Simple Rules for Controlling Step Size in Up-Down Testing

Abstract

A common problem in up-down testing is the choice of step size. Too large a step size results in imprecise estimation, and too small a step size is inefficient in that many data may be badly placed at the start of a test. A highly efficient rule [Wetherill, J. Roy. Statist. Soc. B.25, 1–48 (1963)] is to use a step size on trial n proportional to 1/(nb), where b is the slope of the response curve at the point to be estimated. Simple approximations to this rule are considered for practical applications that limit the size and number of changes in step size. Difficulties arise if both slope and location are unknown prior to the experiment. Fortunately, the efficiency of the procedure is not critically dependent on the slope constant and for practical purposes a rough estimate of slope will do. The technique has interesting possibilities in forced-choice experiments, where, under certain conditions, estimates of slope may be derived from the location estimates.