Academic journal article Attention, Perception and Psychophysics

On the Ability to Directly Evaluate Sensory Ratios

Academic journal article Attention, Perception and Psychophysics

On the Ability to Directly Evaluate Sensory Ratios

Article excerpt

Abstract The study explored whether participants could directly evaluate sensory ratios. The results indicate that they did not exhibit this ability for the extensive continuum of length and the intensive continua of brightness and brightness difference. Functional measurement analysis, combined with a chronometric analysis of responses, indicated that participants used mental counting for length and used difference evaluation for brightness and brightness difference. The finding that participants evaluated brightness differences under instructions to evaluate brightness ratios suggests that difference judgments may be a general human capability. It resolves questions raised by prior tests of Torgerson's conjecture and by prior consistency tests of ratio evaluation.

Keywords Psychophysical measurement. Ratio evaluation. Mental counting

(ProQuest:... denotes formulae omitted.)

Published online: 17 October 2012

# Psychonomic Society, Inc. 2012

The processes underlying metric responses are largely unknown despite the wide use of metric response measures in all fields of psychology, especially in social and personality psychology and in sensory psychophysics (Anderson, 2008; Gescheider, 1997; Marks, 1974; Wegener, 1982). A widespread and persistent assumption is that these processes are based on people's ability to directly evaluate ratios of mental intensities (Fullerton & Cattell, 1892; Lim, 2011; Luce, 2002; Merkel, 1888; Narens, 2007; Richardson & Ross, 1930; Stevens, 1975).

Torgerson's conjecture

Garner (1954b) found that participants subdivided a sensory interval in the same manner whether they were asked to subdivide it in terms of sensory differences or of sensory ratios. Using this finding, Torgerson (1961) hypothesized that people fail to distinguish sensory ratios from sensory differences. This hypothesis has been called Torgerson's conjecture (Birnbaum & Veit, 1974). The following are tests of Torgerson's conjecture.

For fixed sensory intensities, one may rank-order all the possible pairs of these intensities in terms of theoretical differences, theoretical ratios, judged differences, or judged ratios between the intensities in each pair. Theoretical differences and theoretical ratios imply different rank orders of pairs of intensities. Instead, judged differences and judged ratios have been found to yield the same rank order of pairs of intensities, in agreement with Torgerson's conjecture (Birnbaum & Elmasian, 1977; Mellers, Davis, & Birnbaum, 1984; Parker & Schneider, 1974; Parker, Schneider, & Kanow, 1975).

For a number n and the sensory intensities ΨA, ΨB, and Ψ, Ellermeier, Narens, and Dielmann (2003) had participants first produce the intensity n. Ψ and then produce the intensity ΨC by adding the difference |ΨA - ΨB| to n. Ψ. They also had participants first produce the intensity ΨD by adding |ΨA - ΨB| to Ψ and then produce the intensity n. ΨD. As predicted by Torgerson's conjecture, it turned out that ΨC 0 n. ΨD, as if participants did not distinguish ratios from differences.

These tests suggest that people do not discriminate sensory ratios from sensory differences. They fail to determine whether people evaluate only sensory ratios or only sensory differences. The following consistency tests help resolve this indeterminacy.

Given the sensory intensities ΨA, ΨB, and ΨC (ΨA < ΨB < ΨC), Fagot and Stewart (1969) had participants directly evaluate the ratios ΡAB 0 ΨA/ΨB, ΡBC 0 ΨB/ΨC, and ΡAC 0 ΨA/ΨC and the differences ΔAB 0 |ΨA - ΨB|, ΔBC 0 |ΨB - ΨC|, and ΔAC 0 |ΨA - ΨC|. Consistent ratio and difference evaluations imply that ΡAC 0 ΡAB. ΡBC and ΔAC 0 ΔAB + ΔBC, respectively. It turned out that ΡAC ≠ ΡAB. ΡBC and ΔAC 0 ΔAB + ΔBC. If Torgerson's hypothesis that people cannot distinguish ratios from differences holds, then Fagot and Stewart's (1969) results suggest that people are able only to evaluate sensory differences. …

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