Adaptive staircase techniques in psychoacoustics: a comparison of human data and a mathematical model

Data from a simple tone-in-noise simultaneous masking task were used to evaluate each of two common adaptive staircase rules (a "1 up 2 down" rule and a "1 up 3 down" rule) and the parameter estimation by sequential testing (PEST) technique in combination with each of two psychophysical procedures [a two-alternative forced-choice (2AFC) and a three-alternative forced-choice (3AFC) procedure]. These human data were compared to predictions generated by a mathematical model based on Markov theory. The model predicts that threshold estimates obtained with the adaptive techniques should be equal to those derived with equivalent "fixed signal level" techniques. However, the human data indicate that the adaptive techniques tend to yield lower thresholds. The model predicts that the standard error of a threshold estimate obtained from an adaptive technique will decrease and approach zero as the number of trials used to compute the estimate increases. The human data show greater variability than predicted and approach a nonzero value as the number of trials increases. The predictions of the model suggest that the commonly used combination of the 2AFC procedure and the 1 up 2 down rule is the least efficient method of estimating a threshold and that the 3AFC procedure in combination with the 1 up 3 down rule is the most efficient method. The human data are less consistent, but generally show the combination of the 2AFC procedure and the 1 up 2 down rule to be one of the least efficient methods. Possible explanations for the differences between the model's predictions and the human data, as well as suggestions for laboratory practice, are discussed.