Modifications to the BUDTIF procedure

During the decade that has passed since describing the Block-Up-and-Down, Two-Interval, Forced-choice (BUDTIF) psychophysical procedure in this Journal, several modifications have resulted from actual and computer-simulated experience with the procedure and from discussions of the PEST and UDTR procedures by Taylor, Creelman, Hall, Levitt, and others. Modifications include using a level change decision rule similar to, but more efficient for small N's than, the Weld sequential rule, stopping rules based on the number of decisions and weighted number of trials at a given level, and basing threshold estimates on the mean of revisited levels weighted by the number of trials in the run and restricted to only five levels near the most frequently revisited one. These changes have reduced the effect of starting level on the variance of repeated estimates and the bias in the area of greatest interest for psychoacoustics, that is, stopping rules that yield threshold estimates in less than 100 trials, with the target performance lying at or near the midpoint of the psychometric function. Based on computer simulations, the tendency for the threshold estimate to be biased toward the starting level and for the variance to be related to the absolute difference between the starting and “true” threshold level has been markedly reduced. For example, when starting over a range of 16 logit units, an average of 68 trials per threshold, the starting level effect was less than 0.2 logit unit with the standard deviation being 0.67 unit: This seems to compare favorably with a standard deviation of 0.76 at 68 trials obtained with simulated PEST runs reported by Hall with the starting level always + 4 units. The modifications and simulated results will be reported in greater detail.