Open Access
July, 1980 Trend-Free Block Designs: Theory
Ralph A. Bradley, Ching-Ming Yeh
Ann. Statist. 8(4): 883-893 (July, 1980). DOI: 10.1214/aos/1176345081

Abstract

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.

Citation

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Ralph A. Bradley. Ching-Ming Yeh. "Trend-Free Block Designs: Theory." Ann. Statist. 8 (4) 883 - 893, July, 1980. https://doi.org/10.1214/aos/1176345081

Information

Published: July, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0451.62059
MathSciNet: MR572632
Digital Object Identifier: 10.1214/aos/1176345081

Subjects:
Primary: 62K10
Secondary: 05B05 , 62K05

Keywords: Analysis of covariance , connected designs , Design criteria , design optimality , elimination of trend effects , trend analysis

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 4 • July, 1980
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