As time goes by: The role of variability in category belief revision

As time goes by: The role of variability in category belief revision Lauren Kearney (lkearney@psy.unsw.edu.au) Brett K. Hayes (B.Hayes@unsw.edu.au) School of Psychology, University of New South Wales Sydney, 2052, Australia Abstract Two studies examined the effect of category variability on revision of stereotypical and non-stereotypical beliefs. In Experiment 1, participants learned the characteristics of various groups via exposure to numerical distributions of category attributes. These distributions had the same mean values, but either high or low levels of variability around the mean. The categories were either stereotyped categories or non-stereotyped categories. After learning category attributes, participants were exposed to disconfirming exemplars (drawn from a sample with higher or lower means). Participants were then asked to re-estimate the central tendency of the category and to rate the likelihood that the category had changed. Beliefs about categories with low variability were more influenced by disconfirming information than beliefs about highly variable categories. This relationship was the same across category domains. This same general pattern was found in Experiment 2 where participants had to request information about test instances before deciding whether category values had changed. The results are consistent with Bayesian models of belief revision. Keywords: statistics Categorization, Belief revision, Bayesian Introduction Imagine that you were a climate change researcher and you discovered that the average number of cyclones in a particular location had increased by 30 per cent over the past three years. You then have to decide whether this represents good evidence for change in the underlying weather patterns. To answer this question one needs to consider not only the mean number of cyclones in the past, but also the past variability of cyclone activity. If the mean number of cyclones in the area had shown little variability prior to the recent increase, then you may be more convinced that some underlying change had occurred than if you knew that the past pattern of cyclone activity was highly variable. This sort of problem can be construed as one of category belief revision. After encountering instances with unexpected properties can we conclude that the typical properties (e.g., annual frequency) of a category (e.g., cyclones) have changed? It seems evident that in order to remain useful, knowledge and beliefs about category properties need to reflect changes in underlying category structure (Garcia-Marques & Mackie, 1999). The challenge then for perceivers is to determine when meaningful change has actually occurred. As highlighted in the earlier example, one factor that seems important in determining when it is appropriate to revise category beliefs is the variability of the category exemplars that form the basis for the belief. Although some work has examined the influence of category variability in related areas such as category learning (Stewart & Chater, 2002), category discrimination (Hahn, Bailey & Elvin, 2005), and induction (Nisbett, Jepson, Kunda and Krantz, 1993), relatively few studies have directly examined the impact of category variability on belief revision. In one of the few studies to examine this issue, Rehder and Hastie (1996) presented participants with category attributes. Each attribute was represented by a numerical value (e.g., a politeness score). Half the participants saw categories with highly variable attribute distributions while the other half saw distributions with low variability. Critically, the high and low variable distributions had the same mean; hence participants were expected to acquire similar beliefs about the central tendency of category attributes, but have different expectations about the level of variability around this value. When participants were subsequently exposed to novel exemplars with highly discrepant attribute values (higher or lower), participants who had initially seen the low variable distribution changed their central tendency beliefs more than did those who had initially seen the high variable distribution. In addition to the experimental evidence, Rehder (1996) proposed a normative model outlining how people might use variability information. If the task is cast as one of Bayesian inference, whereby observation of a set of category exemplars allows one to calculate a central tendency estimate, then the variability of the original information should be of paramount importance. When one is presented with novel information, the calculation of the most likely posterior mean should be made on the basis of the prior mean, the variability of the initial distribution of exemplars, and the new single observation. As the standard deviation of the initial distribution increases, the weight of each piece of disconfirming information decreases and vice versa. Although the Rehder and Hastie (1996) results support a Bayesian model of belief revision, some evidence suggests that people do not always respond to disconfirming information in a normative manner. One obvious domain where disconfirming information often fails to change existing beliefs is in social stereotyping (see Hilton & von Hippel, 1996 for a review). Moreover, there is evidence to suggest that, in the social domain, category variability may play a very different role in mediating belief change than the