The k‐in‐a‐row up‐and‐down design,revisited

The percentile‐finding experimental design known variously as ‘forced‐choice fixed‐staircase’, ‘geometric up‐and‐down’ or ‘k‐in‐a‐row’ (KR) was introduced by Wetherill four decades ago. To date, KR has been by far the most widely used up‐and‐down (U&D) design for estimating non‐median percentiles; it is implemented most commonly in sensory studies. However, its statistical properties have not been fully documented, and the existence of a unique mode in its asymptotic treatment distribution has been recently disputed. Here we revisit the KR design and its basic properties. We find that KR does generate a unique stationary mode near its target percentile, and also displays better operational characteristics than two other U&D designs that have been studied more extensively. Supporting proofs and numerical calculations are presented. A recent experimental example from anesthesiology serves to highlight some of the ‘up‐and‐down’ design family's properties and advantages. Copyright © 2009 John Wiley & Sons, Ltd.