Predictor Sort Sampling, Tight T'S, and the Analysis of Covariance

Abstract

In this article we revisit a method of sample allocation that has long been known to statisticians and has recently been “discovered” by wood strength researchers. The method allocates experimental units to blocks on the basis of the values of a variable, x, that is known to be correlated with the response, y We call this allocation method “predictor sort sampling.” We demonstrate that the associated paired T analysis recommended in statistical texts is deficient if the sample size is small and the correlation between x and y is high. We temper this criticism of standard statistical intuition with a proof that the approach is asymptotically correct. In a related development we show that a modified pooled T approach can be taken to this data with a resultant increase in power. We compare these approaches to an analysis of covariance approach and discuss the advantages of each. Finally, we warn against the intuitively attractive but incorrect power calculations that are likely to be performed in association with a predictor sort experiment.

KEY WORDS:

• Analysis of covariance
• Asymptotics
• Experimental design
• Paired T
• Pooled T
• Power
• Sample size
• T distribution