Small-sample statistical analysis of Levitt's psychophysical procedure
Brent Edwards, Gregory H. Wakefield · The Journal of the Acoustical Society of America · 1988
Levitt's 2IFC adaptive procedure is a widely used psychophysical method for estimating detection or discrimination threshold. The commonly accepted analysis shows that the average of the levels at which reversals occur approaches the 0.707 point on the psychometric function when the levels are updated according to the “2-up, 1-down” rule. This analysis is based on a continuous representation of the psychometric function and on the asymptotic behavior of the tracks. The more practical case was considered in which the psychometric function is represented by a set of discrete levels and in which the stopping criterion is a fixed number of reversals. A Markov model for the reversal levels is proposed as a method for determining the statistics of the estimator. Based on this approach, the estimator is significantly biased for small numbers of reversals, and decreases monotonically as this number becomes large. Convergence to the 0.707 point, however, is not guaranteed and depends on the sampling of the psychometric function. These results hold, in general, regardless of the form of the psychometric function or the method by which the psychometric function is sampled. More rapid convergence with less bias may be achieved by tailoring the sampling to the psychometric function. Several approaches to the design of such sampling will be discussed. [Research supported by AFOSR.]