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Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two sided alternatives they may not be ideal for testing for order between two groups. In this article we introduce the notion of the linear stochastic order and investigate its properties. Statistical theory and methodology are developed to both estimate the direction which best separates two arbitrary ordered distributions and to test for order between the two groups. The new methodology generalizes Roy's classical largest root test to the nonparametric setting and is applicable to random vectors with discrete and/or continuous components. The proposed methodology is illustrated using data obtained from a a 90-day pre-chronic rodent cancer bioassay study conducted by the National Toxicology Program (NTP). Not only is the proposed methodology more sensitive in detecting a dose-related increase in response, but is also simple to use.
Ori is an Associate Professor of statistics at the University of Haifa where he has been on the faculty since late 1999. Ori received a doctorate in Biostatistics from Harvard in 1996 where his thesis advisor had been Marvin Zelen. He was a postdoc at Seattle's Fred Hutchinson Cancer Center and had also worked at Merck Research Labs in Rahway NJ. His research interest are in Order Restricted Inference, General Methodology in Biostatistics and especially case control studies, early detection (screening) programs and ROC methodology. His research has been funded by the Israeli Science Foundation, the Binational Science Foundation and the NIH. Ori has have held various service and organizational positions both within and outside of the University. For example, he headed the Biostatistics track in his department and has served as the secretary and treasurer of the Eastern Mediterranean Region (EMR) of the International Biometrics Society (IBS) and as the IBS's general secretary.