a1 Department of Psychology, Ohio State University, Columbus, OH432 10-1222
How does subjective magnitude, S. increase as physical magnitude or intensity, I, increases? Direct ratings (magnitude scales; partition or category scales) can be fitted by the power function, S = aIb, in which S equals I raised to a power or exponent, b, and multiplied by a measure constant, a. The exponent is typically about twice as large for the magnitude scale (Stevens) as for the corresponding partition or category scale, but the higher exponent may be explained by the overly expansive way people use numbers in making magnitude estimations. The partition or category scale and the adjusted (for the use of number) magnitude scale for a given modality or condition generally agree with the neurelectric scale and the summated just noticeable difference (jnd) scale. A unified psychophysical law is proposed in which each jnd has the same subjective magnitude for a given modality or condition, subjective magnitude increases as approximately a power function of physical magnitude with the exponent ranging from near 0 to 1 (compressive function), and subjective magnitude depends primarily on peripheral sensory processes, that is, no nonlinear central transformations occur. An undue reliance on Weber's law blinded Fechner to the fact that the true psychophysical scale is approximately a power function. Rejecting Weber's law, which is not valid, means that we no longer have to choose between letting the summated jnd scale be a logarithmic function (Fechner's law) and introducing a nonlinear central transformation to make it into a power function (Brentano–Ekman-Teghtsoonian's law). Fechner and Stevens erred equally about the true psychophysical power function, whose exponent lies halfway between that of Fechner (an exponent approaching zero) and that of Stevens. To be reconciled, Fechnerians must give up the assumptions that Webers law is valid and that the jnd has the same subjective magnitude across modalities and conditions; Stevensians must give up the assumption that the unadjusted (for the use of number) magnitude scale is a direct measure of subjective magnitude.