On regression adjustments in experiments with several treatments

TL;DR

This paper critically examines the use of regression adjustments in experiments with multiple treatments, highlighting potential biases and providing conditions for unbiased estimation within Neyman's nonparametric framework.

Contribution

It generalizes previous results on regression adjustments, offers more intuitive proofs, and isolates bias terms to establish conditions for unbiased estimates in finite samples.

Findings

Regression adjustments can introduce bias in experiments with multiple treatments.

Conditions for unbiased estimation are identified within Neyman's nonparametric model.

The paper provides generalized results and clearer proofs for understanding bias in regression adjustments.

Abstract

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.