Are Judgments a Form of Data Clustering? Reexamining Contrast Effects With theK-Means Algorithm

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Abstract

A number of theories have been proposed to explain in precise mathematical terms how statistical parameters and sequential properties of stimulus distributions affect category ratings. Various contextual factors such as the mean, the midrange, and the median of the stimuli; the stimulus range; the percentile rank of each stimulus; and the order of appearance have been assumed to influence judgmental contrast. A data clustering reinterpretation of judgmental relativity is offered wherein the influence of the initial choice of centroids on judgmental contrast involves 2 combined frequency and consistency tendencies. Accounts of the k-means algorithm are provided, showing good agreement with effects observed on multiple distribution shapes and with a variety of interaction effects relating to the number of stimuli, the number of response categories, and the method of skewing. Experiment 1 demonstrates that centroid initialization accounts for contrast effects obtained with stretched distributions. Experiment 2 demonstrates that the iterative convergence inherent to the k-means algorithm accounts for the contrast reduction observed across repeated blocks of trials. The concept of within-cluster variance minimization is discussed, as is the applicability of a backward k-means calculation method for inferring, from empirical data, the values of the centroids that would serve as a representation of the judgmental context.

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