Design-based Causal Inference for Incomplete Block Designs

Researchers often turn to block randomization to increase the precision of their inference or due to practical considerations, such as in multisite trials. However, if the number of treatments under consideration is large it might not be feasible or practical to assign all treatments within each block. We develop novel inference results under the finite-population design-based framework for natural alternatives to the complete block design that do not require reducing the number of treatment arms, the incomplete block design (IBD) and the balanced incomplete block design. This includes deriving the properties of two design-based estimators, developing a finite-population central limit theorem, and proposing conservative variance estimators. Comparisons of the design-based estimators are made to linear model-based estimators. Simulations and a data illustration further demonstrate performance of IBD estimators. This work highlights IBDs as practical and currently underutilized designs.