Analysis of individual differences in the size-numerosity illusion by Scalar Product Model

YASUHARU OKAMOTO

doi:10.4992/psycholres1954.32.48

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Keywords: illusion, numerosity, Scalar Product Model, averaging model, information integration theory, pair comparison method, individual differences

JOURNAL FREE ACCESS

1990 Volume 32 Issue 1 Pages 48-53

DOI https://doi.org/10.4992/psycholres1954.32.48

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Published: February 26, 1990 Received: May 02, 1988 Available on J-STAGE: February 24, 2009 Accepted: July 15, 1989 Advance online publication: - Revised: -
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Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : Stevens and Rubin (1970) investigated the size-weight illusion using magnitude estimation method and Anderson (1970) investigated the same illusion by rating method. But, in general, both methods of magnitude estimation and rating were criticized as biased (cf. Anderson, 1981; Parducci, 1983). In this paper, size-numerosity illusion was investigated using simultaneous pair comparison method, which did not force the subject to make magnitude estimation or rating of the quantity, and applying the scalar product model to the data. The nonmetric solution of the analysis was very successful and indicated that the size-numerosity illusion can be described by the same information integration process as in the case of the size-weight illusion, i.e. the averaging model, and Scalar Product Model can clearly display individual differences of the illusion.
Right : Stevens and Rubin (1970) investigated the size-weight illusion using magnitude estimation method and Anderson (1970) investigated the same illusion by rating method. But, in general, both methods of magnitude estimation and rating were criticized as biased (el, Anderson, 1981; Parducci, 1983). In this paper, size-numerosity illusion was investigated using simultaneous pair comparison method, which did not force the subject to make magnitude estimation or rating of the quantity, and applying the scalar product model to the data. The nonmetric solution of the analysis was very successful and indicated that the size-numerosity illusion can be described by the same information integration process as in the case of the size-weight illusion, i.e. the averaging model, and Scalar Product Model can clearly display individual differences of the illusion.

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Anderson, N. H. 1970 Averaging model applied to the size-weight illusion. Perception and Psychophysics, 8, 1-4.
Anderson, N. H. 1974 Algebraic models in perception. In E. C. Carterette & M. P. Friedman (Eds.), Handbook of Perception. Vol. 2. Psychophysical judgment and measurement. New York: Academic Press. Pp. 215-298.
Anderson, N. H. 1981 Foundations of information integration theory. New York: Academic Press.
Anderson, N. H. 1982 Methods of information integration theory. New York: Academic Press.
Bechtel, G. G., Tucker, L. R., & Chang, W. 1971 A scalar product model for the multidimensional scaling of choice. Psychometrika, 36, 369-388.
Hellstrom, A. 1985 The time-order error and its relatives: Mirrors of cognitive processes in comparing, Psychological Bulletin, 97, 35-61.
Keller, J. B. 1962 Factorization of matrices by least-squares. Bionietrika, 49, 239-242.
Parducci, A. 1983 Category ratings and the relational character of judgment. In G. E. Stelmach & P. A. Vroon (Eds.), Advances in psychology. Vol. 11. Modern issues in perception. Amsterdam: North-Holland. Pp. 262-282.
Ross, R. T. 1934 Optimum orders for the presentation of pairs in the method of paired comparisons. Journal of Educational Psychology, 25, 375-382.
Stevens, J. C., & Rubin, L. L. 1970 Psychophysical scales of apparent heaviness and the size-weight illusion. Perception and Psychophysics, 8, 225-230.

Right : Anderson, N. H. 1970 Averaging model applied to the size-weight illusion. Perception and Psychophysics, 8, 1-4.
Anderson, N. H. 1974 Algebraic models in perception. In E. C. Carterette&M. P. Friedman (Eds.), Handbook of perception. Vol.2. Psychophysical judgment and measurement. New York: Academic Press, Pp.215-298.
Anderson, N. H, 1981 Foundations of information integration theory. New York: Academic Press.
Anderson, N. H. 1982 Methods of information integration theory. New York: Academic Press.
Bechtel, G. G., Tucker, L. R., &Chang, W. 1971 A scalar product model for the multidimensional scaling of choice. Psychometrika, 36, 369-388.
Hellstrom, A. 1985 The time-order error and its relatives: Mirrors of cognitive processes in comparing. Psychological Bulletin, 97, 35-61.
Keller, J. B. 1962 Factorization of matrices by least-squares. Biometrika, 49, 239-242.
Parducci, A. 1983 Category ratings and the relational character of judgment. In G. E. Stelmach&P. A. Vroon (Eds.), Advances in psychology. Vol.11. Modern issues in perception. Amsterdam: North-Holland. Pp.262-282.
Ross, R. T. 1934 Optimum orders for the presentation of pairs in the method of paired comparisons. Journal of Educational Psychology, 25, 375-382.
Stevens, J. C., &Rubin, L. L. 1970 Psychophysical scales of apparent heaviness and the size-weight illusion. Perception and Psychophysics, 8, 225-230.

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

Date of correction: February 24, 2009 Reason for correction: - Correction: TITLE Details: Wrong : Analysis of individual differences in the sizenumerosity illusion by Scalar Product Model
Right : Analysis of individual differences in the size-numerosity illusion by Scalar Product Model

Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : Stevens and Rubin (1970) investigated the size-weight illusion using magnitude estimation method and Anderson (1970) investigated the same illusion by rating method. But, in general, both methods of magnitude estimation and rating were criticized as biased (el, Anderson, 1981; Parducci, 1983). In this paper, size-numerosity illusion was investigated using simultaneous pair comparison method, which did not force the subject to make magnitude estimation or rating of the quantity, and applying the scalar product model to the data. The nonmetric solution of the analysis was very successful and indicated that the size-numerosity illusion can be described by the same information integration process as in the case of the size-weight illusion, i.e. the averaging model, and Scalar Product Model can clearly display individual differences of the illusion.
Right : Stevens and Rubin (1970) investigated the size-weight illusion using magnitude estimation method and Anderson (1970) investigated the same illusion by rating method. But, in general, both methods of magnitude estimation and rating were criticized as biased (cf, Anderson, 1981; Parducci, 1983). In this paper, size-numerosity illusion was investigated using simultaneous pair comparison method, which did not force the subject to make magnitude estimation or rating of the quantity, and applying the scalar product model to the data. The nonmetric solution of the analysis was very successful and indicated that the size-numerosity illusion can be described by the same information integration process as in the case of the size-weight illusion, i.e. the averaging model, and Scalar Product Model can clearly display individual differences of the illusion.

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Anderson, N. H. 1970 Averaging model applied to the size-weight illusion. Perception and Psychophysics, 8, 1-4.
Anderson, N. H. 1974 Algebraic models in perception. In E. C. Carterette&M. P. Friedman (Eds.), Handbook of perception. Vol.2. Psychophysical judgment and measurement. New York: Academic Press, Pp.215-298.
Anderson, N. H, 1981 Foundations of information integration theory. New York: Academic Press.
Anderson, N. H. 1982 Methods of information integration theory. New York: Academic Press.
Bechtel, G. G., Tucker, L. R., &Chang, W. 1971 A scalar product model for the multidimensional scaling of choice. Psychometrika, 36, 369-388.
Hellstrom, A. 1985 The time-order error and its relatives: Mirrors of cognitive processes in comparing. Psychological Bulletin, 97, 35-61.
Keller, J. B. 1962 Factorization of matrices by least-squares. Biometrika, 49, 239-242.
Parducci, A. 1983 Category ratings and the relational character of judgment. In G. E. Stelmach&P. A. Vroon (Eds.), Advances in psychology. Vol.11. Modern issues in perception. Amsterdam: North-Holland. Pp.262-282.
Ross, R. T. 1934 Optimum orders for the presentation of pairs in the method of paired comparisons. Journal of Educational Psychology, 25, 375-382.
Stevens, J. C., &Rubin, L. L. 1970 Psychophysical scales of apparent heaviness and the size-weight illusion. Perception and Psychophysics, 8, 225-230.

Right : Anderson, N. H. 1970 Averaging model applied to the size-weight illusion. Perception and Psychophysics, 8, 1-4.
Anderson, N. H. 1974 Algebraic models in perception. In E. C. Carterette & M. P. Friedman (Eds.), Handbook of perception. Vol.2. Psychophysical judgment and measurement. New York: Academic Press. Pp.215-298.
Anderson, N. H, 1981 Foundations of information integration theory. New York: Academic Press.
Anderson, N. H. 1982 Methods of information integration theory. New York: Academic Press.
Bechtel, G. G., Tucker, L. R., & Chang, W. 1971 A scalar product model for the multidimensional scaling of choice. Psychometrika, 36, 369-388.
Hellstrom, A. 1985 The time-order error and its relatives: Mirrors of cognitive processes in comparing. Psychological Bulletin, 97, 35-61.
Keller, J. B. 1962 Factorization of matrices by least-squares. Biometrika, 49, 239-242.
Parducci, A. 1983 Category ratings and the relational character of judgment. In G. E. Stelmach & P. A. Vroon (Eds.), Advances in psychology. Vol.11. Modern issues in perception. Amsterdam: North-Holland. Pp.262-282.
Ross, R. T. 1934 Optimum orders for the presentation of pairs in the method of paired comparisons. Journal of Educational Psychology, 25, 375-382.
Stevens, J. C., & Rubin, L. L. 1970 Psychophysical scales of apparent heaviness and the size-weight illusion. Perception and Psychophysics, 8, 225-230.

Abstract

Stevens and Rubin (1970) investigated the size-weight illusion using magnitude estimation method and Anderson (1970) investigated the same illusion by rating method. But, in general, both methods of magnitude estimation and rating were criticized as biased (cf, Anderson, 1981; Parducci, 1983). In this paper, size-numerosity illusion was investigated using simultaneous pair comparison method, which did not force the subject to make magnitude estimation or rating of the quantity, and applying the scalar product model to the data. The nonmetric solution of the analysis was very successful and indicated that the size-numerosity illusion can be described by the same information integration process as in the case of the size-weight illusion, i.e. the averaging model, and Scalar Product Model can clearly display individual differences of the illusion.

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