Regression adjustments are often made to experimental data. Since randomization does not justify the models, bias is likely; nor are the usual variance calculations to be trusted. Here, we evaluate regression adjustments using Neyman’s nonparametric model. Previous results are generalized, and more intuitive proofs are given. A bias term is isolated, and conditions are given for unbiased estimation in finite samples.
"On regression adjustments in experiments with several treatments." Ann. Appl. Stat. 2 (1) 176 - 196, March 2008. https://doi.org/10.1214/07-AOAS143