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 multi-site trials. However, if the number of treatments under consideration is large it might not be practical or even feasible 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 (BIBD). This includes deriving the properties of two estimators and proposing conservative variance estimators. To assist practitioners in understanding the trade-offs of using these designs, precision comparisons are made to standard estimators for the complete block, cluster-randomized, and completely randomized designs. Simulations and a data illustration further demonstrate the trade-offs. This work highlights IBDs as practical and currently underutilized designs.