Ratios and differences in perceptual comparison: A reexamination of Torgerson’s conjecture

Publication date: August 2018Source: Journal of Mathematical Psychology, Volume 85Author(s): Randolph C. Grace, Nicola J. Morton, Matthew D. Ward, Anna J. Wilson, Simon KempAbstractHow do we compare stimuli that vary in magnitude? According to a well-known conjecture by Torgerson (1961), observers perceive only a single relation between stimuli, that is either a ratio or difference, but which one cannot be determined empirically. Previous research has used direct scaling procedures in which observers have judged ratios and differences numerically, but with mixed results. We used a novel behavioral task in which observers learned to produce non-symbolic ratios and differences by feedback and without explicit instruction. In two sets of experiments, observers viewed pairs of stimuli that varied in brightness, number of dots, or circle areas, and responded by clicking along a bar. Feedback was provided based on either the stimulus ratios or differences and the response location. Observers produced ratios and differences accurately, with average individual correlations of r=.94 and .95 across experiments, respectively. Regressions showed that responding was controlled jointly by ratios and differences, with the untrained relation predicting significant variance in approximately half of individual cases. Results were further supported by rank-order analyses, non-metric scaling analyses, and Monte Carlo simulations. Although Torgerson’s conjecture was originally proposed in expli...
Source: Journal of Mathematical Psychology - Category: Psychiatry & Psychology Source Type: research