A Theory of Order Relations in Perceptual Matching

A theory of order relations in the perceptual matching task relates order manipulations to research on retrieval processes and the representation of order information in memory. In experimental tests of the theory, presentation of a study string of letters to the subject was followed by a test string to which the subject responded same or different. The data of main interest concern the case where the test string is a permutation of the study string. When adjacent letters are switched, reaction time is long and accuracy low, suggesting that, in the comparison process, a test letter is not simply compared to the letter in the same position in the study string; rather, the comparison is distributed across positions. The memory model assumes that the representation of a letter is distributed (spread) over position and that the comparison process assesses the amount of overlap between the test string and the memory representation. The amount of overlap is transformed by a power function into the drift rate in a diffusion (random walk) comparison process. The diffusion retrieval model and overlap memory model are fitted to the data and goodness-of-fit is assessed. Shortcomings of alternative models are considered and applications of the model to related matching tasks are described.