extend those formulated for the yes-no tasks of Signal Detection Theory. The 2 × 2 analyses also extend the concepts advanced in Tanner theory of recognition ( 1956), in which detection and identification performance are measured in separate blocks of trials.
The vector representation of the 2 × 2 paradigm presented here also leads to tests of independent processing that do not depend on the Gaussian assumption. We demonstrated how a single performance measure, the I/D ratio, describes performance on both detection and identification tasks when they are performed simultaneously. We illustrated (a) how this measure is related to the angle between the vectors in the yes-no task; (b) how it is computed, including procedures to minimize the effects of response bias; and (c) provided examples of its use in tests of independence, in estimates of bandwidth, and in distinguishing unipolar pairs of independent processors from bipolar processing mechanisms.
Development of the vector model, related experiments, and preparation of this chapter were supported by U.S. Department of Health and Human Services research grant EY00360 from the National Eye Institute.