Abstract
Abstract Two estimators of the median based on sequentially obtained quantal response data are studied. The design is essentially the up-and-down method and consists of taking K observations per trial at sequentially determined levels until some fixed total sample size is obtained. The asymptotic distribution of the sample average, , of the levels is studied and an estimate of its variance is proposed. The bias and mean square error of , which have been numerically evaluated for the normal distribution, indicate there is often little loss in efficiency using K up to 5 instead of the conventional K = 1. The asymptotic properties of the Spearman-Karber estimator, , show that its large sample efficiency can decrease as the number of distinct levels increases. Small sample results using K = 1 indicate that is quite robust with respect to the choice of initial level and spacing between levels.
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