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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.
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,
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