Abstract
Averaging across observers is common in psychological research. Often, averaging reduces the measurement error and, thus, does not affect the inference drawn about the behavior ofindividuals. However, in other situations, averaging alters the structure of the data qualitatively, leading to an incorrect inference about the behavior of individuals. In this research, the influence of averaging across observers on the fits of decision bound models (Ashby, 1992a) and generalized context models (GCM; Nosofsky, 1986) was investigated through Monte Carlo simulation of a variety of categorization conditions, perceptual representations, and individual difference assumptions and in an experiment. The results suggest that (1) averaging has little effect when the GCM is the correct model, (2) averaging often improves the fit of the GCM and worsens the fit of the decision bound model when the decision bound model is the correct model, (3) the GCM is quite flexible and, under many conditions, can mimic the predictions of the decision bound model, whereas the decision bound model is generally unable to mimic the predictions of the GCM, (4) the validity of the decision bound model’s perceptual representation assumption can have a large effect on the inference drawn about the form of the decision bound, and (5) the experiment supported the claim that averaging improves the fit of the GCM. These results underscore the importance of performing single-observer analysis if one is interested in understanding the categorization performance of individuals.
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Ashby, F. G. (1988). Estimating the parameters of multidimensional signal detection theory from simultaneous ratings on separate stimulus components.Perception & Psychophysics,44, 195–204.
Ashby, F. G. (1992a). Multidimensional models of categorization. In F. G. Ashby (Ed.),Multidimensional models of perception and cognition (pp. 449–483). Hillsdale, NJ: Erlbaum.
Ashby, F. G. (1992b). Multivariate probability distributions. In F. G. Ashby (Ed.),Multidimensional models of perception and cognition pp. 1–34). Hillsdale, NJ: Erlbaum.
Ashby, F. G., &Alfonso-Reese, L. A. (1995). Categorization as probability density estimation.Journal of Mathematical Psychology,39, 216–233.
Ashby, F. G., Alfonso-Reese, L. A., Türken, A., &Waldron, E. (1998). Competition between verbal and implicit rules of category learning.Psychological Review,105, 442–481.
Ashby, F. G., &Lee, W. W. (1991). Predicting similarity and categorization from identification.Journal of Experimental Psychology: General,120, 150–172.
Ashby, F. G., &Lee, W. W. (1993). Perceptual variability as a fundamental axiom of perceptual science. In S. C. Masin (Ed.),Foundations of perceptual theory (pp. 369–397). New York: Elsevier, North-Holland.
Ashby, F. G., Lee, W. W., &Balakrishnan, J. D. (1992). Comparing the biased choice model and multidimensional decision bound models of identification.Mathematical Social Sciences,23, 175–197.
Ashby, F. G., &Maddox, W. T. (1990). Integrating information from separable psychological dimensions.Journal of Experimental Psychology: Human Perception & Performance,16, 598–612.
Ashby, F. G., &Maddox, W. T. (1991). A response time theory of perceptual independence. In J. P. Doignon & J. C. Falmagne (Eds.),Mathematical psychology: Current developments (pp. 389–413). New York: Springer-Verlag.
Ashby, F. G., &Maddox, W. T. (1993). Relations between exemplar, prototype, and decision bound models of categorization.Journal of Mathematical Psychology,37, 372–400.
Ashby, F. G., &Maddox, W. T. (1994). A response time theory of perceptual separability and perceptual integrality in speeded classification.Journal of Mathematical Psychology,38, 423–466.
Ashby, F. G., Maddox, W. T., &Lee, W. W. (1994). On the dangers of averaging across subjects when using multidimensional scaling or the similarity-choice model.Psychological Science,5, 144–150.
Ashby, F. G., &Perrin, N. A. (1988). Toward a unified theory of similarity and recognition.Psychological Review,95, 124–150.
Ashby, F. G., &Townsend, J. T. (1986). Varieties of perceptual independence.Psychological Review,93, 154–179.
Brainard, D. H. (1995). Colorimetry. In M. Bass (Ed.),Handbook of optics: Vol. 11. Fundamentals, techniques, and design (pp. 26.1–26.54). New York: McGraw-Hill.
Estes, W. K. (1956). The problem of inference from curves based on group data.Psychological Bulletin,53, 134–140.
Garner, W. R. (1974).The processing of information and structure. New York: Wiley.
Kruskal, J. B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika,29, 1–27.
Kruskal, J. B. (1964b). Nonmetric multidimensional scaling: A numerical method.Psychometrika,29, 115–129.
Lamberts, K. (1995). Categorization under time pressure.Journal of Experimental Psychology: General,124, 161–180.
Luce, R. D. (1963). Detection and recognition. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.),Handbook of mathematical psychology (pp. 103–189). New York: Wiley.
Macadam, D. L. (1942). Visual sensitivities to color differences in daylight.Journal of the Optical Society of America,32, 247–274.
Maddox, W. T. (1992). Perceptual and decisional separability. In F. G. Ashby (Ed.),Multidimensional models of perception and cognition (pp. 147–180). Hillsdale, NJ: Erlbaum.
Maddox, W. T. (1995). Baserate effects in multidimensional perceptual categorization.Journal of Experimental Psychology: Learning, Memory, & Cognition,21, 288–301.
Maddox, W. T., &Ashby, F. G. (1993). Comparing decision bound and exemplar models of categorization.Perception & Psychophysics,53, 49–70.
Maddox, W. T., &Ashby, F. G. (1996). Perceptual separability, decisional separability, and the identification-speeded classification relationship.Journal of Experimental Psychology: Human Perception & Performance,22, 795–817.
Maddox, W. T., &Ashby, F. G. (1998). Selective attention and the formation of linear decision boundaries: Comment on McKinley and Nosofsky ( 1996).Journal of Experimental Psychology: Human Perception & Performance,24, 301–321.
Massaro, D. W., &Cohen, M. M. (1993). The paradigm and the fuzzy logical model of perception are alive and well.Journal of Experimental Psychology: General,122, 115–124.
Mckinley, S. C, &Nosofsky, R. M. (1995). Investigations of exemplar and decision bound models in large, ill-defined category structures.Journal of Experimental Psychology: Human Perception & Performance,21, 128–148.
Mckinley, S. C, &Nosofsky, R. M. (1996). Selective attention and the formation of linear decision boundaries.Journal of Experimental Psychology: Human Perception & Performance,22, 294–317.
Nosofsky,R. M. (1984). Choice, similarity, and the context theory of classification.Journal of Experimental Psychology: Learning, Memory, & Cognition,10, 104–114.
Nosofsky, R. M. (1986). Attention, similarity, and the identification-categorization relationship.Journal of Experimental Psychology: General,115, 39–57.
Nosofsky, R. M. (1987). Attention and learning processes in the identification and categorization of integral stimuli.Journal of Experimental Psychology: Learning, Memory, & Cognition,13, 87–109.
Nosofsky,R. M. (1989). Further tests of an exemplar-similarity approach to relating identification and categorization.Perception & Psychophysics,45, 279–290.
Nosofsky, R. M. (1990). Relations between exemplar-similarity and likelihood models of classification.Journal of Mathematical Psychology,34, 393–418.
Nosofsky, R. M. (1991). Tests of an exemplar model for relating perceptual classification and recognition memory.Journal of Experimental Psychology: Human Perception & Performance,17, 3–27.
Nosofsky, R. M. (1992). Exemplar-based approach to relating categorization, identification and recognition. In F. G. Ashby (Ed.),Multidimensional models of perception and cognition (pp. 363–393). Hillsdale, NJ: Erlbaum.
Nosofsky, R. M. (1998). Selective attention and the formation of linear decision boundaries: Reply to Maddox and Ashby (1998).Journal of Experimental Psychology: Human Perception & Performance,24, 322–339.
Nosofsky, R. M., Palmeri, T. J., &Mckinley, S. C. (1994). Rule-plus-exception model of classification learning.Psychological Review,101, 53–79.
Shepard, R. N. (1957). Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space.Psychometrika,22, 325–345.
Shepard, R. N. (1962a). The analysis of proximities: Multidimensional scaling with unknown distance function I.Psychometrika,27,125–140.
Shepard, R. N. (1962b). The analysis of proximities: Multidimensional scaling with unknown distance function II.Psychometrika,27,219–246.
Shepard, R. N. (1964). Attention and the metric structure of the stimulus space.Journal of Mathematical Psychology,1, 54–87.
Shepard, R. N. (1987). Toward a universal law of generalization for psychological science.Science,237, 1317–1323.
Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children’s addition.Journal of Experimental Psychology: General,116, 250–264.
Smith, E. R., &Zarate, M. A. (1992). Exemplar-based model of social judgment.Psychological Review,99, 3–21.
Smith, L. B. (1989). A model of perceptual classification in children and adults.Psychological Review,96, 125–144.
Torgerson, W. S. (1958).Theory and methods of scaling. New York: Wiley.
Tversky, A. (1977). Features of similarity.Psychological Review,84, 327–353.
Wandell, B. A. (1995).Foundations of vision. Sunderland, MA: Sinauer.
Wickens, T. D. (1982).Models for behavior: Stochastic processes in psychology. San Francisco: Freeman.
Wyszecki, G., &Stiles, W. S. (1982).Color science: Concepts and methods, quantitative data and formulae (2nd ed). New York: Wiley.
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Maddox, W.T. On the dangers of averaging across observers when comparing decision bound models and generalized context models of categorization. Perception & Psychophysics 61, 354–374 (1999). https://doi.org/10.3758/BF03206893
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DOI: https://doi.org/10.3758/BF03206893