Nonparametric Hypotheses and Rank Statistics for Unbalanced Factorial Designs

Journal of the American Statistical Association

Volumn 92, Issue 437, 1997, Pages 258-265

  Akritas, Michael G ^a   Arnold, Steven F ^a   Brunner, Edgar ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Factorial designs; Nonparametric hypotheses; Ordinal data; Rank test; Ties; Unbalanced designs

Indexed keywords

EID: 0031482353     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1997.10473623     Document Type: Article

References (29)

1. Akritas, M. G. (1990) “The Rank Transform Method in Some Two-Factor Designs. Journal of the American Statistical Association, 85, 73-78.
2. Akritas, M. G (1993) “Limitations of the Rank Transform Procedure: A Study of Repeated Measures Designs, Part 11,” Statistics and Probability Letters, 17, 149-156.
3. 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.
4. Akritas, M. G., Arnold, S. F., and Brunner, E. (1995), “Nonparametric Hypotheses and Rank Statistics for Unbalanced Factorial Designs,” Technical Report 95-07, Pennsylvania State University, Dept. of Statistics.
5. Arnold, S. F. (1981), The Theory of Linear Models and Multivariate Analysis, New York Wiley.
6. Boos, D. D., and Brownie, C. (1992). “Rank-Based Mixed Model Approach to Multisite Clinical Trials,” Biometrics, 48, 61-72.
7. Brunner, E., and Denker, M. (1994). “Rank Statistics Under Dependent Observations and Applications to Factorial Designs,” Journal of Statistical Planning and Inference, 42, 353-378.
8. Brunner, E., and Dette, H. (1992), “Rank Procedures for the Two-Factor Mixed Model,” Journal of the American Statistical Association, 87,884-888.
9. Brunner, E., Dette, H., and Munk, A. (1995), “Box-type approximations in nonparametric factorial designs,” unpublished manuscript.
10. Brunner, E., and Puri, M. L. (1995). “Nonparametric Methods in Design and Analysis of Experiments,” unpublished manuscript.
11. Brunner, E., Puri, M. L., and Sun, S. (1995). “Nonparametric Methods for Stratified Two-Sample Designs With Application to Multiclinic Trials,” Journal of the American Statistical Association, 1004-1014.
12. Chung, K. L. (1974). A Course in Probability Theory, New York: Academic Press.
13. Groggel, D. J., and Skillings, J. H. (1986). “Distribution-Free Tests for Main Effects in Multifactor Designs,” The American Statistician, 40
14. Hettmansperger, T. P. (1984). Statistical Inference Based on Ranks, New York: Wiley.
15. Hettmansperger, T. P., and McKean, J. W. (1977). “A Robust Alternative Based on Ranks to Least Squares in Analyzing Linear Models:’ Technometrics, 19, 275-284.
16. Hodges, J., and Lehmann, E. (1962), “Rank Methods for Combinations of Independent Experiments in Analysis of Variance,” The Annals of Mathematical Statistics, 33,482-497.
17. Hollander, M., and Wolfe, D. A. (1973). Nonparametric Statistical Methods, New York Wiley.
18. Kirk, R. (1982), Experimental Design (2nd ed.), Monterey, CA Brooks/Cole.
19. Koch, G. (1970), “The Use of Nonparametric Methods in the Statistical Analysis of a Complex Split Plot Experiment,” Biometrics, 26, 105-128.
20. Lehmann, E. L. (1975), Nonparametrics, New York: Holden-Day.
21. 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.
22. McKean, J. W., and Hettmansperger, T. P. (1976), ‘Tests of Hypotheses Based on Ranks in the General Linear Model,” Communications of Statistics, Part A-Theory and Methods, A5(8), 693-709.
23. Puri, M. L., and Sen, P. K. (1971), Nonparametric Methods in Multivariate Analysis, New York Wiley.-(1988) Nonparametric Methods in General Linear Models, New York: Wiley.
24. Rai, S. C. (1987). “Rank Analysis of Block Designs Having Different Cell Frequencies,” Biometrical Journal, 29, 293-298.
25. Randles, R. H., and Wolfe, D. A. (1979), Introduction to the Theory of Nonparametric Statistics, New York Wiley.
26. Serfling, R. J. (1980). Approcimation Theorems of Mathematical Statistics, New York: Wiley.
27. Shorack, G. R., and Wellner, J. A. (1986), Empirical Processes With Applications to Statistics, New York: Wiley.
28. Winer, B. J. (1971). Statistical Principles in Experimenial Designs (2nd ed.), New York McGraw-Hill.
29. Wittkowski, K. M. (1988), “Friedman-T&e Statistics and Consistent Multiple Comparisons for Unbalanced Designs With Missing Data,” Journal of the American Statistical Association, 83, 1163-1170.