Estimating psychometric functions in forced-choice situations: significant biases found in threshold and slope estimations when small samples are used.

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.