Journal of the American Statistical Association · 1965 · 233 citations · 0 references
Public HealthBiostatisticsExperimental DesignExperimental PerformanceGenomic Data AnalysisHypothesis TestingPower AnalysisSample SizeSensitivity AnalysisAssay SensitivityMaximum Likelihood InferenceSample Size CalculationSample Size Estimation
The method is illustrated with examples from two analysis of variance designs. The study presents a modified up‑and‑down method for sensitivity testing that provides maximum‑likelihood LD50 estimates for nominal sample sizes up to six. The design sequentially selects test levels and sample sizes. The method yields LD50 estimates with mean‑square error largely independent of starting level and spacing, and the actual sample size rarely exceeds the nominal size by more than two, with approximate estimates available for larger samples.
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.