Optimal setups for forced-choice staircases with fixed step sizes

Forced-choice staircases with fixed step sizes are used in a variety of formats whose relative merits have never been studied. This paper presents a comparative study aimed at determining their optimal format. Factors included in the study were the up/down rule, the length (number of reversals), and the size of the steps. The study also addressed the issue of whether a protocol involving three staircases running for N reversals each (with a subsequent average of the estimates provided by each individual staircase) has better statistical properties than an alternative protocol involving a single staircase running for 3N reversals. In all cases the size of a step up was different from that of a step down, in the appropriate ratio determined by García-Pérez (Vision Research, 1998, 38, 1861 - 1881). The results of a simulation study indicate that a) there are no conditions in which the 1-down/1-up rule is advisable; b) different combinations of up/down rule and number of reversals appear equivalent in terms of precision and cost: c) using a single long staircase with 3N reversals is more efficient than running three staircases with N reversals each: d) to avoid bias and attain sufficient accuracy, threshold estimates should be based on at least 30 reversals: and e) to avoid excessive cost and imprecision, the size of the step up should be between 2/3 and 3/3 the (known or presumed) spread of the psychometric function. An empirical study with human subjects confirmed the major characteristics revealed by the simulations.