Constructing and Analyzing Two-Level Trend-Robust Designs

ABSTRACT

Blocking is one means of shielding comparisons of interest from unwanted sources of variation. When the experimental units are time (or spatially) ordered and are suspected of producing a trend in the errors, certain run orders provide an alternative means of isolating such variation. Beginning with Daniel and Wilcoxon (1966), statisticians have proposed run orders for 2 ^k and 2 ^k − p designs that are robust to linear and quadratic trend. This article discusses the rationale for using such designs and presents an example to illustrate the analysis of trend-robust designs.

KEYWORDS:

• blocking
• covariate
• fractional factorial
• randomization
• run order

ACKNOWLEDGEMENTS

The authors are thankful for a particularly thorough referee who improved the clarity of this article by his very careful reading and numerous suggested improvements.

Notes

Error = 0.004Run² − 2 + standard Normal; Y = 22 + 2D + E + .75D*E − 0.5H + Error.

PSE = 1.402, based on standardized estimates (= Estimate/Rel. Std. Error).