Detection theory,micromatching, and the constant-ratio rule

The conformance of detection theory and micromatching with the constant-ratio rule (CRR) was determined by calculations for sets of three stimuli and subsets of two stimuli. For an arbitrary selection of sets, the CRR would be expected to hold quite well if either detection theory or micromatching lay behind the responses. For specific stimulus configurations, however, detection theory and micromatching differ considerably from one another and from the CRR. These configurations are found particularly for the univariate distributions, and this corresponds to empirical findings that the CRR holds better for multidimensional than for unidimensional stimuli. It is shown how the differences between the three theories in the implied constancies of ratios can be used in diagnosis of the basis ofempirical confusion matrices.