Generalized orthogonal contrast tests for homogeneity of ordered means

Canadian Journal of Statistics

Volumn 27, Issue 3, 1999, Pages 457-470

  McDermott, Michael P ^a  

^a UNIVERSITY OF ROCHESTER MEDICAL CENTER   (United States)

Author keywords

Analysis of variance; Combining independent tests; Fisher's combination method; Likelihood ratio test; Order restricted inference; Polyhedral cones

Indexed keywords

EID: 0033261211     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316104     Document Type: Article

References (28)

1. R. P. Abelson & J. W. Tukey (1963). Efficient utilization of non-numerical information in quantitative analysis: general theory and the case of simple order. The Annals of Mathematical Statistics, 34, 1347-1369.
2. J. C. Akkerboom (1990). Testing Problems with Linear or Angular Inequality Constraints. Springer-Verlag, New York.
3. D. J. Bartholomew (1959). A test of homogeneity for ordered alternatives. Biometrika, 46, 36-48.
4. D. J. Bartholomew (1961a). A test of homogeneity of means under restricted alternatives (with discussion). Journal of the Royal Statistical Society Series B, 23, 239-281.
5. D. J. Bartholomew (1961b). Ordered tests in the analysis of variance. Biometrika, 48, 325-332.
6. G. R. Chase (1974). On testing for ordered alternatives with increased sample size for a control. Biometrika, 61, 569-578.
7. M. Conaway, C. Pillers, T. Robertson & J. Sconing (1991). A circular cone test for testing homogeneity against a simple tree order. The Canadian Journal of Statistics, 19, 283-296.
8. C. W. Dunnett (1955). A multiple comparisons procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50, 1096-1121.
9. R. A. Fisher (1932). Statistical Methods for Research Workers, Fourth Edition. Oliver & Boyd, Edinburgh.
10. R. V. Hogg (1962). Iterated tests of the equality of several distributions. Journal of the American Statistical Association, 57, 579-585.
11. IMSL - International Mathematical and Statistical Libraries, Inc. (1991). IMSL Library, Version 2.0. IMSL, Houston, TX.
12. T. Liptak (1958). On the combination of independent tests. A Magyar Tudományos Akadémia Matematikai Kutató Intézetének Közleményei, 3, 171-197.
13. M. P. McDermott & G. S. Mudholkar (1993). A simple approach to testing homogeneity of order constrained means. Journal of the American Statistical Association, 88, 1371-1379.
14. G. S. Mudholkar & E. O. George (1979). The logit statistic for combining probabilities - an overview. In Optimizing Methods in Statistics (J. S. Rustagi, ed.), Academic Press, New York, pp. 345-365.
15. G. S. Mudholkar & M. P. McDermott (1989). A class of tests for equality of ordered means. Biometrika, 76, 161-168.
16. H. Mukerjee, T. Robertson & F. T. Wright (1987). Comparison of several treatments with a control using multiple contrasts. Journal of the American Statistical Association, 82, 902-910.
17. NAG - Numerical Algorithms Group (1988). Numerical Algorithms Group Library, Mark 13. Numerical Algorithms Group, Downers Grove, IL.
18. R. Pincus (1975). Testing linear hypotheses under restricted alternatives. Mathematische Operations-forschung und Statistik, 6, 733-751.
19. T. Robertson & E. J. Wegman (1978). Likelihood ratio tests for order restrictions in exponential families. The Annals of Statistics, 6, 485-505.
20. T. Robertson, F. T. Wright & R. L. Dykstra (1988). Order Restricted Statistical Inference. Wiley, New York.
21. W. Schaafsma & L. J. Smid (1966). Most stringent somewhere most powerful tests against alternatives restricted by a number of linear inequalities. The Annals of Mathematical Statistics, 37, 1161-1172.
22. H.-J. Sun (1988). A general reduction method for n-variate normal orthant probability. Communications in Statistics - Theory and Methods, 17, 3913-3921.
23. D.-I. Tang, C. Gnecco & N. L. Geller (1989). An approximate likelihood ratio test for a normal mean vector with nonnegative components with application to clinical trials. Biometrika, 76, 577-583.
24. D. -I. Tang & S. P. Lin (1997). An approximate likelihood ratio test for comparing several treatments to a control. Journal of the American Statistical Association, 92, 1155-1162.
25. L. H. C. Tippett (1931). The Method of Statistics, First Edition. Williams & Northgate, London.
26. C. van Eeden (1958). Testing and Estimating Ordered Parameters of Probability Distributions. Studentendrukkerij Poortpers, Amsterdam.
27. D. A. Williams (1971). A test for differences between treatment means when several dose levels are compared with a zero dose control. Biometrics, 27, 103-117.
28. D. A. Williams (1972). The comparison of several dose levels with a zero dose control. Biometrics, 28, 519-531.