Advantages of statistical testing of high-throughput screens include P-values, which provide objective benchmarks of compound activity, and false discovery rate estimation. The cost of replication required for statistical testing, however, may often be prohibitive. We introduce the single assay-wide variance experimental (SAVE) design whereby a small replicated subset of an entire screen is used to derive empirical Bayes random error estimates, which are applied to the remaining majority of unreplicated measurements.