Rank Tests for Main and Interaction Effects in Analysis of Variance

References

• Akritas , M. G. and Arnold , S. F. 1994 . “Fully Nonparametric Hypotheses for Factorial Designs I: Multivariate Repeated Measures Designs,” . Journal of the American Statistical Association , 89 : 336 – 343 .
   Web of Science ®Google Scholar
• Benard , A. and vanElteren , P. H. 1953 . “A Generalization of the Method of m Rankings,” . Indagtiones Mathematicae , 15 : 358 – 369 .
   Google Scholar
• Bhapkar , V. P. and Gore , A. P. 1974 . “A Nonparametric Test for Interaction in Two-Way Layouts,” . Sankhya , : 261 – 272 . Ser. A, Part 3
   Google Scholar
• Bradley , J. V. 1968 . Distribution-Free Statistical Tests , Englewood Cliffs , NJ : Prentice-Hall .
   Google Scholar
• Chung , L. and Marden , J. I. 1991 . “Use of Nonnull Models for Rank Statistics in Bivariate, Two-Sample, and Analysis-of-Variance Problems,” . Journal of the American Statistical Association , 86 : 188 – 200 .
   Web of Science ®Google Scholar
• Chung , L. and Marden , J. I. 1993 . “Extensions of Mallows' ϕ Model,” . In Probability Models and Statistical Analyses for Ranking Data , Edited by: Verducci , J. S. and Fligner , M. A. New York : Springer-Verlag .
   Google Scholar
• Conover , W. J. and Iman , R. L. 1981 . “Rank Transformations as a Bridge Between Parametric and Nonparametric Statistics,” . The American Statistician , 35 : 124 – 128 .
   Web of Science ®Google Scholar
• Crouse , C. F. 1966 . “Distribution-Free Tests Based on the Sample Distribution Function,” . Biometrika , 53 : 99 – 108 .
   PubMed Web of Science ®Google Scholar
• Crouse , C. F. 1967 . “A Class of Distribution-Free Analysis of Variance Tests,” . South African Statistical Journal , 1 : 75 – 80 .
   Google Scholar
• De Kroon , J. and Van Der Laan , P. 1981 . “Distribution-Free Test Procedures in Two-Way Layouts: A Concept of Rank Interaction,” . Statistica Neerlandica , 35 : 189 – 213 .
   Google Scholar
• Fligner , M. A. 1981 . “Comments on ‘Rank Transformations as a Bridge Between Parametric and Nonparametric Statistics,’” . The American Statistician , 35 : 131 – 132 .
   Web of Science ®Google Scholar
• Fligner , M. A. 1985 . “Pairwise Versus Joint Ranking: Another Look at the Kruskal-Wallis Statistic,” . Biometrika , 72 : 705 – 709 .
   Web of Science ®Google Scholar
• Fligner , M. A. and Wolfe , D. A. 1982 . “Distribution-Free Tests for Comparing Several Treatments With a Control,” . Statistica Neerlandica , 36 : 119 – 127 .
   Google Scholar
• Friedman , M. 1937 . “The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance,” . Journal of the American Statistical Association , 32 : 675 – 701 .
   Web of Science ®Google Scholar
• Gibbons , J. D. and Chakraborti , S. 1992 . Nonparametric Statistical Inference , New York : Marcel Dekker .
   Google Scholar
• Gore , A. P. 1973 . “Some Nonparametric Tests and Selection Procedures for Main Effects in Two-Way Layouts,” . Annals of the Institute of Statistical Mathematics , 27 : 487 – 500 .
   Web of Science ®Google Scholar
• Govindarajulu , Z. 1968 . “Distribution-Free Confidence Bounds for P(X < Y),” . Annals of the Institute of Statistic Mathematics , 20 : 229 – 238 .
   Web of Science ®Google Scholar
• Groggel , D. J. and Skillings , J. H. 1986 . “Distribution-Free Tests for Main Effects in Multifactor Designs,” . The American Statistician , 40 : 99 – 102 .
   Web of Science ®Google Scholar
• Hájek , J. and Šidák , Z. 1967 . Theory of Rank Tests , New York : Academic Press .
   Google Scholar
• Hora , S. C. and Iman , R. L. 1988 . “Asymptotic Relative Efficiencies of the Rank-Transform Procedure in Randomized Complete-Block Designs,” . Journal of the American Statistical Association , 83 : 462 – 470 .
   Web of Science ®Google Scholar
• Koziol , J. A. and Reid , N. 1977 . “On the Asymptotic Equivalence of Two Ranking Methods for K-Sample Linear Rank Statistics,” . The Annals of Statistics , 5 : 1099 – 1106 .
   Web of Science ®Google Scholar
• Kruskal , W. H. and Wallis , W. A. 1952 . “Use of Ranks in One-Criterion Variance Analysis,” . Journal of the American Statistical Association , 47 : 583 – 621 .
   Web of Science ®Google Scholar
• Lehmann , E. L. 1975 . Nonparametrics: Statistical Methods Based on Ranks , San Francisco : Holden-Day .
   Google Scholar
• Lemmer , H. H. and Stoker , D. J. 1967 . “A Distribution-Free Analysis of Variance for the Two-Way Classification,” . South African Statistical Journal , 1 : 67 – 74 .
   Google Scholar
• Mack , G. A. and Skillings , J. H. 1980 . “A Friedman-Type Rank Test for Main Effects in a Two-Factor ANOVA,” . Journal of the American Statistical Association , 75 : 947 – 951 .
   Web of Science ®Google Scholar
• Mehra , K. L. and Sen , P. K. 1969 . “On a Class of Conditionally Distribution-Free Tests for Interactions in Factorial Experiments,” . Annals of Mathematical Statistics , 40 : 658 – 664 .
   Google Scholar
• Patil , K. M. and Hoel , D. G. 1973 . “A Nonparametric Test for Interaction in Factorial Experiments,” . Journal of the American Statistical Association , 68 : 615 – 620 .
   Web of Science ®Google Scholar
• Puri , M. L. and Sen , P. K. 1967 . “Some Optimum Nonparametric Procedures in Two-Way Layouts,” . Journal of the American Statistical Association , 62 : 1214 – 1229 .
   Web of Science ®Google Scholar
• Quade , D. 1979 . “Using Weighted Rankings in the Analysis of Complete Blocks With Additive Block Effects,” . Journal of the American Statistical Association , 74 : 680 – 683 .
   Web of Science ®Google Scholar
• Sen , P. K. 1968 . “On a Class of Aligned Rank Order Tests in Two-Way Layouts,” . Annals of Mathematical Statistics , 39 : 1115 – 1124 .
   Google Scholar
• Simpson , D. G. and Margolin , B. H. 1986 . “Recursive Nonparametric Testing for Dose–Response Relationships Subject to Downturns at High Doses,” . Biometrika , 73 : 589 – 596 .
   Web of Science ®Google Scholar
• Snedecor , G. W. and Cochran , W. G. 1989 . Statistical Methods , Ames , IA : Iowa State University Press .
   Google Scholar
• Terpstra , T. J. 1952 . “The Asymptotic Normality and Consistency of Kendall's Test Against Trend When Ties are Present in One Ranking,” . Indagtiones Mathematicae , 14 : 327 – 333 .
   Google Scholar
• Thompson , G. L. 1991 . “A Note on the Rank Transform for Interactions,” . Biometrika , 78 : 697 – 701 .
   Web of Science ®Google Scholar
• Thompson , G. L. and Ammann , L. P. 1989 . “Efficacies of Rank Transform Statistics in Two-Way Models With No Interaction,” . Journal of the American Statistical Association , 84 : 325 – 330 .
   Web of Science ®Google Scholar
• Wolfe , D. A. , Dean , A. M. , Wiers , M. D. and Hartlaub , B. A. 1992 . “Nonparametric Rank Based Main Effects Test Procedures for the Two-Way Layout in the Presence of Interaction,” . Journal of Nonparametric Statistics , 1 : 241 – 252 .
   Google Scholar