 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

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