Huttenlocher Hedges

Journal of Experimental Psychology: General Copyright 2000 by the American Psychological Association, Inc. 2000, Vbl. 129, No. 2, 220-241 0096-3445/M/$5.0Q DOT: 10.1Q37//0096-3445.129.2320 Why Do Categories Affect Stimulus Judgment? Janellen Huttenlocher, Larry V. Hedges, and Jack L. Vevea University of Chicago The authors tested a model of category effects on stimulus judgment. The model holds that the goal of stimulus judgment is to achieve high accuracy. For this reason, people place inexactly represented stimuli in the context of prior information, captured in categories, combining inexact fine-grain stimulus values with prior (category) information. This process can be likened to a Bayesian statistical procedure designed to maximize the average accuracy of estimation. If people follow the proposed procedure to maximize accuracy, their estimates should be affected by the distribution of instances in a category. In the present experiments, participants reproduced one-dimensional stimuli. Different prior distributions were presented. The experiments verified that people's stimulus estimates are affected by variations in a prior distribution in such a manner as to increase the accuracy of their stimulus reproductions. It is well known that categorization affects stimulus judgment in which people use prior information, in the form judgment. Two stimuli that are actually equidistant may be of categories, to adjust inexactly represented stimuli; this judged as more similar or may be harder to discriminate if gives rise to bias but improves accuracy by reducing the they are from a common category than if they are from variability of estimates. Indeed, if the goal of stimulus different categories, and an individual stimulus from a judgment is to maximize average accuracy, it would be particular category may be judged closer to the center of that irrational for the cognitive system not to produce biased category than it actually is. There is an extensive literature estimates. starting early in the century, and continuing to the present, Recently, a variety of findings, originally interpreted as showing bias due to categories in many domains. For showing bias and flawed reasoning, have been reexamined example, the social categories that people use may affect to determine whether people might actually be using rational their judgment of individuals, the set (category) of experimen- processes, appropriate to their goals. Oaksford and Chater tal stimuli presented to people may affect their judgment of (1996) have reinterpreted apparent errors on deductive particular stimuli, and so forth (e.g., Bartlett, 1932; Brewer reasoning tasks (e.g., Wason 1968), showing that people & Nakamura, 1984; Hollingworth, 1910; Poulton, 1989; actually may treat the tasks as inductive problems where "a Tajfel, 1959). Bayesian approach to optimal data selection" is used to In the present article, we test a model that holds that maximize "expected information gain" (p. 382). Earlier, category effects on stimulus judgments arise in pursuit of an Kahneman and Tversky (1972) investigated whether people adaptive goal—to maximize accuracy. Anderson (1990, use Bayesian procedures to improve the accuracy of their 1991) has suggested that establishing what goals an organ- judgments under uncertainty. In categorization tasks, where ism is pursuing should be the first step in cognitive it is uncertain what category a stimulus belongs to, differ- modeling. Models of goals should precede detailed models ences in the likelihood of the alternatives should be taken of cognitive processing, he argues, because goals constrain account of in decision making. Kahneman and Tversky processes. We propose a Bayesian model of stimulus found that the relative frequencies of alternatives were often ignored (base rate neglect), seemingly indicating that hu- Editor's Note: Eleanor M. Saflran served as the action editor mans are not rational operators. However, in an extensive for this article.—NSN review of the literature, Koehler (1996) found that base rate neglect is not the rule; in many tasks, people do use base rates in making decisions. Kruschke (1996) presented evi- Janellen Huttenlocher, Larry V. Hedges, and Jack L. Vevea, Department of Psychology, University of Chicago. Jack L. Vevea is dence that even in cases of apparent base rate neglect, it can now at the Department of Psychology, University of North be shown that people actually are sensitive to base rates in Carolina. category decisions. Nosofsky (1998) has shown that his We thank Judith Avrahami, Lawrence Barsalou, Beth Crawford, exemplar model of how people decide what category a and Yakov Kareev for their helpful comments on drafts of this stimulus belongs to actually constitutes an explicit Bayesian article and Peder Hans Engebretson for his help in early work on model, even though the model arose from other this project. Special thanks are due to William Goldstein for considerations. illuminating discussions of the psychophysical literature. This Although the use of relative frequencies across categories research was supported in part by Grant R01 MH45402 from the National Institute of Mental Health. to improve the accuracy of category membership judgments Correspondence concerning this article should be addressed to has been explored, the possibility that relative frequencies Janellen Huttenlocher, Department of Psychology, University of within a category are used in a parallel fashion in judgments Chicago, 5848 South University Avenue, Chicago, Illinois 60637. of individual stimulus values has not been systematically 220 WHY DO CATEGORIES AFFECT STIMULUS JUDGMENT? 221 explored. Yet it is widely accepted that, at least in certain with statistical aspects of the representation of stimuli and ways, prior information about relative frequency within categories. We treat a stimulus as a point on a set of categories is used adaptively; notably, correlational structure dimensions, and a category as a distribution of stimuli. is used to infer the unobservable features of stimuli (Rosch, Although inductive categories are treated as statistical 1975; e.g., the more green a liquid is, the more likely it is to distributions in our model, we recognize that this is an be poisonous). In general, relative frequency is potentially incomplete characterization of such categories. Inductive functional information. Consistent with this view, Murphy categories tend to capture statistical regularities that matter and Ross (1994) found that people even preserve relative for human purposes, and they are often embedded in general frequency for nondefining attributes of categories. Here we theories (e.g., Goodman, 1972; Murphy & Medin, 1985). examine whether within-category relative frequencies are Hence in modeling categories as distributions of observed used to increase accuracy in the judgment of inexactly sets of stimuli, one should remember that some categories represented stimuli from those categories. also incorporate expectations (general principles, theories) Our model is a precisely specified Bayesian model. It about what the new distribution should be like (e.g., where holds that in pursuing the goal of maximizing accuracy, boundaries are located, distribution shape, etc.). For ex- people use prior information in estimating stimulus values ample, a person might set an upper boundary for the width of that are represented inexactly. Prior information is incorpo- trucks as some proportion of the presumed width of highway rated into decision making hi the form of an explicit prior lanes.1 distribution, and the inexactness of the fine-grained informa- In this article we have chosen categories that, it seems, tion is incorporated as a sampling distribution. Given a would incorporate only distributional information, allowing category (an explicit prior distribution) and an inexact us to evaluate a critical prediction of our Bayesian model: If stimulus value (a sampling distribution describing the uncer- people use prior distributions to increase the accuracy of tainty of current data), Hayes's theorem provides a method their judgments of stimuli, then the characteristics of those for combining the information to provide estimates with distributions should affect estimation in the ways we de- certain optimal properties. A posterior distribution summa- scribe in this article. We test the predictions using a simple rizes uncertainty after combining the uncertain data and the task. We present, one at a time, unidimensional stimuli that prior information. The mean of this posterior distribution is vary over a bounded range. After each stimulus is removed, called the Bayesian estimate; it has the property of being the people reproduce it, providing us with information about the "most accurate" estimate in the sense that it minimizes bias and variability of their estimates. By varying the average error. distribution hi which exactly the same stimuli are embedded, In our model, category effects arise at estimation when we can examine whether estimates of those stimuli vary as people combine fine-grain and category information to they should if people follow procedures to maximize the achieve high accuracy of judgment. Other recent approaches average accuracy of estimates. posit that category effects arise at encoding. Category We first provide the background for the predictions tested learning, it is argued, alters the way stimulus dimensions are in this article by summarizing our earlier work, laying out represented in memory. For example,

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