Causal Inference for Balanced 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 a natural alternative to the complete block design that does not require reducing the number of treatment arms, the balanced incomplete block design (BIBD). This includes deriving the properties of two estimators for BIBDs and proposing conservative variance estimators. To assist practitioners in understanding the trade-offs of using BIBDs over other designs, the precisions of resulting estimators are compared to standard estimators for the complete block design, the cluster-randomized design, and the completely randomized design. Simulations and a data illustration demonstrate the strengths and weaknesses of using BIBDs. This work highlights BIBDs as practical and currently underutilized designs.