NONPARAMETRIC INDEXES FOR SENSITIVITY AND BIAS: COMPUTING FORMULAS

NONPARAMETRIC INDEXES FOR SENSITIVITY AND BIAS: COMPUTING FORMULAS

1971 | J. BROWN GRIER
This paper presents computing formulas for two nonparametric indexes of sensitivity and bias used in signal detectability studies. These indexes are derived from the geometry of the unit square and are free of assumptions about underlying distributions. The sensitivity index is related to the area under the operating characteristic curve, and the bias index measures how far an outcome lies from the negative diagonal. The paper shows how these indexes can be computed from data and provides examples of their use. The sensitivity index, derived from the area under the operating characteristic curve, is shown to be related to the statistic P(I), which has known sampling variability. The bias index is calculated as the difference between two areas divided by their sum, and it yields identical isobias contours as another proposed index. The paper also provides formulas for computing these indexes and their associated isosensitivity and isobias contours. The paper illustrates the use of these indexes with data from two studies. In the first study, data from an auditory detection experiment are analyzed, and the results suggest that the nonparametric index provides a better fit to the data than the normal operating characteristic curve. In the second study, data from a recognition memory experiment are analyzed, and the nonparametric index is found to provide a more accurate characterization of the data than the normal operating characteristic curve. The paper also discusses the limitations of these indexes, including their dependence on the shape of the operating characteristic curve and the need for further research on their sampling distributions. Overall, the paper provides a new set of nonparametric indexes for sensitivity and bias that are both informative and computationally feasible.This paper presents computing formulas for two nonparametric indexes of sensitivity and bias used in signal detectability studies. These indexes are derived from the geometry of the unit square and are free of assumptions about underlying distributions. The sensitivity index is related to the area under the operating characteristic curve, and the bias index measures how far an outcome lies from the negative diagonal. The paper shows how these indexes can be computed from data and provides examples of their use. The sensitivity index, derived from the area under the operating characteristic curve, is shown to be related to the statistic P(I), which has known sampling variability. The bias index is calculated as the difference between two areas divided by their sum, and it yields identical isobias contours as another proposed index. The paper also provides formulas for computing these indexes and their associated isosensitivity and isobias contours. The paper illustrates the use of these indexes with data from two studies. In the first study, data from an auditory detection experiment are analyzed, and the results suggest that the nonparametric index provides a better fit to the data than the normal operating characteristic curve. In the second study, data from a recognition memory experiment are analyzed, and the nonparametric index is found to provide a more accurate characterization of the data than the normal operating characteristic curve. The paper also discusses the limitations of these indexes, including their dependence on the shape of the operating characteristic curve and the need for further research on their sampling distributions. Overall, the paper provides a new set of nonparametric indexes for sensitivity and bias that are both informative and computationally feasible.
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Understanding Nonparametric indexes for sensitivity and bias%3A computing formulas.