Theories of stimulus scaling in visual psychophysics have been dominated by some form of a power function of stimulus strength. For example, Nachmias and Kocher (
1970) and Pelli (
1987) added a power function to signal detection theory with Gaussian distributions to predict psychometric functions. Similarly, the Weibull function (Quick,
1974) contains a power function of the stimulus strength. Pelli (
1987) compared the two models of the psychometric function and found they are very similar: In a two-alternative forced-choice experiment, the two exponents are approximately proportionally related with a Gaussian exponent of 1.0 equivalent to a Weibull exponent of about 1.2. In this article, power function scaling is incorporated into the power-rate diffusion model and fit to both response time and accuracy. The results were similar to previous measurements based on accuracy alone. For direction-of-motion discrimination, we find best-fitting power function exponents of 1.2, 1.2, and 1.0 for
Experiments 1,
2, and
4, respectively. These values are in the range of exponents estimated using a Weibull function of accuracy data (Weibull exponent = 0.9−1.4, Gold & Shadlen,
2003; see also Britten, Shadlen, Newsome, & Movshon,
1992). For contrast discrimination, we find a mean exponent of 1.15 on the change in contrast. This value is similar to the value of the exponent of Gaussian functions fit to accuracy data (exponent = 1.05, Leshowitz et al.,
1968). For contrast detection, we find a mean exponent of 2. This value is also similar to the value of exponents reported in earlier experiments (Gaussian exponent = 2.0, Leshowitz et al.,
1968; Weibull exponent = 3.0, Foley & Legge,
1981). In summary, for the three cases studied, the exponents measured in response time experiments are similar to those measured in accuracy experiments.