Signal Detection Analyses of Dimensional Interactions
Helena Kadlec Purdue University
James T. Townsend Indiana University
This chapter traces the development and impact of Signal Detection Theory in the study of perception. Emphasis is on the extension of Signal Detection Theory to visual perception in two-dimensional perceptual spaces, although the results presented here are general and not restricted to the visual domain or the two- dimensional case. Within the context of General Recognition Theory (GRT; Ashby & Townsend, 1986; see also chaps. 6 and 16 in this volume), theoretical relationships exist between the unobservable notions of perceptual separability and perceptual independence and the observable (and estimable) concepts of sampling independence, marginal response invariance, and two sets of signal detection parameters ( Kadlec & Townsend, 1992). These relationships and their applications will be presented.
A procedure for testing perceptual independence and perceptual and decisional separabilities follows from these theoretical results. We illustrate it with three sets of data. The first data set is a direct application of the results in a two- dimensional space where the stimuli have two components each at one of two possible levels of presentation. The second data set illustrates the generalization to a situation where stimuli are composed of four components each at one of two possible levels. The third data set generalizes the procedure to a case where stimuli are two-dimensional, but each component has one of four possible levels of presentation. Some issues related to these generalizations of Signal Detection Theory to more than one and two dimensions will be discussed.
The organization of the chapter is as follows. In the first section we briefly review unidimensional Signal Detection Theory and some of its applications and