The role of subtractions and comparisons in comparative judgments involving numerical reference points

Experiments in which subjects are asked to decide which of two digits is closer in magnitude to a third raise problems for many theories of linear orders. Holyoak (1978), for example, performed a number of these reference point experiments and concluded that they posed serious difficulties for a number of leading models. In their place, he offered the distance ratio model in which the ease of the decision in a reference point task is a function of the ratio of the distances between each stimulus and the reference point. In the present article, three experiments are presented that bear on the adequacy of Holyoak's position. In the first two studies, we present evidence that an important assumption of the distance ratio model is incorrect. In the third experiment, we compare the empirical adequacy of the distance ratio model with our own subtraction model. This model treats the reference point task as a concatenation of two subtractions and a simple digit comparison. This comparison operation is equivalent to the magnitude comparison required in standard linear order experiments. Overall, the subtraction model gives a somewhat better account than the distance ratio.     

Categorization processes in mental comparisons

Five experiments explore categorization and category-based congruity effects in mental comparisons. The first 4 experiments concentrate on categorization of infinite-set small items. The experiments vary the additional items presented and whether those items appear once (Experiments 1-2) or repeatedly (Experiments 3-4). Additional items include other small items (Experiment 1), relatively large items (Experiments 2-4), and items involving nonsize dimensions (Experiment 4). The critical small items show a complete congruity effect only in Experiments 1 and 3. Results suggest that categorization of infinite-set items may be based on range information alone (Experiment 1) but that multiple categorizations based on multiple ranges (Experiment 2) may require attentional effort. Results implicate categorization as a central process in mental comparison, despite differences in ease of categorization across paradigm.     

Context effects in symbolic magnitude comparisons

Five experiments demonstrate that context has an effect on the ease with which people can determine the relative sizes of pairs of large and small animals. In a standard context, people are faster at choosing the larger of two large animals and the smaller of two small animals. However, when only pairs of small animals are presented (Experiment 1), relatively large pairs (RABBIT-BEAVER) are treated as if they were large animals and are discriminated more rapidly under the choose larger instruction. Similarly, when only large animals are presented (Experiment 2), the smaller of these are now treated as if they were small animals. Several models are presented that account for these effects of context, and these models are examined in subsequent experiments that impose yet other variations in magnitude pairings. The results demonstrate the importance of context in comparative judgement and place important constraints on theories of linear orders.