Scurfield BK
Victoria University of Wellington, , Wellington, , , New Zealand
J Math Psychol. 1996 Sep;40(3):253-69. doi: 10.1006/jmps.1996.0024.
Receiver operating characteristic (ROC) analysis is generalized to unidimensional forced-choice tasks involving three or more events. It is shown that the performance of an observer in a unidimensional identification task with n independent events can be represented in n! ROC spaces of dimension n. Each ROC space is associated with a unique pairing of the events and decisions. A hypersurface can be generated in each ROC space by manipulating the observer's decision criteria. Using information theory, a new measure of discriminability based on the hypervolumes under the hypersurfaces is defined. This measure, denoted D, is nonparametric and independent of the criteria. The value of D is shown to increase monotonically with n and to be equal to the channel capacity of an observer in an n-interval forced-choice task. Procedures to compute ROC hypersurfaces from ratings and from ROC curves are given.
接收者操作特征（ROC）分析被推广到涉及三个或更多事件的一维强制选择任务。结果表明，在具有n个独立事件的一维识别任务中，观察者的表现可以用n维的n!个ROC空间来表示。每个ROC空间都与事件和决策的唯一配对相关联。通过操纵观察者的决策标准，可以在每个ROC空间中生成一个超曲面。利用信息论，基于超曲面下的超体积定义了一种新的可辨别性度量。这个度量记为D，是非参数的，且与标准无关。结果表明，D的值随n单调增加，并且等于观察者在n区间强制选择任务中的通道容量。给出了从评分和ROC曲线计算ROC超曲面的程序。
