Statistical Tables for Multivariate Analysis

An English translation of my "Statistisahe Tafeln zur multivariaten Analysis - Ein Handbuah mit Hinweisen zur Anwendung" was planned already in 1975 when I prepared the German volume. The tables were immediately supplied with German and English headings for the inten ded photo-offset printing. In the meantime. new and important tables for multivariate statistiaal hypotheses and proaedures have been aompiled and published. Only four of them have been inaorporated in the present volume. The seleation of these tables must be on an individual basis for reasons of spaae. Let me mention only the new tables for sample size determination in MANOVA. The instruations for using the tables are all organized in the same way. They are kept short sinae it is not the task of suah a work to provide an introduation to the theory and praatiae of multivariate analysis. I have renounaed giving examples for the same reason. I wish instead to refer the reader to the many good textbooks that are avai lable. as well as to my own works on methods that are in preparation. Furthermore. I am of the opinion that statistiaal tables should aaaom pany the textbook rather than be inaluded in it. vii viii Finally, my thanks go to the translator, Mr. Peter R. Wadsack, as ~ell as to the ladies and gentlemen of Springer-Verlag for their pleasant collaboration and their indulgence of my numerous requests.

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An English translation of my "Statistisahe Tafeln zur multivariaten Analysis - Ein Handbuah mit Hinweisen zur Anwendung" was planned already in 1975 when I prepared the German volume. The tables were immediately supplied with German and English headings for the inten­ ded photo-offset printing. In the meantime. new and important tables for multivariate statistiaal hypotheses and proaedures have been aompiled and published. Only four of them have been inaorporated in the present volume. The seleation of these tables must be on an individual basis for reasons of spaae. Let me mention only the new tables for sample size determination in MANOVA. The instruations for using the tables are all organized in the same way. They are kept short sinae it is not the task of suah a work to provide an introduation to the theory and praatiae of multivariate analysis. I have renounaed giving examples for the same reason. I wish instead to refer the reader to the many good textbooks that are avai­ lable. as well as to my own works on methods that are in preparation. Furthermore. I am of the opinion that statistiaal tables should aaaom­ pany the textbook rather than be inaluded in it. vii viii Finally, my thanks go to the translator, Mr. Peter R. Wadsack, as ~ell as to the ladies and gentlemen of Springer-Verlag for their pleasant collaboration and their indulgence of my numerous requests.

Contenu
I: The Primary Tables for Testing Multivariate Statistical Hypotheses.- Preliminary Remarks.- 0: A Brief Summary of the Test Criteria for the Multivariate General Linear Hypothesis.- Table 1: The Likelihood Ratio Criterion ? of S. S. Wilks: Tables of F. J. Wall.- Table 2: The ?max Criterion of K. C. S. Pillai: A Version of the Maximum Root Criterion of S. N. Roy.- Table 3: The Generalized F-Criterion of R. D. Bock: A Version of the Maximal Root Criterion of S. N. Roy.- Table 4: The Nomograms of D. L. Heck for the Distribution of the ?max Criterion of S. N. Roy.- Table 5: The ?max Criterion of F. G. Foster and D. H. Rees: A Version of the Maximum Root Criterion of S. N. Roy.- Table 6: The Trace Criterion To2 of H. Hotelling and D. N. Lawley in the Version of K. C. S. Pillai.- Table 7: The Trace Criterion of H. Hotelling and D. N. Lawley in the Version V(s) of K. C. S. Pillai.- Table 8: The T2-Criterion of H. Hotelling: Tables of D. R. Jensen and R. B. Howe.- II: Tables Related to the Multivariate Normal Distribution.- Preliminary Remarks.- Table 9: The Multivariate Normal Distribution with Equal Correlations: Tables of S. S. Gupta.- Table 10: The Distribution of the Maximum of N Equally Correlated Normal Standardised Random Variables: Tables of S. S. Gupta, K. Nagel, and S. Panchapakesan.- Table 11: The Sphericity Test of J. W. Mauchly: Tables of B. N. Nagarsenker and K. C. S. Pillai.- Table 12: The Test Criteria Lmvc, Lvc and Lm of S. S. Wilks: Tables of S. S. Wilks and also of J. Roy and V. K. Murthy.- Table 13: The Multivariate Outlier Criteria of S. S. Wilks.- Table 14: Multivariate Tolerance Regions with ?-Expectation (Type 2): Tables of D. A. S. Fraser and I. Guttman.- Table 15: Multivariate Tolerance Regions with ?-Content (Type 1): Tables of V.Chew.- Table 16: Testing a Single Covariance Matrix: Tables of B. P. Korin.- Table 17: Testing the Equality of k Covariance Matrices: Tables of B. P. Korin.- Table 18: Distribution of the Extreme Roots of a WISHART Matrix: Tables of R. Ch. Hanumara and W. A. Thompson.- Table 19: The Multivariate t-Distribution: Tables of P. R. Krishnaiah and J. V. Armitage.- III: Further Tables for Multivariate Problems.- Preliminary Remarks.- Table 20: The Gamma Distribution: Tables of M. B. Wilk, R. Gnanadesikan, and M. J. Huyette.- Table 21: The BARGMANN Test for Simple Structure of a Factor Pattern: Tables of R. Bargmann.- Table 22: Upper Percentage Points of the BONFERRONI Chi-Square Statistic: Tables of G. B. Beus and D. R. Jensen.- Table 23: Lower Percentage Points of the BONFERRONI Chi-Square Statistic: Tables of G. B. Beus and D. R. Jensen.- Table 24: The Sequential Chi-Square Criterion for Multivariate Comparisons of Means: Tables of R. J. Freund and J. E. Jackson.- Table 25: The Sequential T2 -Criterion for Multivariate Testing for Means: Tables of R. J. Freund and J. E. Jackson.- IV (Appendix): Supplement.- Preliminary Remarks.- Table 26: The MARDIA-Test for Multivariate Normality, Skewness, and Kurtosis: Tables by K. V. Mardia.- Table 27: Sample Size Requirements for the T2-Test of MANOVA in One-Way Classifications: Tables of J. Läuter.- Table 28: Critical Values for Simultaneous and Sequential BONFERRONI z-Tests: Tables of G. A. Lienert, O. Ludwig, and K. Rockenfeller.- Table 29: Upper Percentage Points of the BONFERRONI t-Statistic: Tables of B. J. R. Bailey.- Table 30: Upper Percentage Points of Statistics for Testing Covariance Matrices: Tables of J. C. Lee, T. C. Chang, and P. R. Krishnaiah.- Final Remarks: Univariate Test Distributions as a Special Case of TheirMultivariate Analogs.