Slope bias of psychometric functions derived from adaptive data

Several investigators have fit psychometric functions to data from adaptive procedures for threshold estimation. Although the threshold estimates are in general quite correct, one encounters a slope bias that has not been explained up to now. The present paper demonstrates slope bias for parametric and nonparametric maximum-likelihood fits and for Spearman-Kärber analysis of adaptive data. The examples include staircase and stochastic approximation procedures. The paper then presents an explanation of slope bias based on serial data dependency in adaptive procedures. Data dependency is first illustrated with simple two-trial examples and then extended to realistic adaptive procedures. Finally, the paper presents an adaptive staircase procedure designed to measure threshold and slope directly. In contrast to classical adaptive threshold-only procedures, this procedure varies both a threshold and a spread parameter in response to double trials.