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Methods for Estimating Background Variation in Field Experiments¹

A widely useful method for estimating background variation in field experiments would provide experimenters with a diagnostic tool that could be used to reveal trials for which customary design-based analyses are inadequate. Such a diagnostic tool would provide reassurance for cases suited for customary analyses and would signal a need for corrective analyses when plot to plot variation has not been properly accounted for.

This paper is an early step in the search for such a widely useful diagnostic tool. It examines the performance of a number of methods that have been proposed for describing plot to plot variation and explores the effectiveness of these methods over widely different data sets from uniformity trials.

Methods were assessed primarily on the basis of consistency of providing residual mean squares usable as a diagnostic measure of background variation. In addition, methods were compared in terms of how well they described plot to plot variation (R² for estimated and observed responses).

Results obtained made it clear that the suitability of a method forestimating background variation must be evaluated over a number of different trials, including trials sensitive to block size and orientation. Most methods performed well in at least one or two trials. Few were generally effective. Preliminary indications were that the Best Blocks of Two Method was most generally useful and that Polynomial Regressions and the Modified Papadakis method were promising. The versions used of the following methods were not consistently effective in estimating background variation: Rows and Columns, Ordinary Papadakis, Fourier Analysis and Inverse Polynomial.

Key Words: Blocking • Trend • Method x trial interaction • Dummy blocks • Uniformity trials • Regression • Papadakis • Rows and columns • Fourier • inverse polynomial

² Director of the Office of Biometrics, Univ. of New Hampshire; professor, Institute de Investigaciones en Mathematicas Applicadas y en Sistemnas, Universidad Nacional Autonoma de Mexico, Mexico.

Received for publication June 29, 1981.

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