Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview
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2. In an important special case of the same-different task when "same" and "different" trials are balanced in the experimental design, the optimal decision rule specifies that the observer should separately categorize the stimuli appearing in the two presentation intervals, and then give his response based on the resulting categorical information.
3. In the optimal decision strategy for the ABX discrimination task, the observer matches forced-choice information from the two standards against information from the third, test stimulus exactly as if he were making an optimal same-different judgment on the basis of the two sources of information.
4. For both the same-different and ABX discrimination tasks, it is straightforward to construct examples that show how the optimal decision strategy differs from a decision strategy in which the observer uses differences in sensations. Nevertheless, in many cases the two theoretical approaches give very similar values for the predicted percentage of correct responses. For the tone frequency discrimination data of Creelman and Macmillan ( 1979), both of these approaches correctly predict that the percentage of correct responses should increase as one successively examines same-different, ABX, yes-no and two-alternative forced-choice tasks, and the numerical values of the models' predictions provide at least a first-order approximation of the obtained values.
5. The optimal decision rule analysis can be used to generate predictions of an observer's performance in a variety of other paradigms. For instance, it predicts identical percentage correct scores for important special cases of ABX and AXA discrimination tasks, and this prediction was found to be approximately true for the data of Creelman and Macmillan ( 1979). A number of other new predictions await detailed experimental tests.


Creelman C. D. and Macmillan N. A. "Auditory phase and frequency discrimination: A comparison of nine procedures". Journal of Experimental Psychology: Human Perception and Performance, 1979, 5, 146-156.

Green D. M. and Swets J. A. Signal detection theory and psychophysics. Huntington, New York: Robert E. Krieger Publishing Company, 1974.

Hefner R. A. Extensions of the law of comparative judgment to discriminable and multidimensional stimuli. Unpublished doctoral dissertation, University of Michigan, 1958.

Kac M. "A note on learning signal detection". IRE Transactions on Information Theory, 1962, IT-8, 126-128.

Kac M. "Some mathematical models in science". Science, 1969, 166, 695-699.

Kaplan H. L., Macmillan N. A., and Creelman C. D. "Tables of d′ for variable-standard discrimination paradigms". Behavior Research Methods and Instrumentation, 1978, 10, 796- 813.

Krueger L. E. "A theory of perceptual matching". Psychological Review, 1978, 85, 278-304.

Laming D. Mathematical psychology. New York: Academic Press, 1973.


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