Theoretical analysis of an alphabetic confusion matrix

A study was undertaken to acquire a confusion matrix of the entire upper-case English alphabet with a simple nonserifed font under tachistoscopic conditions. This was accomplished with two experimental conditions, one with blank poststimulus field and one with noisy poststimulus field, for six Ss run 650 trials each. Three mathematical models of recognition, two based on the concept of a finite number of sensory states and one being the choice model, were compared in their ability to predict the confusion matrix after their parameters were estimated from functions of the data. In order to ascertain the facility with which estimates of similarity among the letters could lead to a psychological space containing the letters, η_ij, the similarity parameter of the choice model was input to an ordinally based multidimensional scaling program. Finally, correlation coefficients were computed among parameters of the models, the scaled space, and a crude measure of physical similarity. Briefly, the results were: (1) the finite-state model that assumed stimulus similarity (the overlap activation model) and the choice model predicted the confusion-matrix entries about equally well in terms of a sum-of-squared deviations criterion and better than the all-or-none activation model, which assumed only a perfect perception or random-guessing state following a stimulus presentation; (2) the parts of the confusion matrix that fit best varied with the particular model, and this finding was related to the models; (3) the best scaling result in terms of a goodness-of-fit measure was obtained with the blank poststimulus field condition, with a technique allowing different distances for tied similarity values, and with the Euclidean as opposed to the city-block metric; and (4) there was agreement among the models in terms of the way in which the models reflected sensory and response bias structure in the data, and in the way in which a single model measured these attributes across experimental conditions, as well as agreement among similarity ami distance measures with physical Similarity.