On the Efficiency of Psychophysical Measurement

Abstract

A previously proposed upper bound on the performance of psychophysical techniques that attempt to determine points on psychometric functions is shown to be a least upper bound. The existence of a realizable technique (the Robbins-Monro process) which asymptotically attains the performance of the proposed ideal shows that this ideal provides an appropriate basis from which to calculate the absolute as opposed to relative efficiency of real psychophysical measurement techniques. The concept of incremental efficiency is introduced. It is shown to be useful in analyzing the performance of measurement techniques when the initial uncertainty of the estimate, often ignored in simulation studies, is neither infinite nor zero, and to permit independent assessment of the efficiency of separate portions of a measurement process.

Adaptive psychophysical procedures

“…Preliminary results of simulations indicate that the accelerated stochastic approximation has a similar performance as mean-Bayesian methods, which seems to be near optimal performance. Besides other valuable theoretical results (for overviews see Dupa6, 1984;Sampson, 1988), Taylor (1971) has used the asymptotic variance of the Robbins-Monro process, i.e. stochastic approximation, as the touchstone for evaluating performance of adaptive procedures.…”

“…The precision r O of r estimated thresholds /gr can be defined (see Taylor, 1971) as the inverse of the variance of the best threshold estimates t) of a particular method, i.e.…”

“…Taylor and Creelman (1967) and Taylor (1971) have defined the sweat factor K as a measure of the efficiency of a psychophysical procedure. It is the product of o-~, the variance of the best threshold estimate, and n, the fixed number of trials, which were necessary to obtain that estimate…”

“…If an absolute measure of efficiency is desired then an ideal procedure as a standard of reference has to be assumed. Taylor (1971) proposed as a measure of an ideal procedure the asymptotic variance O'~M of the Robbins-Monro process (see section on stochastic approximation) for a given target probability qb and a given number of trials n…”

The single interval adjustment matrix (SIAM) yes–no task: an empirical assessment using auditory and gustatory stimuli

“…The discrepancy between the two studies is likely explained by the fact that in Gu and Green's study 16 of the 22 participants were highly practiced listeners, rather than the group of inexperienced listeners used in this study. The standard deviations reported in Table 3 index reliability (or, as conceptualised by Taylor, 1971, andKollmeier, Gilkey, &Sieben, 1988, precision), where an inverse relationship between standard deviation and reliability exists. Inspection of Table 3 reveals that standard deviations averaged across participants are greater in the 2AFC task than in the SIAM YN task, while the SIAM-rapid task, which as we described above suffers from procedural problems, had the largest standard deviation of the three.…”