Varieties of perceptual independence.

TLDR: A general multivariate perceptual theory is developed, and a precise definition of perceptual independence is offered, and it is shown that if separability holds, then sampling independence is equivalent to perceptual independence.

Abstract: Several varieties of perceptual independence are investigated. These include sampling independence, dimensional orthogonality, stimulus separability and integrality, and performance parity. A general multivariate perceptual theory is developed, and a precise definition of perceptual independence is offered. Each of these related concepts is then examined within the framework of this theory, and their theoretical interrelationships are explicated. It is shown that none of the concepts are equivalent to perceptual independence but that if separability holds, then sampling independence is equivalent to perceptual independence. Several simple tests of separability are suggested that can be applied to the same data as sampling independence. Dimensional orthogonality is shown to test for independence only if some strong distributional assumptions are made about the perceptual effects of stimuli. Reaction time and information-based performance parity criteria are examined. The potential for empirically testing each of these concepts is discussed.