An experimental check on Stevens’s explanation of the partition paradox by successive doubling and bisecting

Abstract

Scaling methods based on direct estimation of sensory ratios and intervals give discrepant results (the partition paradox). Stevens's explanation of this discrepancy was tested here. Given a psychological magnitude, 1jJ, observers were required to select a magnitude 21jJ, and subsequently to bisect the interval between IjJ and 21jJ. Stevens's hypothesis predicts that the bisected psychological magnitude falls between 1.411jJ and 1.501p. The hypothesis is not substantiated, since a bisected magnitude of 1.551jJ was obtained. Furthermore, observers had to bisect the interval between IjJ and an imagined magnitude of 21jJ. The results show that observers are able to producereliably both a visual and a representational double.Ratio scaling is based on the assumption that the human observer is capable of directly reporting sensory ratios between two values of a perceptual variable. The method of fractionation or multiplication requires the observer to estimate, or produce, fractions or multiples (ratios) of given values of a perceptual variable. Interval scaling is based on the assumption that the observer is capable of directly reporting sensory intervals. The method of bisection requires the observer to set the value of a perceptual variable until it is midway between two fixed values of the same perceptual variable, thus producing two equal-appearing intervals.Typically, the exponent of a power function obtained by the method of bisection is smaller than the exponent obtained by a method based on ratio scaling (Stevens, 1955). Thus, methods based on direct estimation of sensory intervals and ratios do not give consistent results (the partition paradox). According to Stevens (Stevens, 1971, 1975Stevens & Davis, 1938), this discrepancy originates in the method of bisection. In bisecting a sensory interval, the observer can adopt two different strategies: He can set the middle value midway between the two end values to obtain two equal-appearing intervals, or he can set the middle value so that the ratio of the middle value to the lower value equals the ratio of the higher value to the middle value. The actual performance, Stevens argued, represents a compromise between these two possibilities.In an experiment by Garner (1954), a group of observers set a variable stimulus so that the corresponding perceptual value, lIIv' stood in the middle of the I wish to thank Martha Teghtsoonian for a careful reading of the first draft of this manuscript. 294two perceptual values lIIi and lpj' The setting was carried out under two conditions. In one condition, the observers were instructed to set the variable stimulus to produce equal distances, that is, lpv-lpi =lpj -lIIv'In the other condition, they had to set the variable stimulus to produce equal ratios, that is, lpv/lpi = lpj!lpv' For most observers, the selected value for the variable stimulus was the same under the two conditions. If an estimate of the values lpi and lpj were at our disposal, we would be in a position to know whether the observer under the bisection task ap...

The judgment operation of ratio production

“…Masin (1983) had participants produce the sensory intensity 2 s and subsequently the intensity b that bisected the interval between s and 2 s . If v 2, then b 1.5 s .…”