  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, cluster-randomized, and completely
randomized designs. Simulations and a data illustration demonstrate the
trade-offs of using BIBDs. This work highlights BIBDs as practical and
currently underutilized designs.
