Stevens’ idea of “direct measurement” of stimulus magnitude is extended to the direct measurement of stimulus differences. An important extension of Wave Theory provides predictions of response probabilities from single direct measures of comparative difference. As an illustration of the method, in an experiment 20 university students compared, only once, each of 16 job pairs, judging which has the larger salary and creating the size of salary differences. The correlation between a theoretical measure of the size of perceived salary difference and the direct measures of perceived salary difference is 0.99. The probability of correctly predicting individual binary choices between jobs, based on the students’ generated measures of perceived stimulus difference, ranges to 1.00 from 0.935. This new theory draws together Stevens and Fechner by showing that they perceived the same underlying psychological events through perfectly related measures of subjective experience.