Construction and optimality of nearly linear trend-free designs

Abstract

The necessary condition that a proper block design can be converted to a (linear) trend-free design is r( k + 1) ≡ 0 (mod 2) (Yeh and Bradley, Comm. Statist. Theory Methods 12 (1983) 1–24). When this condition does not hold, the best we can do is try to convert the design to a nearly (linear) trend-free design (Yeh et al., J. Amer. Statist. Assoc. 80 (1985) 985–992). Our results include: 1. (i) construction of the nearly trend-free version of BIB designs; 2. (ii) A-, D- and E-optimality of BIB designs for models that include trend effects.