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The irrelevance of distributional assumptions on reaction times in multidimensional scaling of same/different judgment tasks

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Abstract

Takane and Sergent developed a model (MAXRT) for scaling same/different judgments and response times (RTs) simultaneously. The model assumes that RTs are distributed lognormally. Our experiment showed that the RT distribution of the judgments might be task dependent. It is shown that lognormal RTs provide a far better fit than exponential, normal, and Pareto distributed RTs (with the same means and variances), but that the final parameter estimates from the data set with lognormal RTs hardly differ from the alternatively distributed RTs. Finally, despite the robustness of the distributional assumption of the RTs with respect to the parameter estimates, it is shown that RTs have an informational value that is not contained in the same/different judgments alone.

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References

  • Akaike, H. (1974). A new look at the statistical model identification.IEEE Transactions on Automatic Control, 19, 716–723.

    Google Scholar 

  • Anderson, J. R., & Bower, G. H. (1973).Human associative memory. Washington: Winston & Sons.

    Google Scholar 

  • Behrman, B. W., & Brown, D. R. (1968). Multidimensional scaling of form: A psychophysical analysis.Perception & Psychophysics, 4, 19–25.

    Google Scholar 

  • Brown, D. R., & Andrews, M. H. (1968). Visual form discrimination: Multidimensional analysis.Perception & Psychophysics, 3, 401–406.

    Google Scholar 

  • Chocholle, R. (1940). Variations des temps de réaction auditifs en fonction de l'intensité à diverses fréquences [Variations of auditory reaction times as a function of intensity at varying frequences].L'Année Psychologique, 41, 65–124.

    Google Scholar 

  • D'Agostino, R., & Stephens, M. A. (1986).Goodness-of-fit techniques. New-York: Dekker.

    Google Scholar 

  • De Soete, G. (1986). A perceptual study of the Flury-Riedwyl faces for graphically displaying multivariate data.International Journal for Man-Machine Studies, 25, 549–555.

    Google Scholar 

  • De Soete, G., & Carroll, J. D. (1983). A maximum likelihood method for fitting the wandering vector model.Psychometrika, 48, 553–566.

    Google Scholar 

  • Flury, B., & Riedwyl, H. (1981). Graphical representation of multivariate data by means of asymmetrical faces.Journal of the American Statistical Association, 76, 757–765.

    Google Scholar 

  • Flury, B., & Riedwyl, H. (1983).Some applications of asymmetrical faces. Unpublished manuscript, Institut für Mathematische Statistik und Versicherungslehre, Universitaet Bern.

  • Green, D. M., & Luce, R. D. (1967). Detection of auditory signals presented at random times.Perception & Psychophysics, 2, 441–449.

    Google Scholar 

  • Green, D. M., & Luce, R. D. (1971). Detection of auditory signals presented at random times III.Perception & Psychophysics, 9, 257–268.

    Google Scholar 

  • Harrington, L. F., & Brown, D. R. (1972). Visual pattern perception: Multidimensional analysis of discrimination difficulty for children.Psychonomic Science, 29, 219–221.

    Google Scholar 

  • Ida, M. (1980). The application of the Weibull distribution to the analysis of the reaction time data.Japanese Psychological Review, 22, 207–212.

    Google Scholar 

  • Johnson, N. L., & Kotz, S. (1970).Distributions in statistics: Continuous univariate distributions-2. Boston: Houghton Miffin.

    Google Scholar 

  • Kak, A. V., & Brown, D. R. (1979). Visual pattern perception: Multidimensional analysis of development of children's reading skills.Perceptual and Motor Skills, 49, 819–830.

    Google Scholar 

  • Kirk, R. E. (1982).Experimental design. Procedures for the behavioral sciences (2nd ed.). Belmont, CA: Brooks/Cole.

    Google Scholar 

  • Kohfeld, D. L., Santee, J. L., & Wallace, N. D. (1981). Loudness and reaction time: II. Identification of detection components at different intensities and frequencies.Perception & Psychophysics, 2, 550–562.

    Google Scholar 

  • Kruskal, J. B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 29, 1–27.

    Google Scholar 

  • Kruskal, J. B. (1964b). Multidimensional scaling: A numerical method.Psychometrika, 29, 115–129.

    Google Scholar 

  • Luce, R. D. (1986).Response times. Their role in inferring elementary mental organization. New York: Oxford University Press.

    Google Scholar 

  • Luce, R. D., & Green, D. M. (1970). Detection of auditory signals presented at random times II.Perception & Psychophysics, 7, 1–14.

    Google Scholar 

  • McGill, W. J., & Gibbon, J. (1965). The general gamma distribution and reaction times.Journal of Mathematical Psychology, 2, 1–18.

    Google Scholar 

  • Medin, D. L., & Schaffer, M. M. (1978). Context theory of classification learning.Psychological Review, 85, 207–238.

    Google Scholar 

  • Melara, R. D. (1989). Similarity relations among synesthetic stimuli and their attributes.Journal of Experimental Psychology: Human Perception and Performance, 15, 212–231.

    Google Scholar 

  • Murdock, B. B. (1985). An analysis of the strength-latency relationship.Memory and Cognition, 13, 511–521.

    Google Scholar 

  • Pearson, E. S., D'Agostino, R. B., & Bowman, K. O. (1977). Tests for departure from normality: Comparison of powers.Biometrika, 64, 231–246.

    Google Scholar 

  • Podgorny, P., & Garner, W. R. (1979). Reaction time as a measure of inter and intra-object visual similarity.Perception & Psychophysics, 26, 37–52.

    Google Scholar 

  • Ratcliff, R. (1978). Theory of memory retrieval.Psychological Review, 85, 59–108.

    Google Scholar 

  • Ratcliff, R., & Murdock, B. B. (1976). Retrieval processes in recognition memory.Psychological Review, 86, 190–214.

    Google Scholar 

  • Royston, J. P. (1982). An extension of Shapiro and Wilk'sW test for normality to large samples.Applied Statistics, 31, 115–124.

    Google Scholar 

  • Scheiblechner, H. (1979). Specifically objective stochastic latency mechanisms.Journal of Mathematical Psychology, 19, 18–38.

    Google Scholar 

  • Sergent, J., & Takane, Y. (1987). Structures in two-choice reaction-time data.Journal of Experimental Psychology: Human Perception and Performance, 13, 300–315.

    Google Scholar 

  • Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples).Biometrika, 52, 591–611.

    Google Scholar 

  • Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: uses in assessing rater reliability.Psychological Bulletin, 86, 420–428.

    Google Scholar 

  • Snodgrass, J. G., Luce, R. D., & Galanter, E. (1967). Some experiments on simple and choice reaction times.Journal of Experimental Psychology, 75, 1–17.

    Google Scholar 

  • Takane, Y., & Sergent, J. (1983). Multidimensional scaling models for reaction times and same-different judgments.Psychometrika, 48, 393–423.

    Google Scholar 

  • Townsend, J. T., & Ashby, F. G. (1983).The stochastic modeling of elementary psychological processes. Cambridge: University Press.

    Google Scholar 

  • Tversky, A. (1977). Features of similarity.Psychological Review, 84, 327–352.

    Google Scholar 

  • Young, F. W. (1970). Nonmetric scaling for line length using latencies, similarity, and same-different judgments.Perception & Psychophysics, 8, 363–369.

    Google Scholar 

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The authors thank Jan Beirlant, Geert De Soete, Yoshio Takane, the three reviewers, and the Editor, for their useful comments on earlier versions of this manuscript. We are also indebted to Noël Bovens for his help in programming the experiments.

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Storms, G., Delbeke, L. The irrelevance of distributional assumptions on reaction times in multidimensional scaling of same/different judgment tasks. Psychometrika 57, 599–614 (1992). https://doi.org/10.1007/BF02294422

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  • DOI: https://doi.org/10.1007/BF02294422

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