Identity and position: Dependence originates from independence

Abstract

Experiments investigating identity processing and position processing show a variety of results. Especially the parameters used to quantify the dependence relation between identity and position, the phi-coefficient and the chi-square, differ wildly. In this study an attempt is made to find out how these differences originate. The results of an experiment with oriented line-segments as stimuli are reported. The overall data showed a complete dependence of orientation responses upon position responses in the sense that there was no orientation information without position information. It is argued and shown that the overall response matrix consists of two independent submatrices, one for the set of trials with (position) information and one for the set of trials without (position) information. This result made it possible to identify three factors that affect the phi-coefficients and chi-squares: The proportion of trials with and without (position) information, the discriminability within the identity dimension and the number of response alternatives. The conditional probability identity correct given position incorrect ( p(I+ βP−)) is not affected by these factors. Therefore, this conditional probability is the best indicator of (in)dependence.