Properties of some variants of adaptive staircases with fixed step sizes

Because the estimation of thresholds is daily practice in sensory psychophysics, efficient methods must be used to reduce experimental cost and burden. A large number of such methods are available, and each one further has a multitude of variants. All methods presumably provide a threshold estimate that is the stimulus level at which repeated testing would result in a specific percentage of correct responses on a forced-choice task, a percentage that varies across methods and variants thereof. A recent study (García-Pérez, 1998) showed that the most popular method (up-down staircases with fixed step sizes) yields threshold estimates that do not correspond to the presumed percent-correct points. Two modifications of this type of staircase have recently been proposed. In one (Zwislocki and Relkin, 2001), the up-down rule does not require correct responses to occur consecutively. In the other (Kaernbach, 1999), subjects are allowed to respond 'don't know' instead of guessing at random when unsure. Although the statistical basis of either modification were described in general, only a few of their many variants were subjected to evaluation under a limited set of conditions. This paper provides an extensive evaluation of a reasonable number of variants of either modification under a broad set of conditions. The results show that they are generally unfit for threshold estimation because in most cases the percent-correct point that is targeted varies greatly with the relative size of the steps with respect to the spread of the psychometric function. Dependable conditions for the use of these modified staircases are also determined.