Nearly Trend-Free Block Designs

Trend-free block designs were developed to permit elimination of effects of low-order components of common within-block trends over experimental units. It is known that, for certain combinations of design parameters, trend-free block designs do not exist. In this article, concepts and properties of nearly trend-free block designs are presented in general, and complete block designs with linear or quadratic trends over plots within blocks are studied in particular. It is found that, under a linear trend, if trend-free complete block designs do not exist, nearly trend-free block designs can be constructed and they are A- and D-optimal. When the trend is quadratic, highly efficient designs can be obtained.