A Theory of "Ratios" Birnbaum (1978) theorized that judgments of "ratios" of psychophysical magnitudes such as loudness (Birnbaum & Elmasian, 1977) satisfy the following equation, Rij = ae(si - sj) + b, where Rij is the judged "ratio" of sensation of stimulus i to stimulus j; si and sj are the subjective values of the stimuli; ex is the exponential function; a and b are constants.
References Birnbaum, M. H. (1978). Differences and ratios in psychological measurement. In N.J. Castellan & F. Restle, (Eds.), Cognitive Theory, Vol. 3. Hillsdale, N.J.: Lawrence Erlbaum Associates, p. 33-74. Birnbaum, M. H., & Elmasian, R. (1977). Loudness ratios and differences involve the same psychophysical operation. Perception & Psychophysics, 22,383-391. Return to Index of Examples