Predictor sort sampling and one-sided confidence bounds on quantiles

Abstract

Predictor sort experiments attempt to make use of the correlation between a predictor that can be measured prior to the start of an experiment and the response variable that we are investigating. Properly designed and analyzed, they can reduce necessary sample sizes, increase statistical power, and reduce the lengths of confidence intervals. However, if the non- random nature of the predictor sort is not taken into account, problems can occur. In particular, standard one-sided lower confidence bounds on quantiles of a normal distribution are overly conservative in a predictor sort situation. For lumber strength applications, this leads to “allowable properties” that are too low. We have developed asymptotic theory that yields the correct k value in the y - ks approach to obtaining a confidence bound. The resulting confidence bounds have coverages that approach the nominal values faster than bounds based on maximum likelihood estimation. In a subsequent paper we will provide k values that are appropriate for small sample sizes.

Citation

Verrill, Steve; Herian, Victoria L.; Green, David W. 2002. Predictor sort sampling and one-sided confidence bounds on quantiles. Proceedings, 2001 American Statistical Association Annual Meeting, Physical Sciences and Engineering Section, 2001 August 5-9, Atlanta, GA. Alexandria, VA : American Statistical Association, 2002.