Comparison of two theories of "ratio" and "difference" judgments.

This article examines the hypothesis that judges compare stimuli by ratio and subtractive operations when instructed to judge" "ratios" and "differences." Rule and Curtis hold that magnitude estimations are a power function of subjective values, with an exponent between 1.1 and 2.1. Accordingly, the two-operation model tested assumes magnitude estimations of "ratios" are a comparable power function of subjective ratios. In contrast, Birnbaum and Veit theorize that judges compare two stimuli by subraction for both "ratio" and "difference" instructions and that magnitude estimations of "ratios" are approximately an exponential function of subjective differences. Three tests were used to compare the theory of one operation with the two-operation theory for the data of nine experiments. The results strongly favor the theory that observers use the same operation for both instructions.

[1]  S. Parker,et al.  The perceptual basis of loudness ratio judgments , 1976 .

[2]  D. W. Curtis,et al.  Magnitude judgments and difference judgments of lightness and darkness: a two-stage analysis. , 1974, Journal of experimental psychology.

[3]  D. Weiss.  Averaging: An empirical validity criterion for magnitude estimation , 1972 .

[4]  Michael H. Birnbaum,et al.  Using contextual effects to derive psychophysical scales , 1974 .

[5]  Clairice T. Veit,et al.  Scale convergence as a criterion for rescaling: Information integration with difference, ratio, and averaging tasks , 1974 .

[6]  M. Birnbaum.  Reply to Eisler: On the subtractive theory of stimulus comparison , 1979 .

[7]  S. S. Stevens.  Issues in psychophysical measurement. , 1971 .

[8]  D. W. Curtis,et al.  Input and output transformations from magnitude estimation. , 1970, Journal of experimental psychology.

[9]  Patrick Suppes,et al.  Foundations of measurement , 1971 .

[10]  D. W. Curtis,et al.  Conjoint scaling of subjective number and weight. , 1973, Journal of experimental psychology.

[11]  C T Veit,et al.  Ratio and subtractive processes in psychophysical judgment. , 1978, Journal of experimental psychology. General.

[12]  D. W. Curtis,et al.  Magnitude judgments of brightness and brightness difference as a function of background reflectance. , 1972, Journal of experimental psychology.

[13]  A. Einstein.  Relativity: The Special and the General Theory , 2015 .

[14]  G. H. Robinson.  Biasing power law exponents by magnitude estimation instructions , 1976 .

[15]  B. Mellers,et al.  Measurement and the mental map , 1978 .

[16]  Lawrence E. Marks,et al.  On scales of sensation: Prolegomena to any future psychophysics that will be able to come forth as science , 1974 .

[17]  C. T. Veit.  Analyzing "ratio" and "difference" judgments: A reply to Rule and Curtis. , 1980 .

[18]  T. L. Harrington,et al.  Erratum to: A test of a two-stage model of magnitude judgment , 1968 .

[19]  D. W. Curtis,et al.  Subject differences in input and output transformations from magnitude estimation of differences. , 1977, Acta psychologica.

[20]  William P. Banks,et al.  The apparent magnitude of number scaled by random production , 1974 .

[21]  Clairice T. Veit,et al.  Scale-flee tests of an additive model for the size-weight illusion , 1974 .

[22]  D. W. Curtis.  Magnitude estimations and category judgments of brightness and brightness intervals: a two-stage interpretation. , 1970, Journal of Experimental Psychology.

[23]  Warren S. Torgerson,et al.  Distances and ratios in psychophysical scaling , 1961 .

[24]  D. W. Curtis,et al.  Ordinal properties of subjective ratios and differences: Comment on Veit. , 1980, Journal of experimental psychology. General.

[25]  Michael H. Birnbaum,et al.  Nonmetric tests of ratio vs. subtractive theories of stimulus comparison , 1978 .

[26]  D. W. Curtis,et al.  Reevaluation of two models for judgments of perceptual intervals , 1973 .

[27]  S. J. Rule.  Comparisons of intervals between subjective numbers , 1972 .

[28]  S. Parker,et al.  Ratio scale measurement of the perceived lengths of lines. , 1975, Journal of experimental psychology. Human perception and performance.

[29]  Koch Sigmund Ed,et al.  Psychology: A Study of A Science , 1962 .

[30]  H. Eisler.  On the ability to estimate differences: A note on Birnbaum’s subtractive model , 1978 .

[31]  Michael H. Birnbaum,et al.  Judgments of differences and ratios of numerals , 1975 .

[32]  M. Birnbaum,et al.  Loudness “ratios” and “differences” involve the same psychophysical operation , 1977 .

[33]  E. Poulton.  The new psychophysics: Six models for magnitude estimation. , 1968 .

[34]  Fred Attneave,et al.  Perception and related areas. , 1962 .