The Annals of Statistics

Trend-Free Block Designs: Theory

Ralph A. Bradley and Ching-Ming Yeh

Full-text: Open access


A common polynomial trend in one or more dimensions is assumed to exist over the plots in each block of a classical experimental design. An analysis of covariance model is assumed with trend components represented through use of orthogonal polynomials. The objective is to construct new designs through the assignment of treatments to plots within blocks in such a way that sums of squares for treatments and blocks are calculated as though there were no trend and sums of squares for trend components and error are calculated easily. Such designs are called trend-free and a necessary and sufficient condition for a trend-free design is developed. It is shown that these designs satisfy optimality criteria among the class of connected designs with the same incidence matrix. The analysis of variance for trend-free designs is developed. The paper concludes with two examples of trend-free designs.

Article information

Ann. Statist., Volume 8, Number 4 (1980), 883-893.

First available in Project Euclid: 12 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62K10: Block designs
Secondary: 05B05: Block designs [See also 51E05, 62K10] 62K05: Optimal designs

Design criteria analysis of covariance trend analysis elimination of trend effects design optimality connected designs


Bradley, Ralph A.; Yeh, Ching-Ming. Trend-Free Block Designs: Theory. Ann. Statist. 8 (1980), no. 4, 883--893. doi:10.1214/aos/1176345081.

Export citation