Robustness of connected balanced block designs

Summary It is well known that the connected incomplete block designs with the highest intrablock efficiency factors are balanced. In a connected balanced block (BB) design, every elementary contrast is estimated with the same variance. If a treatment is lost in a connected BB design, then the residual design is not balanced for the most part. In this paper, an upper bound and a lower bound for efficiency of a residual design are derived with some illustrations. Moreover, from these discussions it is conceivable that the loss of efficiency even in the unbalanced case is, in general, small.