Analyzing coefficients of psychophysical power functions.

Some mathematical properties of coefficients of power functions were analyzed. The size of correlations between intercepts (the logarithm of the coefficient) and exponents depends on the choice of unit of measurement of the physical stimuli. When the mean of logarithms of a set of responses is uncorrelated with the exponent, the absolute size of the correlation between the intercept and the exponent increases as the geometric mean of the stimulus measures deviates from one. When the geometric mean is less than one, the correlation is positive, and when it is greater than one, the correlation is negative. Similar trends hold for a nonzero correlation between the exponent and the mean logarithm of a set of responses. The power of statistical tests of differences between mean intercepts also depends on the geometric mean of the stimuli. Power is reduced as the geometric mean deviates from one. Effects are illustrated with real data.