Psychophysical scaling of similarity of pentagons

HIROSHI HOJO

doi:10.4992/psycholres1954.28.11

HIROSHI HOJO

Author information

Keywords: form perception, psychophysical scaling, maximum likelihood estimation, directional rank orders, Akaike's information criterion (AIC) statistic

JOURNAL FREE ACCESS

1986 Volume 28 Issue 1 Pages 11-20

DOI https://doi.org/10.4992/psycholres1954.28.11

Details

Published: April 30, 1986 Received: October 29, 1984 Available on J-STAGE: February 24, 2009 Accepted: November 09, 1985 Advance online publication: - Revised: -
Correction information
Date of correction: February 24, 2009 Reason for correction: - Correction: TITLE Details: [in Japanese]

Date of correction: February 24, 2009 Reason for correction: - Correction: SUBTITLE Details: [in Japanese]

Date of correction: February 24, 2009 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Department of Educational Psycholugy, School of Education, Haseda University

Right :
1) Department of Educational Psychology, School of Education, Hascda University

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Akaike, H. 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
Attneave, F. 1950 Dimensions of similarity. American Journal of Psychology, 63, 516-556.
Attneave, F. 1957 Physical determinants of the judged complexity of shapes. Journal of Experimental Psychology, 53, 221-227.
Attneave, F., & Arnoult, M. D. 1956 The quantitative study of shape and pattern perception. Psychological Bulletin, 53, 452-471.
Beals, R., Krantz, D. H., & Tversky, A. 1968 Foundations of multidimensional scaling. Psychological Review, 75, 127-142.
Behrman, B. W., & Brown, D. R. 1968 Multidimensional scaling of form: A psychophysical analysis. Perception _??_ Psychophysics, 4, 19-25.
Brown, D. R., & Owen, D. H. 1967 The metrics of visual form: Methodological dyspepsia. Psychological Bulletin, 68, 243-259.
Hojo, H. 1983 A maximum likelihood method for additive clustering and its applications. Japanese Psychological Research, 25, 191-201.
Hojo, H. 1985 Psychophysical scaling of dot dispersion. Japanese Psychological Research, 27, 1-10.
Hojo, H. (In press) Psychophysical scaling of smiling faces. Japanese Psychological Research.
Kaiho, H. 1970 Multidimensional approach to the study of form perception. Japanese Psychological Review, 13, 305-317. (In Japanese)
Krantz, D. H., & Tversky, A. 1975 Similarity of rectangles: An analysis of subjective dimensions. Journal of Mathematical Psychology, 12, 4-34.
Künnapas, T., Mälhammar, G., & Svenson, O. 1964 Multidimensional ratio scaling and multidimensional similarity of simple geometric figures. Scandinavian Journal of Psychology, 5, 249-256.
Leeuwenberg, E. L. J. 1971 A perceptual coding language for visual and auditory patterns. American Jounral of Psychology, 84, 307-350.
Schönemann, P. H. 1977 Similarity of rectangles. Journal of Mathematical Psychology, 16, 161-165.
Schönemann, P. H., & Carroll, R. M. 1970 Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika, 35, 245-255.
Stenson, H. H. 1968 The psychophysical dimensions of similarity among random shapes. Perception _??_ Psychophysics, 3, 201-214.
Takane, Y. 1978 A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical pairwise orderings are independent-theory. Japanese Psycholngical Research, 20, 7-17.
Takane, Y. 1981 Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
Takane, Y., & Garroll, J. D. 1981 Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychomelrika, 46, 389-405.
Takane, Y., & Sergent, J. 1983 Multidimensional scaling models for reaction times and same-different judgments. Psychometrika, 48, 393-423.
Tone, K. 1981 BASIC. (Microcomputer programs series 1.) Baifukan. (In Japanese)
Torgerson, W. S. 1965 Multidimensional scaling of similarity. Psychometrika, 30, 379-393.
Tversky, A., & Krantz, D. H. 1969 Similarity of schematic faces: A test of interdimensional additivity. Perception _??_ Psychnphysics, 5, 124-128.

Right : Akaike, H. 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
Attneave, F. 1950 Dimensions of similarity. American Journal of Psychology, 63, 516-556.
Attneave, F. 1957 Physical determinants of the judged complexity of shapes. Journal of Experimental Psychology, 53, 221-227.
Attneave, F., & Arnoult, M. D. 1956 The quantitative study of shape and pattern perception. Psychological Bulletin, 53, 452-471.
Beals, R., Krantz, D. H., & Tversky, A. 1968 Foundations of multidimensional scaling. Psychological Review, 75, 127-142.
Behrman, B. W., & Brown, D. R. 1968 Multidimensional scaling of form: A psychophysical analysis. Perception Psychophysics, 4, 19-25.
Brown, D. R., & Owen, D. H. 1967 The metrics of visual form: Methodological dyspepsia. Psychological Bulletin, 68, 243-259.
Hojo, H. 1983 A maximum likelihood method for additive clustering and its applications. Japanese Psychological Research, 25, 191-201.
Hojo, H. 1985 Psychophysical scaling of dot dispersion. Japanese Psychological Research, 27, 1-10.
Hojo, H.(In press) Psychophysical scaling of smiling faces. Japanese Psychological Research.
Kaiho, H. 1970 Multidimensional approach to the study of form perception. Japanese Psychological Review, 13, 305-317. (In Japanese)
Krantz, D. H., & Tversky, A. 1975 Similarity of rectangles: An analysis of subjective dimensions. Journal of Mathematical Psychology, 12, 4-34.
Künnapas, T., Mülhammar, G., & Svenson, O. 1964 Multidimensional ratio scaling and multidimensional similarity of simple geometric figures. Scandinavian Journal of Psychology, 5, 249-256.
Leeuwenberg, E. L. J. 1971 A perceptual coding language for visual and auditory patterns. American Journal of Psychology, 84, 307-350.
Schönemann, P. H 1977 Similarity of rectangles. Journal of Mathematical Psychology, 16, 161-165.
Sehönemann, P. H., & Carroll, R. M. 1970 Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika, 35, 245-255.
Stenson, H. H. 1968 The psychophysical dimensions of similarity among random shapes. Pereeption Psychophysics, 3, 201-214.
Takane, V. 1978 A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical Pairwise orderings are independent-theory. Japanese Prychoingical Research, 20, 7-17.
Takane, Y. 1981 Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
Takane, Y., & Carroll, J. D. 1981 Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Pspchometrika, 46, 389-405.
Takane, Y., & Sergent, J. 1983 Multidimensional scaling models for reaction times and samedifferent judgments. Psychometrika, 48, 393-423.
Tone, K. 1981 BASIC. (Microcomputer programs series I.) Baifukan. (In Japanese)
Torgerson, W. S. 1965 Multidimensional scaling of similarity. Psychometrika, 30, 379-393.
Tversky, A., & Krantz, D. H. 1969 Similarity of schematic faces: A test of interdimensional additivity. Perception Psychophysics, 5, 124-128.

Date of correction: February 24, 2009 Reason for correction: - Correction: PDF FILE Details: -

Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : Twelve pentagons, which were each variations of a standard pentagon, were rank ordered by 37 university students according to their similarity to the standard. The data were analyzed by a nonmetric maximum likelihood scaling method for rank order data. We proposed various assumptions about the manners in which physical difference measures between two stimuli were defined. The physical difference measures defined were each assumed to be linearly related to the perceived dissimilarity. Fitting this linear function model to the rank order data has revealed (a) that the measure defined on the distance between a pair of corresponding vertices of two pentagons, using the difference limen as a unit, after translating one stimulus pattern so that its centroid may coincide with that of the other, works best; (b) that the linear function of this measure is a fairly good account of the data, but that it is not good enough to explain all meaningful variations in the data.
Right : Twelve pentagons, which were each variations of a standard pentagon, were rank ordered by 37 university students according to their similarity to the standard. The data were analyzed by a nonmetric maximum likelihood scaling method for rank order data. We proposed various assumptions about the manners in which physical difference measures between two stimuli were defined. The physical difference measures defined were each assumed to be linearly related to the perceived dissimilarity. Fitting this linear function model to the rank order data has revealed (a) that the measure defined on the distance between a pair of corresponding vertices of two pentagons, using the difference limen as a unit, after translating one stimulus pattern so that its centroid may coincide with that of the other, works best;(b) that the linear function of this measure is a fairly good account of the data, but that it is not good enough to explain all meaningful variations in the data.

Date of correction: February 24, 2009 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Department of Educational Psychology, School of Education, Hascda University

Right :
1) Department of Educational Psychology, School of Education, Waseda University

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Akaike, H. 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
Attneave, F. 1950 Dimensions of similarity. American Journal of Psychology, 63, 516-556.
Attneave, F. 1957 Physical determinants of the judged complexity of shapes. Journal of Experimental Psychology, 53, 221-227.
Attneave, F., & Arnoult, M. D. 1956 The quantitative study of shape and pattern perception. Psychological Bulletin, 53, 452-471.
Beals, R., Krantz, D. H., & Tversky, A. 1968 Foundations of multidimensional scaling. Psychological Review, 75, 127-142.
Behrman, B. W., & Brown, D. R. 1968 Multidimensional scaling of form: A psychophysical analysis. Perception Psychophysics, 4, 19-25.
Brown, D. R., & Owen, D. H. 1967 The metrics of visual form: Methodological dyspepsia. Psychological Bulletin, 68, 243-259.
Hojo, H. 1983 A maximum likelihood method for additive clustering and its applications. Japanese Psychological Research, 25, 191-201.
Hojo, H. 1985 Psychophysical scaling of dot dispersion. Japanese Psychological Research, 27, 1-10.
Hojo, H.(In press) Psychophysical scaling of smiling faces. Japanese Psychological Research.
Kaiho, H. 1970 Multidimensional approach to the study of form perception. Japanese Psychological Review, 13, 305-317. (In Japanese)
Krantz, D. H., & Tversky, A. 1975 Similarity of rectangles: An analysis of subjective dimensions. Journal of Mathematical Psychology, 12, 4-34.
Künnapas, T., Mülhammar, G., & Svenson, O. 1964 Multidimensional ratio scaling and multidimensional similarity of simple geometric figures. Scandinavian Journal of Psychology, 5, 249-256.
Leeuwenberg, E. L. J. 1971 A perceptual coding language for visual and auditory patterns. American Journal of Psychology, 84, 307-350.
Schönemann, P. H 1977 Similarity of rectangles. Journal of Mathematical Psychology, 16, 161-165.
Sehönemann, P. H., & Carroll, R. M. 1970 Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika, 35, 245-255.
Stenson, H. H. 1968 The psychophysical dimensions of similarity among random shapes. Pereeption Psychophysics, 3, 201-214.
Takane, V. 1978 A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical Pairwise orderings are independent-theory. Japanese Prychoingical Research, 20, 7-17.
Takane, Y. 1981 Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
Takane, Y., & Carroll, J. D. 1981 Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Pspchometrika, 46, 389-405.
Takane, Y., & Sergent, J. 1983 Multidimensional scaling models for reaction times and samedifferent judgments. Psychometrika, 48, 393-423.
Tone, K. 1981 BASIC. (Microcomputer programs series I.) Baifukan. (In Japanese)
Torgerson, W. S. 1965 Multidimensional scaling of similarity. Psychometrika, 30, 379-393.
Tversky, A., & Krantz, D. H. 1969 Similarity of schematic faces: A test of interdimensional additivity. Perception Psychophysics, 5, 124-128.

Right : Akaike, H. 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
Attneave, F. 1950 Dimensions of similarity. American Journal of Psychology, 63, 516-556.
Attneave, F. 1957 Physical determinants of the judged complexity of shapes. Journal of Experimental Psychology, 53, 221-227.
Attneave, F., & Arnoult, M. D. 1956 The quantitative study of shape and pattern perception. Psychological Bulletin, 53, 452-471.
Beals, R., Krantz, D. H., & Tversky, A. 1968 Foundations of multidimensional scaling. Psychological Review, 75, 127-142.
Behrman, B. W., & Brown, D. R. 1968 Multidimensional scaling of form: A psychophysical analysis. Perception & Psychophysics, 4, 19-25.
Brown, D. R., & Owen, D. H. 1967 The metrics of visual form: Methodological dyspepsia. Psychological Bulletin, 68, 243-259.
Hojo, H. 1983 A maximum likelihood method for additive clustering and its applications. Japanese Psychological Research, 25, 191-201.
Hojo, H. 1985 Psychophysical scaling of dot dispersion. Japanese Psychological Research, 27, 1-10.
Hojo, H.(In press) Psychophysical scaling of smiling faces. Japanese Psychological Research.
Kaiho, H. 1970 Multidimensional approach to the study of form perception. Japanese Psychological Review, 13, 305-317.(In Japanese)
Krantz, D. H., & Tversky, A. 1975 Similarity of rectangles: An analysis of subjective dimensions. Journal of Mathematical Psychology, 12, 4-34.
Künnapas, T., Mälhammar, G., & Svenson, O. 1964 Multidimensional ratio scaling and multidimensional similarity of simple geometric figures. Scandinavian Journal of Psychology, 5, 249-256.
Leeuwenberg, E. L. J. 1971 A perceptual coding language for visual and auditory patterns. American Journal of Psychology, 84, 307-350.
Schönemann, P. H. 1977 Similarity of rectangles. Journal of Mathematical Psychology, 16, 161-165.
Schönemann, P. H., & Carroll, R. M. 1970 Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika, 35, 245-255.
Stenson, H. H. 1968 The psychophysical dimensions of similarity among random shapes. Perception & Psychophysics, 3, 201-214.
Takane, Y. 1978 A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical pairwise orderings are independent-theory. Japanese Psychological Research, 20, 7-17.
Takane, Y. 1981 Multidimensional successive categories scaling: A maximum likelihood method. Psychometrika, 46, 9-28.
Takane, Y., & Carroll, J. D. 1981 Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychometrika, 46, 389-405.
Takane, Y., & Sergent, J. 1983 Multidimensional scaling models for reaction times and same-different judgments. Psychometrika, 48, 393-423.
Tone, K. 1981 BASIC.(Microcomputer programs series 1.) Baifukan.(In Japanese)
Torgerson, W. S. 1965 Multidimensional scaling of similarity. Psychometrika, 30, 379-393.
Tversky, A., & Krantz, D. H. 1969 Similarity of schematic faces: A test of interdimensional additivity. Perception & Psychophysics, 5, 124-128.

Abstract

Twelve pentagons, which were each variations of a standard pentagon, were rank ordered by 37 university students according to their similarity to the standard. The data were analyzed by a nonmetric maximum likelihood scaling method for rank order data. We proposed various assumptions about the manners in which physical difference measures between two stimuli were defined. The physical difference measures defined were each assumed to be linearly related to the perceived dissimilarity. Fitting this linear function model to the rank order data has revealed (a) that the measure defined on the distance between a pair of corresponding vertices of two pentagons, using the difference limen as a unit, after translating one stimulus pattern so that its centroid may coincide with that of the other, works best;(b) that the linear function of this measure is a fairly good account of the data, but that it is not good enough to explain all meaningful variations in the data.

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