Choosing among Confusably Distributed Stimuli with Specified Likelihood Ratios

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Abstract
A study of choice behavior for overlapping normally distributed stimuli, with specified distribution locations, separations, dispersions, and likelihood ratios was carried out. A distributed stimulus consisted of a set of dots sampled from a bivariate normal distribution and placed on separate cards. Cards with dots from two or three distributions were mixed together and shown one by one to S, who had to choose from which distribution each dot derived, and give a confidence rating. Two theoretical choice models succeeded in bracketing the results: (a) statistical decision theory and (b) a probability micromatching (Mμ) model. Mμ states that choices are made probabilistically and in the proportion defined by the likelihood ratio. Confidence was not always monotonic with likelihood. The perceived distance between distribution centers was about twice the true distance.

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