Basic and Applied Statistical Inference and Measurement

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Over the last decade statistical data and inference have played an important role in establishing the basic facts used for public policy, e.g.estimating the prevalence of AIDS or HIV infection, determining the risk of cancer from occupational or environmental exposures, assessing changes in the income distribution and in the legal setting, e.g. tax assessment inequality. The purpose of this project is to study statistical problems arising in these contexts and to develop appropriate probability models and statistical methodology for their solution. Research on procedures for estimating the prevalence of a rare disease which preserve anonymity by combining individual samples into batches prior to testing is a major goal. These methods should enable health specialists to obtain the cooperation of the public as infected individuals and non- infected persons who are misclassified (false positive) will not be identified. Robust methods which lead to statistically valid inferences when several scientifically plausible models may underlie the data or when a few observations may be erroneous will continue to be emphasized. Recent legal decisions in the equal employment area have raised new questions concerning the measurement of discrimination. It is planned to investigate the statistical approaches used in Watson v. Fort Worth Bank and to examine the implications of the Ward's Cove case for more refined data and methods of analysis. Related problems arising in legal and economic applications, e.g. the analysis of group data, also will be investigated.