@bullet Some Properties of the Two-sample Multidimensional Runs Statistic S<j.1e Properties of Tile Dijo-sample Multidimensional Runs Statistic Advisor Reader -- .- List of Ficljres List of Appendices Iii Viii Xi Xiii Chajyfer I

sional Runs Statistic. (Under the direction of DANA QUADE.) Friedman and Rafsky have generalized the runs statistic presented by Wald and Wolfowitz for testing the homogeneity of two populations to include the comparison of multivariate populations. Their multi-dimensional runs statistic can be defined as the number of links between observations from different populations, where observations may be considered linked if they are "close" to each .other. We discuss three other independently derived statistics that are equivalent to this statistic. We also develop a multidimensional runs statistic that is not conditional on the number and pattern of links between observations, and investigate the asymptotic distribution of both statistics. We consider the method of linking all observations within a specified Euclidean distance or "tolerance". We provide quidelines for choosing the best linkage tolerance for the multivariate normal case, based on theoretical distribution of Euclidean distances between two or more multivariate normal observations and also on an extensive Monte Carlo simulation. Using these guidelines, we also compare the power against differences in location of the multidimensional runs test with that of Hotelling's T 2 , and find that in some instances the multidimen-sional runs test is more powerful. Using a subset of the classic Fisher iris data, we compare 95% confidence regions based on the multidimensional runs test and on Hotelling's T 2 We find that the size of the confidence region using the multidimensional nms test is very sensitive to changes in the tolerance. This is probably due to the lack of precision in the data. The Degree of the Ph.D. (with Apologies to Eric Burdon) There's a degree in Chapel Hill. They call it the Ph.D. And it's been the ruin of many a poor boy. I know that includes me·. My chairman, he revises Everything I write. My friends are thesis writers, too. Toiling through the night. Now, the only things a writer needs Are printouts by the ton. And the only time that he is satisfied Is when his programs run. Oh, Mother, tell your children Not to do what I have done. Spend your life in research misery Working on a dissertation. I got one eye on the sheepskin That seal of great renown. I'm going back to Chapel Hill To wear that cap and gown. Well, there's a degree in Chapel Hill. They call it the Ph.D. And it's been the ruin of many a poor boy. …