Nonparametric indexes for sensitivity and bias: computing formulas.

Abstract

Computing formulas are derived for two indexes of sensitivity and bias that have been suggested for signal detectability studies. A relationship is shown between the sensitivity index and P(I), a statistic whose sampling variability is known. An additional index of bias is proposed, which is free of certain inconveniences, yet yields identical isobias contours. Use of the new indexes is illustrated with several sets of data. Development of the theory of signal detectability has lead to a renewed interest in the possible processes involved in perception, psychophysics, and recognition memory. To a considerable extent both theory and research in these areas have rested on specific assumptions about the underlying distributions (as in the various threshold theories versus normality). But even without explicit assumption about the distributions, data are often judged by how close they lie to operating characteristic curves derived from normal distributions, and different experimental conditions are characterized by their value of d'. Recently there has been a growing interest in various nonparametric analyses of detection/ recognition experiments, where specific underlying distributions are not assumed. Following one line of development, Green (1964) has shown that for experiments using the yes-no procedure, the area under the (theoretical) operating characteristic curve can be interpreted as the percentage correct on an equivalent unbiased forced-choice test, and that this is true for any continuous underlying distributions. The sampling variability of this area measure has been determined by Pollack and Hsieh (1969). A similar proof for ratingscale experiments is due to Green and Moses (1966). However, using data to estimate the area under a curve of unknown theoretical shape presents difficulties. One expedient has been to connect the points and use the trapezoidal rule (Green & Moses, 1966; Pollack, Norman, & Galanter, 1964). If the true func