The relation between the generalized matching law and signal-detection theory.

The generalized matching law can be applied to a signal-detection matrix to give two equations. The first relates responding in the presence of the stimulus to the reinforcements for the responses, and the second relates responding in the absence of the stimulus to the reinforcements for the responses. Evidence for stimulus discrimination is given by biases that are opposite in sign in the two equations. As the logarithmic ratio and z proportion transformations are similar, the combination of the absolute values of the two logarithmic biases gives a measure equivalent to the signal-detection measures d' and eta. The two equations can also be combined to eliminate the biases caused by the signalling stimuli and to produce a generalized matching-law statement relating overall performance to the obtained reinforcements.