Date of Award

2-2013

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

First Advisor

John P. Buonaccorsi

Second Advisor

David L. Duewer

Third Advisor

Edward Stanek

Subject Categories

Mathematics | Statistics and Probability

Abstract

Regulatory Agencies are responsible for monitoring the performance of particular measurement communities. In order to achieve their objectives, they sponsor Intercomparison exercises between the members of these communities. The Intercomparison Exercise Program for Organic Contaminants in the Marine Environment is an ongoing NIST/NOAA program. It was started in 1986 and there have been 19 studies to date. Using this data as a motivation we review the theory and practices applied to its analysis.

It is a common practice to apply some kind of filter to the comparison study data. These filters go from outliers detection and exclusion to exclusion of the entire data from a participant when its measurements are very “different". When the measurements are not so “different" the usual assumption is that the laboratories are unbiased then the simple mean, the weighted mean or the one way random effects model are applied to obtain estimates of the true value.

Instead we explore methods to analyze these data under weaker assumptions and apply them to some of the available data. More specifically we explore estimation of models assessing the laboratories performance and way to use those fitted models in estimating a consensus value for new study material. This is done in various ways starting with models that allow a separate bias for each lab with each compound at each point in time and then considering generalizations of that. This is done first by exploiting models where, for a particular compound, the bias may be shared over labs or over time and then by modeling systematic biases (which depend on the concentration) by combining data from different labs. As seen in the analyses, the latter models may be more realistic.

Due to uncertainty in the certified reference material analyzing systematic biases leads to a measurement error in linear regression problem. This work has two differences from the standard work in this area. First, it allows heterogeneity in the material being delivered to the lab, whether it be control or study material. Secondly, we make use of Fieller's method for estimation which has not been used in the context before, although others have suggested it. One challenge in using Fieller's method is that explicit expressions for the variance and covariance of the sample variance and covariance of independent but non-identically distributed random variables are needed. These are developed.

Simulations are used to compare the performance of moment/Wald, Fieller and bootstrap methods for getting confidence intervals for the slope in the measurement model. These suggest that the Fieller's method performs better than the bootstrap technique. We also explore four estimators for the variance of the error in the equation in this context and determine that the estimator based on the modified squared residuals outperforms the others.

Homogeneity is a desirable property in control and study samples. Special experiments with nested designs must be conducted for homogeneity analysis and assessment purposes. However, simulation shows that heterogeneity has low impact on the performance of the studied estimators. This work shows that a biased but consistent estimator for the heterogeneity variance can be obtained from the current experimental design.

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