Relative estimates of combination weights, decision criteria, and internal noise based on correlation coefficients

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Abstract
A means by which relative combination weights may be determined is described for a signal detection model in which the decision variable is a weighted linear combination of several independent, normally distributed random variables, Xi’s. The first theorem presents the correlation between the binary response variables—signal versus no signal—and the component Xi. The second theorem presents a parallel result for the case that additive internal noise is present. Thus in psychophysical experiments, the relative combination weights may be obtained by correlating the observers’ responses and the input random variables. Third, three numerical methods which allow the evaluation of the relative magnitude of the decision criterion and the variance of a hypothetical additive internal noise are considered.

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