Efficient Block Designs for Correlated Observations

Summary Current methods for the design of efficient incomplete block experiments when the observations within a block are dependent usually involve computer searches of binary designs. These searches give little insight into the features that lead to efficiency, and can miss more efficient designs. This paper aims to develop some approximations which give some insight into the features of a design that lead to high efficiency under a generalized least‐squares analysis for a known dependence structure, and to show that non‐binary designs can be more efficient for some dependence structures. In particular, we show how neighbour balance and end plot balance are related to the design efficiency for low‐order autoregressions, and that under moderate positive dependence, replication at lag two can sometimes increase efficiency.