High-throughput perturbation screens measure the phenotypes of thousands of biological samples under various conditions. The phenotypes measured in the screens are subject to substantial biological and technical variation. At the same time, in order to enable high throughput, it is often impossible to include a large number of replicates, and to randomize their order throughout the screens. Distinguishing true changes in the phenotype from stochastic variation in such experimental designs is extremely challenging, and requires adequate statistical methodology.