O'Regan J K, Humbert R
Percept Psychophys. 1989 Nov;46(5):434-42. doi: 10.3758/bf03210858.
When a theoretical psychometric function is fitted to experimental data (as in the obtaining of a psychophysical threshold), maximum-likelihood or probit methods are generally used. In the present paper, the behavior of these curve-fitting methods is studied for the special case of forced-choice experiments, in which the probability of a subject's making a correct response by chance is not zero. A mathematical investigation of the variance of the threshold and slope estimators shows that, in this case, the accuracy of the methods is much worse, and their sensitivity to the way data are sampled is greater, than in the case in which chance level is zero. Further, Monte Carlo simulations show that, in practical situations in which only a finite number of observations are made, the mean threshold and slope estimates are significantly biased. The amount of bias depends on the curve-fitting method and on the range of intensity values, but it is always greater in forced-choice situations than when chance level is zero.
当将理论心理测量函数拟合到实验数据时（如在获取心理物理阈值的过程中），通常会使用最大似然法或概率单位法。在本文中，针对迫选实验的特殊情况研究了这些曲线拟合方法的行为，在迫选实验中，受试者偶然做出正确反应的概率不为零。对阈值和斜率估计量方差的数学研究表明，在这种情况下，与偶然水平为零的情况相比，这些方法的准确性要差得多，并且它们对数据采样方式的敏感性更大。此外，蒙特卡罗模拟表明，在仅进行有限次数观测的实际情况中，平均阈值和斜率估计存在显著偏差。偏差量取决于曲线拟合方法和强度值范围，但在迫选情况下总是比偶然水平为零时更大。
