Sample size, number of categories and sampling assumptions: Exploring some differences between categorization and generalization

Abstract

Categorization and generalization are fundamentally related inference problems. Yet leading computational models of categorization (as exemplified by, e.g., Nosofsky, 1986) and generalization (as exemplified by, e.g., Tenenbaum & Griffiths, 2001) make qualitatively different predictions about how inference should change as a function of the number of items. Assuming all else is equal, categorization models predict that increasing the number of items in a category increases the chance of assigning a new item to that category; generalization models predict a decrease, or category tightening with additional exemplars. This paper investigates this discrepancy, showing that people do indeed perform qualitatively differently in categorization and generalization tasks even when all superficial elements of the task are kept constant. Furthermore, the effect of category frequency on generalization is moderated by assumptions about how the items are sampled. We show that neither model naturally accounts for the pattern of behavior across both categorization and generalization tasks, and discuss theoretical extensions of these frameworks to account for the importance of category frequency and sampling assumptions.

The influence of reward magnitude on stimulus memory and stimulus generalization in categorization decisions.

“…Moreover, in a study on reward and category preferences, Maddox and Bohil (2001) reported a very similar category bias when one of two categories was associated with a higher reward (see also Figure 2 in Healy & Kubovy, 1981), as Hendrickson et al (2019) reported for stimulus frequency with two exclusive categories. This suggests that in a categorization task with two exclusive categories, the effect of reward on similarity gradients might also be in the opposite direction, as in the "one category" reward-learning task by (Kahnt et al, 2012); that is, the similarity gradients of high-reward items may become broader instead of narrower.…”

“…Indeed, memory strength seems to be a meaningful formal concept to capture frequency effects in tasks that explicitly ask for recalling or recognizing stimuli (e.g., Donkin et al, 2015;Nosofsky, 1991b). However, stimulus frequency also seems to affect categorizations differently from what might be expected from a GCM perspective (e.g., Hendrickson et al, 2019;Homa et al, 2018). In line with Nosofsky's (1991) argument that empirical investigations need to substantiate theorized principles, these findings raise the general question of whether categorization phenomena that seem intuitively related to memory strength (e.g., reward and frequency) might rather point to changes in stimulus-specific similarity gradients (see also Goldstone & Son, 2005;Hendrickson et al, 2019).…”

A Cognitive Category-Learning Model of Rule Abstraction, Attention Learning, and Contextual Modulation

“…We assume that excitatory generalization is self-confirmatory, i.e. reinforces prior expectations (see also Berndsen, van der Pligt, Spears, & McGarty, 1996;Heit, 1997).…”

Peer Tutoring Effects on Students’ Mathematics Anxiety: A Middle School Experience

“…Although the potential positive impact of peer tutoring on middle school students' mathematics anxiety seems quite evident considering the results reported in this research, certain limitations must be considered when interpreting them. First, the sample size, although not considered short or trivial by many researchers in the educational psychology field, cannot be considered large, either (Hendrickson et al, 2019;Sassenberg and Ditrich, 2019). Also, the sample was obtained by means of an intentional sampling (non-probabilistic) and only a single middle school participated in the study, so it is not representative of middle school students in Spain nor students outside the country.…”