Clark McCauley (1994) Stereotypes as Base Rate Predictions. Psycoloquy: 5(05) Base Rate (8)

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PSYCOLOQUY (ISSN 1055-0143) is sponsored by the American Psychological Association (APA).
Psycoloquy 5(05): Stereotypes as Base Rate Predictions

Commentary on Koehler on Base-Rate

Clark McCauley
Psychology Department
Bryn Mawr College
Bryn Mawr, PA 19010


Doubts have been raised about whether or when stereotypes, identified as baserate predictions, can affect judgment about an individual member of a stereotyped group. This commentary argues that stereotypes are more than baserate predictions and, more important, that it is not clear what is baserate and what is individuating information when looking at a member of a stereotyped group. The ambiguity in defining baserate in stereotype studies stems from a similar ambiguity in the research in cognitive psychology that first suggested human neglect of baserates. Without independent definition of what is meant by baserate information, the hypothesis that baserates are neglected is empirically empty and cannot contribute to understanding of stereotype effects.


Base rate fallacy, Bayes' theorem, decision making, ecological validity, ethics, fallacy, judgment, probability.


1. Stereotypes are perceptions of the characteristics of social groups, and are often cited as contributing to intergroup prejudice and hostility (Allport, 1954; Hewstone & Brown, 1986). Thus it was a matter of some surprise to social psychologists when Locksley, Borgida, Brekke and Hepburn (1980) reported evidence that stereotype expectations did not affect judgment about a member of a stereotyped group when relevant evidence of the individual's behavior was available. Locksley suggested that stereotypes could be thought of as baserate predictions and she interpreted her results in terms of research in cognitive psychology (Kahneman & Tversky, 1973) indicating that human judges tend to neglect baserate information when individuating information is available.

2. In this commentary, I argue that stereotypes are not usefully identified as baserate predictions, first, because stereotypes are perceptions of group differences rather than of one group's characteristics, and, second, because it is not clear what distinguishes baserate from individuating information.


3. Recent concern about human neglect of baserate information was stimulated by Kahneman and Tversky (1973), who reported a number of studies in which human judges tended to ignore or underuse baserate information when predicting the category from which a target individual or event had come.

4. In one much-cited study, subjects were given a description of a particular graduate student in terms that amounted to a stereotype of computer science students: Tom W. was described as not too comfortable with people, with a need for order and clarity, a strong drive for competence, and a dull and mechanical writing style enlivened with occasional corny puns. Subjects were asked to rate the likelihood that Tom W. was a graduate student in each of a number of fields of graduate study, including computer science. The subjects rated computer science as the most likely field of study for Tom, despite the low baserate probability of this field. An independent group of subjects estimated the percentage of all graduate students in each field, and these estimates indicated that computer science was seen as a relatively uncommon choice of graduate study. A third group of subjects rated the similarity of the Tom W. description to the typical student in each field, and these ratings indicated that the description was seen as most representative or typical of computer science students.

5. In this study, the predictions of Tom W.'s field were inconsistent with Bayes' rule, the normative model for revising probabilistic predictions. The baserate probability of computer science in the Tom W. study is the probability that any graduate student (a randomly chosen student) is in computer science, and the case information is the Tom W. description. According to Bayes' rule, the probability that Tom W. is in computer science is the baserate probability of this field times a diagnostic ratio that represents the correlation between the description and the field: p(fieldi|description) = p(fieldi) x p(description|fieldi)/p(description).

6. Because p(description) is the same across fields, subjects asked to rate the likelihood of a field given the description should have attended to the remaining terms on the right side of the equation: the baserate p(fieldi) and the representativeness of the description p(description|fieldi). But subjects apparently attended to how representative the description was of computer science students, and neglected the low baserate probability of this field. Across fields, the likelihood rating that Tom W. was in a field was highly correlated with the likelihood rating of the Tom W. description within the field (representativeness), but not correlated with the baserate probability of the field. When the only information available to subjects was that Tom W. was a graduate student, predictions of Tom's field did correlate with the baserate estimates.

7. With these results, and related results from experiments in which baserates of occupations were manipulated (e.g., target individual from a group with 70% lawyers and 30% engineers, or vice versa), Kahneman and Tversky (1973) concluded that human judges generally neglect baserate information when judging the likelihood that an individual or event comes from a particular category. "One of the basic principles of statistical prediction is that prior probability, which summarizes what we knew about the problem before receiving independent specific evidence, remains relevant even after such evidence is obtained. Bayes' rule translates this qualitative principle into a multiplicative relation between prior odds and the likelihood ratio. Our subjects, however, failed to integrate prior probability with specific evidence. When exposed to a description, however scanty or suspect, of Tom W. or of Dick (the engineer/lawyer), they apparently felt that the distribution of occupations in his group was no longer relevant. The failure to appreciate the relevance of prior probability in the presence of specific evidence is perhaps one of the most significant departures of intuition from the normative theory of prediction" (Kahneman & Tversky, 1973, p. 243).

8. McCauley and Stitt (1978) pointed out that the Tom W. study reversed the direction of the usual stereotype study in social psychology. In the Tom W. study, subjects were given traits and asked for the most likely category; social psychologists since Katz and Braly (1933) have given subjects an ethnic or national category and asked for the typical traits. Both kinds of study depend on subjects' perceptions of a correlation between membership in a stereotyped group and certain traits, preferences, or behaviors. Indeed, the measurement of a stereotype is essentially the measurement of this perceived correlation, which can be assessed by asking subjects what percentage of people in the stereotyped group and in some comparison group have a particular trait, preference, or behavior. To the extent that the percentage estimates for the two groups are not the same, subjects are expressing a stereotype (McCauley & Stitt, 1978; McCauley, Stitt & Segal, 1980; McCauley & Thangavelu, 1991; McCauley, Thangavelu & Rozin, 1988).

9. Having understood the Tom W. study as a stereotype study, McCauley and Stitt (1978) attempted to replicate its results when subjects were asked for predictions in the direction familiar to social psychologists -- from stereotyped category to traits. For each of a number of traits, subjects estimated the same three Bayesian probabilities that were of interest in the Tom W. study, but this time in relation to the stereotype of Germans. Across traits, subjects' probability of a trait for Germans, p(traiti|German), correlated both with the representativeness of the trait, p(German|traiti), and with the baserate probability p(traiti). Thus, although the Tom W. study found subjects ignoring category baserate when going from stereotyped traits to category judgment, the German stereotype study indicated that subjects did use trait baserate information when going from stereotype category to stereotyped traits. McCauley and Stitt (1978) concluded that people may not be so generally unable to take account of baserate as Kahneman and Tversky (1973) had suggested.

10. The question of whether or when human judges underuse baserate information has become the focus of a great deal of research, which has produced quite complex results. The precise details of the procedure in which baserate and individuating information are communicated to subjects can make a significant difference in the attention subjects pay to each (Tversky & Kahneman, 1982, p. 154). More substantively, baserate information perceived as having causal connection to the judgment required will tend to get more attention (Ajzen, 1977; Tversky & Kahneman, 1982, p. 154) and, in general, more attention will be paid to baserate information as the diagnosticity of the baserate information increases and as the diagnosticity of the individuating information decreases (Hilton & Fein, 1989; Kreuger & Rothbart, 1988; Lynch & Ofir, 1989; Nelson, Biernat & Manis, 1990; Rasinski, Crocker & Hastie, 1985). The importance of diagnosticity in determining the impact of baserates is consistent with Bayesian prescription, and it appears fair to say that the evidence of the last fifteen years does not support quite so pessimistic a picture of human neglect of baserates as Kahneman and Tversky offered in 1973.

11. For my argument, however, the present status of research on neglect of baserate information is less important than understanding how this research was translated into a hypothesis about stereotype effects.


12. In two influential papers, Locksley (Locksley et al., 1980; Locksley, Hepburn & Ortiz, 1982) argued that a stereotype can be thought of as a baserate, that is, as the perceived probability of a stereotyped trait within the stereotyped group. She showed, for instance, that a male target was perceived as more likely to be assertive than a female target when no other information besides gender was available. This was undoubtedly a stereotype effect on judgment, but it disappeared -- sex of target had no effect on the probability that the target was assertive -- when the target was described as having engaged in assertive behavior. Citing Kahneman and Tversky (1973) on neglect of baserates, Locksley hypothesized that stereotype expectations about a target person -- like other baserates -- are neglected in the presence of individuating information relevant to the prediction required.

13. Locksley's formulation had powerful and surprising implications. It suggested that stereotype expectations will have little impact on the evaluation of individual members of a stereotyped group -- the kind of result obtained in Locksley's studies. Stereotypes might affect judgment about stereotyped groups in the abstract, or about individuals about whom nothing else was known but group membership. But once specific attributes or behaviors of an individual are known, stereotype expectations understood as baserate predictions should have little effect on judgment about the individual. Locksley thus made explicit what stereotype research has not always recognized (Bodenhausen, 1990; Darley & Gross, 1983; Langer & Abelson, 1974), that it is failure to use stereotype expectations that is counternormative.

14. The idea that stereotypes are easily swamped by individuating information has been good news for some (Myers, 1990, pp. 117-118), but others have found it too good to be true (Brown, 1986, pp. 602-608). As noted above, a number of recent studies have found evidence that people can use baserate information when individuating information is available, but my concern is that Locksley's formulation puts together two important issues that should be distinguished. The first is the claim that a stereotype is a baserate prediction. The second is the hypothesis that stereotype expectations are neglected in judgments about individual members of stereotyped groups. The importance of the distinction is that identifying stereotypes as baserate predictions leads to imprecision and ambiguity that need not get in the way of understanding whether stereotype expectations affect the evaluation of individuated targets.


15. The identification of stereotype expectations with baserate predictions leads to two conceptual problems. One is that a stereotype is usually understood to mean a perception of group difference, especially a perception of difference between in-group and out-group that can contribute to intergroup hostility and violence (Allport, 1954; Stephan, 1985; Hewstone & Brown, 1986). The perception of the baserate probability of a stereotyped trait within a stereotyped group, then, is only part of a stereotype. A belief that 85% of AIDS victims are homosexual, for instance, is a baserate belief but does not by itself imply a stereotype. A stereotype is implied when this belief is linked with another: that 5% of people without AIDS are homosexual. Thus it is, at best, imprecise to say that the stereotype belief is a baserate belief; more accurately, a stereotype belief is a perceived correlation of group membership and trait which includes the baserate belief as one half of the correlation.

16. The imprecision of understanding stereotypes as perceived baserates may sometimes be more a matter of shorthand expression than real misunderstanding. This shorthand can be confusing, however, when it leads to assessing stereotype accuracy in terms of the fit between perceived and actual baserates of stereotyped traits. A recent study by Judd, Ryan and Park (1991), for example, begins with a definition of stereotyping in terms of seeing differences: the investigators confirm the existence of a stereotype of engineering versus business students by showing that respondents from both groups see probabilistic differences between their groups (e.g., both estimate that a higher percentage of engineering than business students are analytical). Later, however, these investigators evaluate the "stereotypicality" of group perceptions by comparing perceived with criterion baserate percentages (the perceived percentage of engineers who are analytical versus the percentage of engineers who say they are analytical). Of course it can be of interest to know about the accuracy of the baserate estimates, but these absolute percentage estimates can be quite inaccurate even as the perceived differences that define the stereotype are surprisingly accurate. For example, estimates of Black Americans and all Americans who have completed high school can be in error by ten percentage points (McCauley & Stitt, 1978, Table 2, High School Ss: mean estimates of 48 percent and 70 percent versus U.S. Census 39 percent and 60 percent) even as the mean estimated difference between Black Americans and all Americans is quite accurate (estimated difference 22 percentage points versus Census difference of 21 percentage points). At minimum, therefore, the imprecision of seeing stereotypes as baserates can contribute to communication difficulties in evaluating stereotype accuracy.

17. Beyond this communication problem, the attempt to understand stereotypes as baserates encounters another and deeper kind of problem. What is the definition of baserate, as opposed to individuating information?

18. The hypothesis that people neglect baserate information in favor of individuating information requires, in the first instance, a definition of these two kinds of information. Tversky and Kahneman (1982, p. 153) distinguish between "the baserate probability of the target event in some relevant reference population" and "some specific evidence about the case in hand." It is instructive to apply these definitions to the stereotype judgment problem used by Locksley et al. (1980).

19. Subjects were asked to judge the likelihood that a target person was assertive. The information available was the gender of the person and a description of the person behaving in an assertive or unassertive way. Locksley et al. take the relevant reference population as the population of males (or females) and the behavior as the specific evidence. That is, they interpret the problem as a Bayesian prediction in which the baserate probability of assertive given gender should be revised according to the diagnostic value of the behavior.

20. The Bayesian probabilities for this interpretation are as follows (see McGee, 1971, p. 294): p(assertive|behavior,male) = p(assertive|male) x p(behavior|assertive,male) / p(behavior|male). Here a probability conditioned on two cues appears with the cues separated by comma, e.g., p(assertive|behavior,male) can be read as the probability of being assertive given both that the target person fits the behavior description and that the target is male.

21. Another interpretation is possible, one that takes as the baserate the probability of assertiveness given the behavior and that takes gender as the individuating evidence. The behavior identifies a relevant reference population of persons -- those who behave as described -- and this population is associated with some probability of being assertive. And being male or female is specific evidence about the target person, specific at least in being objective rather than subjective and determinate rather than probabilistic. In this interpretation the baserate probability of assertiveness given behavior should be revised according to the diagnostic value of gender. The Bayesian probabilities for the alternative interpretation are: p(assertive|behavior,male) = p(assertive|behavior) x p(male|assertive, behavior) / p(male|behavior).

22. In short, both gender and behavior are diagnostic for the judgment of assertiveness, and nothing about the problem determines which should be taken as the baserate information. The two Bayesian interpretations are equivalent. Both are correct. The probability of assertiveness given maleness can be taken as the baserate, as Locksley et al. took it, but with equal logic one could take as the baserate the probability of assertiveness given the behavior. The prediction that baserate will be neglected in favor of individuating information requires a distinction between baserate and individuating information, but there is nothing in Bayes' rule that determines which is which.

23. The same ambiguity arises in more recent studies that followed Locksley et al. (1980) in identifying stereotype expectations as baserate predictions. Most of these studies present subjects with a prediction problem like the one just described, that is, a problem involving three nonredundant categories in which the cue value of a stereotype category should compete with the cue value of some other (more or less diagnostic) behavior in determining predictions of the likelihood that a target person fits some third category.

24. For Locksley, Hepburn and Ortiz (1982), the stereotype category was nocturnal-diurnal, the competing information was a description of background and behavior, and the target categories were stereotype-linked traits (e.g., rebellious). For Kreuger and Rothbart (1988), the stereotype category was gender, the competing information was behavior, and the target categories were aggressive behaviors. For Hilton and Fein (1989), the stereotype categories were gender or college major, the competing information was behavior, and the target categories were stereotype-linked traits (assertive or competitive). And for Nelson, Biernat and Manis (1990), the stereotype category was gender, the competing information was a picture, and the target category was height.

25. For all of these studies, the ambiguity of defining baserate is the same as already described for the problem used by Locksley et al. (1980): there is nothing in Bayes' rule to establish that the stereotype expectations are the baserate information whereas the expectations associated with behavior are the individuating information. The ambiguity arises because Bayes' rule prescribes only how to integrate two probabilistic cues; the rule is indifferent to which cue is considered baserate and which individuating information. Without some accessory assumption, there is no way to predict which information should be neglected and which is the individuating information or "specific evidence."

26. The accessory assumption in the studies just cited was that the behavioral information did not establish a relevant reference population. But behavioral information does put the target in a population of persons, the population or category of persons who have behaved or would behave as described. Indeed, if subjects did not take the behavioral information as categorical, if they understood the description as somehow unique to the target person, then the behavioral information would say nothing about the categorical prediction subjects are asked to make. That is, if subjects understood an assertive behavior to be a unique product of the target individual, then the behavior would imply nothing about the likelihood that the target was assertive. The impact of behavioral information was strong in each of the cited studies, however, and this impact is evidence that subjects understood the behavioral description in categorical terms in relation to the categorical prediction they were asked to make.

27. The ambiguity in defining baserate in the cited studies is relatively nonobvious, but a small variation on these studies would make the ambiguity obvious. Suppose the information about the target person included membership in two kinds of stereotyped category. Suppose that a target were described as both female and black, for example, and the target category to be predicted was aggressive behavior. What would now be the prediction from understanding stereotypes as baserates?

28. I have argued in this section that stereotypes are not usefully identified as baserate predictions, at least not until some independent definition of baserate is forthcoming. The obvious place to seek this definition is in a closer examination of the literature in cognitive psychology that gave rise to the hypothesis that humans neglect baserates.


29. Again I begin with the definitions of baserate and case information offered by Tversky and Kahneman (1982, p. 243), this time in application to the Tom W. problem. Subjects are asked to predict the graduate field that Tom W. is enrolled in. As interpreted by Kahneman and Tversky (1973), the baserate probability of a field is the probability that a randomly chosen graduate student is in the field and the specific evidence is the description of Tom W. This is the interpretation represented above in my translation of the Tom W. problem into Bayesian terms.

30. But notice that the personality description of Tom is no less a categorical cue than the information that he is a graduate student. The personality description determines a relevant reference population: all the individuals who fit the description of being uncomfortable with people, liking corny puns, and so forth. The baserate of a field of graduate study for this population is the probability that a person randomly chosen from among those fitting the description will be a graduate student in the field. Note also that the information that Tom W. is a graduate student is specific evidence about Tom. Thus a Bayesian prediction of Tom W.'s graduate field can proceed from consideration of the baserate established by the personality description, with revision of the baserate according to the individuating information that Tom W. is a graduate student.

31. The Bayesian probabilities for this interpretation are as follows: p(fieldi|student,description) = p(fieldi|description) x p(student|fieldi,description) / p(student|description). This interpretation takes p(fieldi|description) as the baserate, but in my first interpretation of the Tom W. problem I followed Kahneman and Tversky (1973) in taking p(fieldi|graduate-student) as the baserate. Actually, the Bayesian interpretation of the Tom W. study that I first offered was a simplification that did not make explicit that the baserate p(fieldi) was conditional on the information that Tom was a graduate student. In practice all Bayesian baserates are conditional.

32. The full Bayesian accounting of Kahneman and Tversky's interpretation of the Tom W. problem would have taken this form: p(fieldi)|student,description) = p(fieldi|student) x p(description|fieldi,student) / p(description|student). The two Bayesian predictions are equivalent; both are correct. If both are correct, the determination of what is baserate and what is case information is again arbitrary.

33. The Tom W. study was purely correlational, but the same ambiguity arises in experiments where "baserates" have been explicitly manipulated. Subjects have been given, for example, a personality description (stereotype of engineer or lawyer) of an individual from a group that is 70% lawyers and 30% engineers (or the reverse). Subjects' judgments of the likelihood that the target was a lawyer often showed neglect of the percentage of engineers and lawyers (Ginossar & Trope, 1987; Kahneman & Tversky, 1973), but again it is not clear why this should be called the baserate information. An equivalent Bayesian prediction of the likelihood that the target is an engineer could begin from an impression of the percentage of persons fitting the description who are lawyers, with revision of this probability according to the diagnostic value of the information that the target came from a group that was 70% lawyers.

34. Similarly, judges have been given the prevalence of blue cabs and yellow cabs and a witness's description of an accident and asked the likelihood that a car involved in an accident was a blue cab or a yellow cab. Subjects often neglect what they have been told about the percentages of blue and yellow cabs (Lynch & Ofir, 1989), but it is not clear why this should be called the baserate information. The baserate might equally be taken as the likelihood of blue cab given only the testimony of the witness.

35. The experimental studies just described have only two categories of information at issue: membership in a group with an explicit percentage of the category to be predicted, and membership in a group defined by personality that has an associated inexplicit percentage of the category to be predicted. In these two-category prediction problems, it seems wrong-headed and unnatural to think of the personality group as the baserate group. Surely subjects should begin with what is most clear and objective, the baserate provided by the experimenter, and then try to take account of the diagnostic value of the case evidence. Surely it is difficult for subjects to arrive at a quantitative baserate estimate (of lawyer or blue cab) given only the qualitative case evidence, and subjects are therefore foolish to begin from this evidence when an explicit baserate probability is available. But these intuitions about what should be anchor and what should be adjustment on the basis of what is simpler, clearer, or more natural are only intuitions. They are no substitute for an an objective definition of what kind of information will be neglected.

36. Suppose, for example, that subjects had only the so-called case information (personality description or witness report) and were asked for a prediction (occupation or cab color). Would this prediction not be baserate prediction if the same subjects were then given the information about the prevalence of occupation or cab color in the population from which the target came?

37. Conventionally, the baserate prediction is understood as the category probability of a target given everything known before or in addition to the cue of interest, the case information. Kahneman and Tversky (1973, p. 243) refer to this convention, as quoted above, in explaining that prior probability "summarizes what we knew about the problem before receiving independent specific evidence." But Kahneman and Tversky (1973; Tversky & Kahneman, 1982) do not suggest that whatever probabilistic information comes first will be neglected in favor of whatever probabilistic information comes second. Rather, they refer to baserate and individuating information as if these were independently defined. Thus, the conventional Bayesian meaning of the term "baserate" does not provide the requisite distinction between baserate and individuating information.

38. Nor does the representativeness hypothesis. Kahneman and Tversky (1973) hypothesize a tendency to make judgments by representativeness, the degree to which the case evidence is representative of or similar to the target category. This hypothesis does not speak to the logically prior problem of how to determine what will be considered the case evidence, as distinct from the baserate evidence. No more than Bayes' rule, then, does representativeness provide a warrant for speaking as if baserate and individuating information are two objectively different kinds of information.

39. It is of course possible that the distinction between baserate and individuating information could be translated, in future research, into terms that do have objective referents. Promising possibilities might include the distinction between vivid information and statistical information (Nisbett & Ross, 1980, p. 45), between more and less salient information (Fiske & Taylor, 1984, pp. 185-190), or the between causal and incidental evidence (Tversky & Kahneman, 1982, p. 118). In the absence of this kind of theoretical advance, however, any prediction about stereotype effects as baserate effects is vacuous; any identification of one probabilistic cue as baserate and another as individuating information is arbitrary.

40. Another possibility for resolving the problem of defining baserate is to get rid of the term entirely. Ginossar and Trope (1987), for example, interpret use and neglect of baserates in terms of general principles of problem solving. These principles predict when subjects will or will not translate probabilistic cues into judgment in a way that does not require calling some cues baserates and others individuating information. In other words, a useful account of when competing sources of information will affect judgment might not need to distinguish baserate and individuating information.


41. The conclusion to be drawn from the preceding discussion is this: identifying stereotypes as baserates does not put the study of stereotyping on a firm foundation in research in cognitive psychology. Rather, this identification wraps stereotype research in the enigma of how to define the baserate information that will be neglected as judges attend to the representativeness of case information.

42. Indeed, the studies in cognitive psychology that originally suggested human neglect of baserates suffer the same ambiguity in distinguishing baserate from individuating information that plagues the stereotype studies. Future research might clarify the definition of baserate and give substance to the hypothesis that people neglect baserates, or it might be that the use and neglect of probabilistic cues are better understood in terms of principles that do not require defining some cues as baserate information. At present, however, the literature on neglect of baserates does not show neglect of baserates. It does show serious violations of the normative Bayesian model for integrating probabilistic cues, violations in which one cue is neglected in favor of another. Missing from this literature, as from the stereotype literature that has attempted to draw on it, is any objective or independent specification of the kind of cue that will be neglected.

43. The ambiguity in defining baserate information means that identifying stereotypes as baserates does not lead to clear predictions about when stereotype expectations will be neglected in evaluating individuals. Identifying stereotypes as baserate predictions can also be misleading in failing to recognize the comparative aspect of stereotyping: stereotypes are perceptions of probabilistic group differences rather than simple perceptions of the characteristics of a stereotyped group. But recognizing the ambiguity and imprecision of trying to understand stereotypes as baserates only sharpens the question of when and to what degree stereotypes affect the evaluation of individuals. This question is as important today as when Locksley et al. (1980, 1982) enunciated it.


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My thanks to Jonathan Baron for helpful suggestions about an earlier version of this paper.

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