Tests of product and additive scaling axioms

Abstract

For convenience in testing, the product axiom may be written in its logarithmic form:A special feature of these axioms is that they are applied before any scale is constructed, and a subset of the data is used to predict the residual data. Tests based on scales constructed from all the data are more likely to obscure possible violations ApparatusThe apparatus, described in detail elsewhere (Eskildsen, 1963), provided four luminous white circular targets 13 mm in diam, placed horizontally and separated by 90 mrn, center to center. The apparatus was located in a light-tight visual tunnel, and Ss were seated at a distance of 12 ft from the targets in an ordinary classroom desk seat. S reported his estimations orally. A brief dark-adaptation period of 15 min preceded each experimental session. METHOD SubjectsSubjects were two male and four female undergraduates at the University of Oregon, and were paid $1.50 per hour for their time. ProcedureThree of the Ss (randomly selected) did the difference estimation task first and the ratio task second, and the other three Ss performed the tasks in reverse order.Difference estimation task. Each trial began with the presentation of the standard pair, which consisted of two adjacent lights, one set at 30 (always on the left) and the other at 100 ft-L. By pushing a button S could then move a shutter to view the comparison pair which was always to the left of the standard pair. The S was told to call the difference in brightness for the standard pair 100, and to assign a number to the difference in brightness for the comparison pair in accord with usual magnitude estimation instructions. The S could move the shutter back and forth as many times as he wished to compare the two pairs. The trial ended when S responded and E turned out the lights. The following instructions were read for the difference estimation task:

On the ability to directly evaluate sensory ratios

“…These results agree with Torgerson's conjecture and Fagot and Stewart's (1969) consistency tests. They suggest that the reason why ratio evaluation and difference evaluation are based on a single judgment operation is that participants use the difference operation for both evaluations.…”

“…It turned out that Ρ AC ≠ Ρ AB ⋅ Ρ BC and Δ AC 0 Δ AB + Δ BC . 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.…”

“…Given the sensory intensities Ψ A , Ψ B , and Ψ C (Ψ A < Ψ B < Ψ C ), Fagot and Stewart (1969) had participants directly evaluate the ratios Ρ AB 0 Ψ A /Ψ B , Ρ BC 0 Ψ B /Ψ C , and Ρ AC 0 Ψ A /Ψ C and the differences Δ AB 0 |Ψ A -Ψ B |, Δ BC 0 |Ψ B -Ψ C |, and Δ AC 0 |Ψ A -Ψ C |. Consistent ratio and difference evaluations imply that Ρ AC 0 Ρ AB ⋅ Ρ BC and Δ AC 0 Δ AB + Δ BC , respectively.…”

Inverse cross-modality matching: A test of ratio judgment consistency for group and individual data

“…IRECT HlsK sClUND PRESSURE !DYNES/50 eM) (Fagot & Stewart,1%9). What has emerged from these studies is that (1) inverse attribute scales tend to be reciprocals of their counterpart scales, but that some evidence suggests they are not perfect reciprocals; (2) multiple and fractional judgments are nearly reciprocally related for group data and for some individuals, but that many individuals do not show reciprocal asymmetry; and (3) multiplicative transitivity does not usually hold for group or individual subject data (Fagot & Stewart, 1969). Inverse cross-modality matching provides a different technique for the assessment of consistency.…”

The judgment operation of ratio production

“…Since v 1 v 2 v 3 , the equality n 1 n 2 n 3 occurs when n i v i (where i 1, 2, or 3). Fagot and Stewart (1969) found that n 1 n 2 n 3 . Consequently, n i v i .…”