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

YASUHARU OKAMOTO

doi:10.4992/psycholres1954.32.48

精神物理学的錯覚における個人差のスカラー積モデルによる分析

岡本安晴

著者情報

ジャーナルフリー

1990 年 32 巻 1 号 p. 48-53

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

詳細

発行日: 1990/02/26 受付日: 1988/05/02 J-STAGE公開日: 2009/02/24 受理日: 1989/07/15 早期公開日: - 改訂日: -
訂正情報
訂正日: 2009/02/24 訂正理由: - 訂正箇所: 論文抄録訂正内容: 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.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 論文タイトル訂正内容: 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

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 論文抄録訂正内容: 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.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

抄録

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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