An extended study of the nonindependence of stimulus properties in human classification learning

Abstract

Categorization researchers have tried to verify their models through laboratory experiments with simplified stimulus sets, a requirement that can rarely be met in real-world situations in which properties are often connected. Still, the targeted simplification of the material might be illusory. We replicate and extend Love and Markman's (2003) study of the nonindependence of canonical stimulus properties such as size, colour, and shape in human classification learning, in which the authors concluded that shape takes precedence over other dimensions. To support their hypothesis, Love and Markman showed that certain classifications are more difficult for participants when shape is combined to one of its putative subordinate features, size or colour, than when shape is irrelevant to the task. A data set of 290 + 50 adult participants completing one or more classification tasks was collected. The results confirm that certain combinations of shape, size, and colour can hinder or facilitate classification learning, but not necessarily in the form expected by the nonindependence postulated by Love and Markman, especially in Experiment 2 where a totally reverse pattern of difficulty is observed (shape does not take precedence over other dimensions). Also, we show that simple similarity effects in clustering retain considerable intuitive appeal and can offer an alternative account to the nonindependence of stimulus properties, especially because slight variations in the dimensions chosen make the observations of Love and Markman unstable.

Keywords:

• Concept learning
• Categorization
• Boolean
• Rules
• Similarity

Acknowledgments

This research was partly supported by a postdoctoral research grant from the Fyssen Foundation awarded to Fabien Mathy in 2005. We thank the students of Rutgers University and the Université de Reims Champagne-Ardenne who kindly volunteered to participate in this study. The authors wish to thank Cordelia Aitkin, Erica Briscoe, David Fass, and Jacob Feldman from the Visual Cognition Lab for their many helpful comments.

Notes

¹ In Figure 1, each stimulus is attached to one vertex of a cube. The cube represents the whole stimulus set. The number of edges separating two stimuli represents the distance between the stimuli. For instance, the three differences between a large grey circle and a small white square are adequately represented by a distance of three edges (this type of distance is called city-block, by opposition to the Euclidean distance, which would compute distance using diagonals).

² Although not pointed out by the authors, an object-oriented language would also have been appropriate for describing these dependencies:

object.shape = triangle

object.shape.colour = red

object.shape.size = large

In programming, then, shape, size, and colour are not taken as properties that are encapsulated at the same level in the object.

³ The idea that shapes, sizes, and colours are not treated equally has been confirmed by research in cognitive development. In several studies where stimuli varying in shape and colour were presented to 4-month-old infants, shape overrode colour as the basis for preferential choice when the stimuli represented combinations of preferred and nonpreferred colours and shapes (Spears, 1964). More recently, Tremoulet, Leslie, and Hall (2000) showed that for 12-month-olds, a difference in shape had a large effect on identification, whereas colour difference did not. Inhelder and Piaget (1959) also noted that children tended to prefer shapes in free classification tasks (although preferences vary with age; Brian & Goodenough, 1929). When the triad shape/colour/size was considered in preferential-matching tasks (with children around 6 years of age), shape was distinctively preferred over colour, and colour was preferred over size (Kagan & Lemkin, 1961). Lee (1965) showed that preschool children have progressively a greater ease in utilizing form over colour and size in concept-identification tasks, with the youngest preschool children making fewer errors with color and size than with form, and with the oldest preschool children making fewer errors with form than with color and size. In another study, children over 5 years have also been shown to prefer colour over size in preferential-matching tasks (Pitchford & Mullen, 2001). Such biases can still be observed in adults when appropriate measures are made. On the dimensional-change card-sort task, for instance, Diamond and Kirkham (2005) showed that response times were longer when participants had to sort cards by colour than when they had to sort them by shape.

⁴ In other words, in the size–shape relevant concepts in Figure 1, the large squares are different in shape from the large circles and different in size from the small squares (idem for the small circles). The only difference is that the clusters within categories (e.g., the large squares and the small circles) differ in terms of both shape and size, which place them further apart than the clusters of the opposite category; the greater distance between the clusters within categories is noticeable in the cube, in which the positive clusters are opposed by a diagonal distance, whereas clusters between categories are only opposed by an edge.

⁵ Another possibility is that participants speeded up the classification when the sample of examples was larger (that is, when the progress bar was longer) because they were eager to complete the progress bar.

⁶ The idea is that the participants are inclined to focus on the dimensions that are relevant and to ignore the ones that are irrelevant. A greater attention weight indicates that participants focus more on the dimension and that dimensional values are better discriminated. The attention weights are constrained to sum to one, which means that more focus on one dimension corresponds to less focus on another one.