Fechnarian Scaling: Metric from Discriminability

Purdue Research Foundation, West Lafayette IN

Investigators

Abstract

This research is based on a new theory of how subjective (Fechnerian) distances among objects that form a continuously parametrized space can be computed from the degree of discriminability of each object from its infinitesimally close neighbors. This theory uses the apparatus of modern differential geometry (generalized Finsler spaces, previously successfully applied to a variety of problems in physics and, more recently, biology) to refine the 150 year-old ideas of G.T. Fechner and generalize them to stimulus spaces of arbitrary dimensionality. The research is aimed at exploring several important theoretical issues stemming from this development, and at empirically testing its applicability to one- and two-dimensional stimulus spaces. The theoretical part of the research includes such issues as (1) the possible ways in which discrimination probabilities may be determined by inter-stimulus distances, and the relationship between these distances and the Fechnerian metric computed from these discrimination probabilities; (2) the constraints imposed on Fechnerian distances by various versions of the perceptual separability and independence assumptions; and (3) the possible ways of generating discrimination probabilities by means of a model in which each stimulus is assumed to be represented by a random variable in a perceptual space, and two stimuli be discriminated in a given trial if and only if their random representations are separated by more than a certain critical distance. The empirical part of the research is aimed at such goals as (A) reconstruction of the vertical and horizontal cross-sections of discrimination probability functions in small vicinities of their minima; (B) testing the invariance of Fechnerian distances computed from discrimination probabilities corresponding to different levels of subjective confidence; and (C) the comparison of the Fechnerian metrics computed from different judgment schemes, such as "same-different" and two-alternative forced choice. The stimulus space used in all the experiments is formed by varying the distance and direction of instantaneous displacements of a small visual target. A successful completion of this project promises to significantly advance the theoretical foundations of measurement in psychology, as well as in any other domain where the objects being studied can be assigned continuously varying coordinates, either by physical measurements or by other scaling procedures, and where the objects with similar coordinates can be discriminated or confused with determinable probabilities. Thus, although the language of the theory that is used and tested in this research is geared towards sensory perception, its sphere of applicability includes a variety of paradigms in electrophysiology, educational testing, attitudinal surveys, consumer choice analysis, decision making research, etc.