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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 57, Iss. 3 — Mar. 1, 1967
  • pp: 380–382

Interval Scales, Ratio Scales, and Additive Scales for the Sizes of Differences Perceived between Members of a Geodesic Series of Colors

DEANE B. JUDD  »View Author Affiliations

JOSA, Vol. 57, Issue 3, pp. 380-382 (1967)

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From larger—smaller judgments of color differences, compared visually two at a time, the perceived sizes may be evaluated on an interval scale. Given numbers B so evaluated, and such that B is linearly connected to some power p, of the physical measure D (such as distance on any chromaticity diagram) of the differences, the additive constant Kbr such that the numbers B+Kbr are expressed on a ratio scale may be found from judgments of the ratio of sizes of pairs of differences. To evaluate p, it is sufficient to observe the three differences, 12, 23, and 13 between the pairs of three colors, 1, 2, 3, forming a geodesic series, and chosen so that B12 is not much different from B23. The scale formed by the numbers (B+Kbr)1/p is additive if the D scale is additive. If the largest of the color differences judged exceeds the smallest by a factor not greater than 3, a close approximation to the (B+Kbr)1/pscale may be found without evaluating Kbr discovery that scales based on the additivity condition: (B12+Kbd)1/p+(B13+Kbd)1/p = (B13+Kbd)1/p, though it implies that Kbd depends strongly on p, are essentially identical regardless of the choice of p between 1 and ⅓. It is sufficient therefore, to derive the additive scale by setting p= 1, and computing Kbd as B13B12B23.

DEANE B. JUDD, "Interval Scales, Ratio Scales, and Additive Scales for the Sizes of Differences Perceived between Members of a Geodesic Series of Colors," J. Opt. Soc. Am. 57, 380-382 (1967)

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  1. G. Wyszecki, J. Opt. Soc. Am. 414, 725 (1954); D. B. Judd, J. Opt. Soc. Am. 45, 673 (1955).
  2. H. A. David, The Method of Paired Comparisons (Hafner Publishing Co., New York, 1963), Sec. 1.3 and Ch. 4, especially p. 55.
  3. J. E. Jackson and M. Fleckenstein, Biometrics 13, 51 (1957).
  4. W. S. Torgerson, Theory and Methods of Scaling (John Wiley & Sons, New York, 1958), p. 271.
  5. D. L. MacAdam, J. Opt. Soc. Am. 53, 754 (1963).
  6. G. L. Howett, Report of Eighth Meeting of OSA Committee on Uniform Color Scales, 20 November 1964, p. 4, unpublished.

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