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Journal of the American Statistical Association Volume 99, 2004 - Issue 468
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Primary Article

Models and Confidence Intervals for True Values in Interlaboratory Trials

Hari K Iyer Hari Iyer is Professor, Department of Statistics, Colorado State University, Fort Collins, CO 80523 . C. M. Jack Wang is Mathematical Statistician, Statistical Engineering Division, National Institute of Standards and Technology, Boulder, CO 80305 . Thomas Mathew is Professor, Department of Mathematics and Statistics, University of Maryland, Baltimore, MD 21250 . The authors thank Andrew Rukhin for his helpful comments and the referees for their valuable suggestions that helped them improve the clarity of presentation as well as correct some errors. The third author acknowledges support of U. S. Army Research Laboratory and U. S. Army Research Office grant DAAD19-01-1-0497. This work is a contribution of the National Institute of Standards and Technology and is not subject to copyright in the United States.
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C. M. Jack Wang Hari Iyer is Professor, Department of Statistics, Colorado State University, Fort Collins, CO 80523 . C. M. Jack Wang is Mathematical Statistician, Statistical Engineering Division, National Institute of Standards and Technology, Boulder, CO 80305 . Thomas Mathew is Professor, Department of Mathematics and Statistics, University of Maryland, Baltimore, MD 21250 . The authors thank Andrew Rukhin for his helpful comments and the referees for their valuable suggestions that helped them improve the clarity of presentation as well as correct some errors. The third author acknowledges support of U. S. Army Research Laboratory and U. S. Army Research Office grant DAAD19-01-1-0497. This work is a contribution of the National Institute of Standards and Technology and is not subject to copyright in the United States.
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Thomas Mathew Hari Iyer is Professor, Department of Statistics, Colorado State University, Fort Collins, CO 80523 . C. M. Jack Wang is Mathematical Statistician, Statistical Engineering Division, National Institute of Standards and Technology, Boulder, CO 80305 . Thomas Mathew is Professor, Department of Mathematics and Statistics, University of Maryland, Baltimore, MD 21250 . The authors thank Andrew Rukhin for his helpful comments and the referees for their valuable suggestions that helped them improve the clarity of presentation as well as correct some errors. The third author acknowledges support of U. S. Army Research Laboratory and U. S. Army Research Office grant DAAD19-01-1-0497. This work is a contribution of the National Institute of Standards and Technology and is not subject to copyright in the United States.
Pages 1060-1071 | Published online: 31 Dec 2011
 
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Abstract

We consider the one-way random-effects model with unequal sample sizes and heterogeneous variances. Using the method of generalized confidence intervals, we develop a new confidence interval procedure for the mean. Additionally, we investigate two alternative models based on different sets of assumptions regarding between-group variability and derive generalized confidence interval procedures for the mean. These procedures are applicable to small samples. Statistical simulation is used to demonstrate that the coverage probabilities of these procedures are close enough to the nominal value so that they are useful in practice. Although the methods are quite general, the procedures are explained with the backdrop of interlaboratory studies.

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