Efficient and unbiased modifications of the QUEST threshold method: Theory, simulations, experimental evaluation and practical implementation

Abstract

QUEST [Watson and Pelli, Perception and Psychophysics, 13, 113–120 (1983)] is an efficient method of measuring thresholds which is based on three steps: (1) Specification of prior knowledge and assumptions, including an initial probability density function (p.d.f.) of threshold (i.e. relative probability of different thresholds in the population). (2) A method for choosing the stimulus intensity of any trial. (3) A method for choosing the final threshold estimate. QUEST introduced a Bayesian framework for combining prior knowledge with the results of previous trials to calculate a current p.d.f.; this is then used to implement Steps 2 and 3. While maintaining this Bayesian approach, this paper evaluates whether modifications of the QUEST method (particularly Step 2, but also Steps 1 and 3) can lead to greater precision and reduced bias. Four variations of the QUEST method (differing in Step 2) were evaluated by computer simulations. In addition to the standard method of setting the stimulus intensity to the mode of the current p.d.f. of threshold, the alternatives of using the mean and the median were evaluated. In the fourth variation—the Minimum Variance Method—the next stimulus intensity is chosen to minimize the expected variance at the end of the next trial. An exact enumeration technique with up to 20 trials was used for both yes-no and two-alternative forced-choice (2AFC) experiments. In all cases, using the mean (here called ZEST) provided better precision than using the median which in turn was better than using the mode. The Minimum Variance Method provided slightly better precision than ZEST. The usual threshold criterion—based on the “ideal sweat factor”—may not provide optimum precision; efficiency can generally be unproved by optimizing the threshold criterion. We therefore recommend either using ZEST with the optimum threshold criterion or the more complex Minimum Variance Method. A distinction is made between “measurement bias”, which is derived from the mean of repeated threshold estimates for a single real threshold, and “interpretation bias”, which is derived from the mean of real thresholds yielding a single threshold estimate. If their assumptions are correct, the current methods have no interpretation bias, but they do have measurement bias. Interpretation bias caused by errors in the assumptions used by ZEST is evaluated. The precisions and merits of yes-no and 2AFC techniques are compared. Practical implementation of the ZEST method is described in the Appendix, with emphasis on the flexibility of the current methods in circumventing experimental problems, and on enhancements to allow for variations in the slope of the psychometric function, drifts in threshold, and correlation between thresholds for different stimuli.