A mathematical model which compares the process of stimulus discrimination to a signal measuring system is proposed and partially evaluated in four experiments. Within this system, response variability is partitioned into two parts, a stimulus component and a component due to variation in the psychological scale. The stimulus component depends on the particular stimulus but not on other stimuli in the set. The other component is shown to be directly proportional to the physical range over which criteria vary. When this subjective or criterial range is small, the measurement error contributed by this component is expected to be small. But when the criterial range is large, when the psychological scale must be magnified to fit a larger range which is to say the same thing, there is a corresponding magnification of the measurement error. This system, which predicts the findings of channel capacity, can be viewed as a physical measuring instrument with the scale to which the instrument is set as the primary determinant of resolution. The studies reported show that this range which affects resolution is not the physical range over which stimuli can vary but is related to the subjective range over which decisions must vary.

Absolute judgments of line lengths and line positions, under easy and difficult viewing conditions, were obtained when the stimulus dimensions were varied separately, together and perfectly correlated, and together and uncorrelated. Results showed that a redundancy gain is obtained-performance is better-from correlated dimensions and that this gain is independent of sensory limitation. Analyses suggest that redundancy gains are obtainable only when stimulus dimensions are integral and that dimensions may also have to be continuous. An empirical method of measuring the amount of integrality of stimulus dimensions is suggested.

It is proposed that people identify multidimensional stimuli as if they are loci in a multidimensional discrimination space and not by combining judgments of the separate values of each stimulus. Identification data from 2-, 3-, and 4-dimensional stimulus sets support the model. According to this proposition, there is no theoretical limit on the number of different stimuli or objects which can he discriminated, although there is a practical limit on the number which can be identified due to the time required to learn and attach labels to each locus in the space.