The Expectation Effect of the Sample Size in Category Learning
2012, 44 (6):
This paper explores the effects of category size expectations on category learning. The expectation effect is the finding that category learning is improved when subjects are told how many items or exemplars are in each category in advance.
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There are three major theories or models of how categories are represented: Rule-based, Prototype-based, and Exemplar-based. Rule-based models assume that category learning is a process of discovering an explicit, verbalizable rule that maximizes categorization accuracy (Ashby, 2005; Seger & Cincotta, 2006). Prototype-based models assume that stimuli are categorized on the basis of their similarity to category prototypes stored in memory (Rosch & Mervis, 1975; Smith, Chapman, & Redford, 2010; Coutinho, Redford, & Smith, 2010). A category prototype is generally defined as the average, or most typical, member of a category. Exemplar-based models assume that the categorization of a new exemplar is based on the similarity of the new exemplar to the representations of all previously encountered exemplars stored in memory (Medin & Schaffer, 1978; Kruschke, 1992; Nosofsky, 1992).
According to Rule-based and Prototype-based models, people abstract the rule or prototype as their final representation without regard to the total number of exemplars in each relevant category; therefore, knowing how many exemplars are in each category should not affect learning. However, according to Exemplar-based models categories are represented as all the, specific exemplars that have been previously experienced. This implies that knowledge of category size may improve exemplar based categorization learning.
Two learning conditions, Known condition (KC) and Unknown condition (UC) were compared in this experiment. In KC participants were instructed as to how many total exemplars (9) they would see across both categories. In UC participants were given no information about category size. The “5-4 category structure” from Medin and Schaffer (1978) was adapted in order to be able to identify which kinds of representation the participants were forming: rule, exemplar or prototype. 106 undergraduate students took part in the experiment. During each trial, an individual exemplar was presented, the participant was then asked to decide and indicate which category (A or B) the exemplar belonged to, and finally feedback as to whether the response was right or wrong was provided. Training continued until participants reached a learning criterion of three consecutive blocks with a combined accuracy of 90%, or until they completed 40 blocks (360 trials). A mathematical technique of “Model Fitting” was introduced to analyze the data from experiment. Different models were used to examine whether participants’ responses were best fit by exemplar or prototype models, to identify which features the participants paid attention to, and to identify which categorization strategy participants used.
The results showed that the expectation effect for category size was significant. Participants who knew the sample size (KC) at the beginning of learning required fewer blocks on average to reach the criterion than the participants who did not know the sample size (UC) in advance; 22 and 27 blocks respectively, t (68)=2.088, p<0.05. This result is consistent with the predictions from the Exemplar-based models but not the Rule-based or Prototype-based models. To explore whether the prototype or exemplar model provided the better account of the participant’s representation, we adopted a mathematical method of parameter estimation (Minda & Smith, 2002) and fitted two models to each participant’s data: exemplar processing was assessed via a five-parameter version of the General Context Model (GCM), and prototype processing was assessed using the Multiplicative Prototype Model (MPM). We found that the fit of the GCM was quantitatively superior to the MPM model for both learning conditions. We also found that the KC group was more sensitive to the diagnostic dimensions of the category than the UC group. Across the blocks of training, the KC group showed three distinct phases of learning: an early phase in which overall accuracy was consistent with a single-rule strategy, followed by a phase in which accuracy was consistent with a rule-plus-exception strategy, and finally a phase in which accuracy was consistent with an information-integration strategies. This three phase pattern was not present in the UC group.