The Up-and-Down Method for Small Samples

Abstract

Abstract A modified up-and-down method for sensitivity testing (all-or-none assays) is presented with maximum likelihood estimates of LD50 tabulated for all sample sequences for nominal sample size N ≤ 6. Approximate estimates for larger sample sizes are given. The design uses sequentially determined test levels and sequentially determined sample sizes. The estimates have mean square error approximately independent of the chosen starting level of the test sequence and the spacing between test levels. The actual sample size rarely exceeds the nominal sample size by more than two for moderately well chosen starting levels. Examples of the use of the method are given for two analyses of variance designs.