Micheyl Christophe, Messing David P
Research Laboratory of Electronics, Massachusetts Institute of Technology, Bldg. 36-758, Cambridge, MA 02139-4307, USA.
Percept Psychophys. 2006 Jul;68(5):725-35. doi: 10.3758/bf03193696.
This article provides a synthetic account of the likelihood ratio, optimal decision rules, and correct response probabilities in a signal detection theoretic model of the observer in the dual-pair comparison, or four-interval AX (4IAX), paradigm. The model assumes a static sampling process, resulting in four, equal-variance normally distributed (i.e., Gaussian) observations on each trial First, a likelihood ratio equation allowing for an arbitrary degree of correlation between observations is provided. Specific solutions for the cases of independent and highly correlated observations are then derived. It is shown that these solutions, and the associated decision rules, correspond to those provided independently in earlier publications. A modified 4IAX paradigm involving, as a standard, an additional stimulus (C) located medially between the A and the B stimuli is also considered. It is shown that the optimal (static, equal-variance, Gaussian) decision model for this paradigm is unaffected by correlation between observations and is equivalent to the standard 4IAX with highly correlated observations. Finally, we consider how, under the considered (static, equal-variance, Gaussian) model, the proportion of correct responses in the different versions of the 4IAX paradigm is related to d', and a solution for the case of independent observations is provided.
本文综合阐述了双对比较或四区间AX（4IAX）范式中观察者的信号检测理论模型中的似然比、最优决策规则和正确反应概率。该模型假设一个静态采样过程，每次试验产生四个等方差正态分布（即高斯分布）的观测值。首先，给出一个允许观测值之间存在任意程度相关性的似然比方程。然后推导出独立观测值和高度相关观测值情况下的具体解。结果表明，这些解以及相关的决策规则与早期出版物中独立给出的解和规则相对应。还考虑了一种修改后的4IAX范式，该范式以位于A和B刺激中间的额外刺激（C）作为标准。结果表明，该范式的最优（静态、等方差、高斯）决策模型不受观测值相关性的影响，并且等同于具有高度相关观测值的标准4IAX范式。最后，我们考虑在所考虑的（静态、等方差、高斯）模型下，4IAX范式不同版本中的正确反应比例与d'是如何相关的，并给出独立观测值情况下的一个解。
