eter representing correlated noise, and the independence model with uncorrelated noise. The data unanimously rejected the simple bipolar model for both cosine and bar stimuli. The addition of the extra parameter to this model did not improve the fit: the correlated bipolar also was rejected in all data sets. These results are not consistent with the notion that bright and dark stimuli are complementary stimuli processed by increases and decreases in activity of the same tuned pathways.
The simple independence model was also rejected for low-frequency cosine grating stimuli, but could not be rejected by this analysis for bar stimuli. As a more powerful test of the independence model, the equality of p(I) and p(D) was tested for each observer by a t-test. The data from one observer with the cosine grating stimuli was consistent with the independence model; however, the model was rejected for all other data sets. Although not tested here, an independence model with correlated noise might serve as a better model for these data.
Because of the possible effects of eye movements, caution is necessary in interpreting data gathered with higher-frequency cosine gratings and thinner bars. Nevertheless, the data again consistently reject the simple and correlated- noise forms of the bipolar processing model. The observed relationship between p(I) and p(D) changes as spatial frequency increases (or width decreases), approaching equality near frequencies of 1 to 2 c/deg (or widths of about 0.25U+00B0). In this region, the independence model cannot be consistently rejected, although both bipolar models can. For bar stimuli, an I/D ratio of 1.0 represents an asymptote; further decreases in bar width do not affect relative performance on the two tasks. For these thinner bars, the independence model provides a satisfactory fit to all data sets. With cosine gratings, however, detection performance exceeds identification performance at 5 c/deg. Neither the bipolar models nor the independence models account for this result.
The multidimensional vector model presented here provides a unifying theoretical structure from which observed relationships between detection and identification performance can be interpreted across several psychophysical paradigms. The general formulation of the model stems from traditional line-element models of sensory processing, more recent concepts from psychoacoustics, and the work of many investigators in visual psychophysics over the past two decades. We have illustrated how the current formulation of the model explicitly considers effects of stimulus uncertainty and response bias in the yes-no task, and described a general test of independent processing for this procedure that does not depend on the restrictive Gaussian assumptions of previous analyses.
The specific concepts and analyses presented for the 2 × 2 paradigm, in which detection and identification performance are simultaneously assessed,