is cross-modality matching, which generally involves subjects altering the magnitude of one physical quantity, such as the brightness of a light, so that its perceived intensity is equal to the perceived intensity of another type of quantity, such as warmth or pressure. Criticisms Stevens generally collected magnitude estimation data from multiple observers, averaged the data across subjects, and then fitted a power function to the data. Because the fit was generally reasonable, he concluded the power law was correct. A principal criticism has been that Stevens' approach provides neither a direct test of the power law itself nor the underlying assumptions of the magnitude estimation/production method: it simply fits curves to data points. In addition, the power law can be deduced mathematically from the Weber-Fechner logarithmic function (Mackay, 1963), and the relation makes predictions consistent with data (Staddon, 1978). As with all psychometric studies, Stevens' approach ignores individual differences in the stimulus-sensation relationship, and there are generally large individual differences in this relationship that averaging the data will obscure . Stevens' main assertion was that using magnitude estimations/productions respondents were able to make judgements on a ratio scale (i.e., if x and y are values on a given ratio scale, then there exists a constant k such that x = ky). In the context of axiomatic psychophysics, formulated a testable property capturing the implicit underlying assumption this assertion entailed. Specifically, for two proportions p and q, and three stimuli, x, y, z, if y is judged p times x, z is judged q times y, then t = pq times x should be equal to z. This amounts to assuming that respondents interpret numbers in a veridical way. This property was unambiguously rejected (, ). Without assuming veridical interpretation of numbers, formulated another property that, if sustained, meant that respondents could make ratio scaled judgments, namely, if y is judged p times x, z is judged q times y, and if y is judged q times x, z is judged p times y, then z should equal z. This property has been sustained in a variety of situations (, ). Critics of the power law also point out that the validity of the law is contingent on the measurement of perceived stimulus intensity that is employed in the relevant experiments. , under the condition that respondents' numerical distortion function and the psychophysical functions could be separated, formulated a behavioral condition