Variations on the Theme of Independence Tasks and Effects of Stroop, Garner, and Townsend

The term perceptual independence is missing from the Melara and Algom article, and the term selective attention is missing from the Ashby and Townsend article. The close association between selective attention and perceptual independence pertains to the pertinent theoretical constructs. Early discussions of independence within psychology date back to the 1960s and are closely associated with an unresolved issue in information theory. Three theoretical notions of independence are identified: perceptual independence, perceptual separability, and decisional separability. Sampling independence in a two-dimensional stimulus holds if and only if the probability of reporting both dimensional features is equal to the probability of reporting one feature times the probability of reporting the other feature. The network of General Recognition Theory (GRT) theorems relate the three theoretical aspects of independence to the various empirical properties observed in the data. The Garner measure introduces a concept foreign to both GRT and Stroop: variation, in particular irrelevant variation.