重さのマグニチュード尺度とカテゴリー尺度における個人差と反応の変動性

村上 隆

doi:10.4992/jjpsy.46.142

INDIVIDUAL DIFFERENCE AND RESPONSE VARIABILITY IN MAGNITUDE SCALE AND CATEGORY SCALE OF WEIGHT

TAKASHI MURAKAMI

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JOURNAL FREE ACCESS

1975 Volume 46 Issue 3 Pages 142-151

DOI https://doi.org/10.4992/jjpsy.46.142

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Published: September 30, 1975 Received: November 06, 1974 Available on J-STAGE: July 16, 2010 Accepted: - Advance online publication: - Revised: -
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Date of correction: July 16, 2010 Reason for correction: - Correction: ABSTRACT Details: Wrong : A simple model concerning the relationship between magnitude scales and category scales is proposed and tested. In the model, the distribution of sensory impressions of individual subject to each value of the stimulus, s, is assumed to be normal with unit variance and the mean f(s) which is called “standard scale” and is assumed to satisfy the following logarithmic function: f(s)=alns+b. (1) This function reflects the individual difference of response variability. As a matter of fact, parameter a in Eq. (1), called “discrimination coefficient”, is approximately equal to the reciprocal of Weber ratio (Eq. (3)).
The experiment reported here, therefore, was to see whether or not (1) standard scales for individual subjects can be represented by logarithmic function, (2) if (1) holds, discrimination coefficients for magnitude estimation, categorical judgments and identification are in the same order, and (3) power law exponents are predictable by discrimination coefficients according to Nakatani's theory.
Using 13 stimuli ranging 13g-200g, magnitude estimation experiments under the three conditions of the moduli, 10, 50 and 100, and 13-steps category rating experiment were run. Two-stimulus two-response identification experiment was also performed. The three sets of 25 magnitude estimates, 50 categorical judgments, and 150 identification responses for each stimulus were obtained from each of 12 Ss. Magnitude scales were defined as the logarithmic means of responses for each stimulus, and standard scales, f_r(s)'s, were derived by dividing these scale values by the square roots of mean logarithmic variances. Standard scales for categorical judgments, f_c(s)'s, were on the other hand, calculated on Condition D of Torgerson's law of categorical judgment in which the discriminal dispersions were fixed for unity.
Main results are as follows:
(1) Individual standard scales are approximated by logarithmic function although slight downward concavity in the mean magnitude scales and upward concavity in the mean category scale are detected (Figs. 1, 2) and component analyses of scale values suggest the existence of non-negligible individual difference (Tables 1, 2, 3).
(2) Discrimination coefficients for the magnitude scales are of the same order as for the category scales in the mean. Moreover, they are relatively correlated with each other. The mean of discrimination coefficients for the identification experiment, however, is remarkably larger than the others (Tables 5, 6).
(3) Power law exponents are independent of discrimination coefficients (Tables 6, 7).
(4) The mean Fechnerian scales derived from arithmetic means and standard deviations of magnitude estimates are more linearly related to the mean category scale than the mean standard magnitude scales (Fig. 3).
Right : Magnitude scales with 3 different moduli and a processed category scale of weight were constructed for each of 12 Ss using 13 stimuli ranging 13g-200g. 2-stimulus 2-response indentification experiment was also performed. Individual magnitude scale and category scale were approximated by power function and logarithmic function respectively, although slight but non-negligible deviations and individual difference existed. The variabilities of these 2 scales were in the same order while the variabilities in indentification experiment were remarkably small. Power law exponents were independent of these variabilities.

Abstract

Magnitude scales with 3 different moduli and a processed category scale of weight were constructed for each of 12 Ss using 13 stimuli ranging 13g-200g. 2-stimulus 2-response indentification experiment was also performed. Individual magnitude scale and category scale were approximated by power function and logarithmic function respectively, although slight but non-negligible deviations and individual difference existed. The variabilities of these 2 scales were in the same order while the variabilities in indentification experiment were remarkably small. Power law exponents were independent of these variabilities.

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