Micheyl Christophe, Dai Huanping
University of Minnesota, Minneapolis, Minnesota, USA.
Percept Psychophys. 2008 Jul;70(5):761-4. doi: 10.3758/pp.70.5.761.
According to a well-known theorem in psychophysics (Green & Swets, 1966), the area under the receiver operating characteristic (ROC) for the yes-no paradigm equals the proportion of correct responses of an unbiased observer in the two-interval, two-alternative, forced choice paradigm (2I2AFC). Here, we demonstrate a similar relationship between the ROC area in the two-interval same-different (AX or 2IAX) paradigm, and the proportion correct in the four-interval same-different (4IAX, also known as dual-pair comparison) paradigm. The theorem demonstrated here is general, in the sense that it does not require that the sensory observations have a specific distribution (e.g., Gaussian), or that they be statistically independent.
根据心理物理学中的一个著名定理（格林和斯韦茨，1966年），是-否范式下的接收者操作特征（ROC）曲线下的面积等于无偏观察者在双区间、二择一、强制选择范式（2I2AFC）中的正确反应比例。在此，我们证明了双区间异同（AX或2IAX）范式下的ROC面积与四区间异同（4IAX，也称为双对比较）范式下的正确比例之间存在类似关系。这里证明的定理具有普遍性，即它不要求感官观察具有特定分布（例如高斯分布），也不要求它们在统计上独立。
