Properties of the rank transformation in factorial analysis of covariance

Communications in Statistics - Theory and Methods

Volumn 29, Issue 4, 2000, Pages 1059-1087

  Headrick, Todd C ^a   Sawilowsky, Shlomo S ^b  

^a SOUTHERN ILLINOIS UNIVERSITY   (United States)

^b WAYNE STATE UNIVERSITY   (United States)

Author keywords

Designed experiments; Nonparametric; Power; Type I error

Indexed keywords

EID: 0000202368     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1080/03610910008813654     Document Type: Article

References (38)

1. Akritas, M. G. (1990). The rank transform method in some two factor designs. Journal of the American Statistical Association, 85, 73-78.
2. Angermeier, P. L., & Winston, M. R. (1998), Local vs. regional influences on local diversity in stream fish communities of Virginia. Ecology, 79, 911-927.
3. Augner, M., Provenza, F. D., & Villalba, J. J. (1998). A rule of thumb in mammalian herbivores? Animal Behaviour, 56, 337-345.
4. Blair, R. C. (1987). RANGEN. Boca Raton, FL: IBM.
5. Blair, R. C., & Sawilowsky, S. S. (1990, April). A test for interaction based on the rank transform. Paper presented at the annual meeting of the American Educational Research Association, Boston.
6. Blair, R. C., Sawilowsky, S. S., & Higgins, J. J. (1987). Limitations of the rank transform in tests of interactions. Communications in Statistics: Simulation and Computation, 16, 1133-1145.
7. Brunner, E., & Neumann, N. (1986). Rank tests in 2 x 2 designs. Statistica Neulandica, 40, 251-272.
8. 3 factorial experiment. Communications in Statistics, 27, 259-274.
9. Conover, W. J., & Iman, R. L. (1976). On some alternative procedures using ranks for the analysis of experimental designs. Communications in Statistics, 5, 1348-1368.
10. Conover, W. J., & Iman, R. L. (1981). Rank transformations as a bridge between parametric and nonparametric statistics. American Statistician, 35, 124-133.
11. Conover, W. J., & Iman, R. L. (1982). Analysis of covariance using the rank transformation. Biometrics, 38, 715-724.
12. Deshon, R. P., & Alexander, R. A. (1996). Alternative procedures for testing regression slope homogeneity when group error variances are unequal. Psychological Methods, 1, 261-277.
13. Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532.
14. Harwell, M. R., & Serlin, R. C. (1988). An experimental study of a proposed test of non-parametric analysis of covariance. Psychological Bulletin, 104, 268-281.
15. Headrick, T. C. (1997). Type I error and power of the rank transform analysis of covariance (ANCOVA) in a 3 x 4 factorial layout. Unpublished doctoral dissertation, Wayne State University, Detroit, MI.
16. Headrick, T. C. & Sawilowsky, S. S. (1999). Simulating correlated multivariate nonnormal distributions: Extending the Fleishman power method. Psychometrika, 64, 25-35.
17. Hettmansperger, T. P. (1984). Statistical inference based on ranks. NY: Wiley.
18. Iman, R. L. (1974). A power study of a rank transform for the two way classification model when interaction may be present. Canadian Journal of Statistics, 2, 227-239.
19. Iman, R. L., & Conover, W. J. (1979). The use of rank transform in regression. Technometrics, 21, 499-509.
20. International Mathematical and Statistical Libraries. (1994). IMSL library, reference manual. Houston, TX: Author.
21. rd). Pacific Grove, CA: Duxbury Press.
22. Knapp, T. R. & Sowyer, V. H. (1967). Some empirical results concerning the power of Bartlett's test of the significance of a correlation matrix. American Educational Research Journal, 4, 13-17.
23. Lahey, Computer Systems, Inc. (1994). Personal Fortran (version 3.0). Incline Village, NV: Author.
24. Olejnik, S. F., & Algina, J. (1984). Parametric ANCOVA and the rank transform ANCOVA when the data are conditionally non-normal and heteroscedastic. Journal of Educational Statistics, 9, 129-150.
25. Olejnik, S. F., & Algina, J. (1985). A review of non-parametric alternatives to analysis of covariance. Evaluation Review, 9, 51-83.
26. Olejnik, S. F., & Algina, J. (1987). An analysis of statistical power of parametric ANCOVA and rank transform ANCOVA. Communications in Statistics: Theory and Methods, 16, 1923-1949.
27. Potvin, C., & Roff, D. A. (1993). Distribution-free and robust statistical methods: viable alternatives to parametric statistics. Ecology, 74, 1617-1628.
28. Puri, M. L., & Sen, P. K. (1969a). Analysis of covariance based on general rank scores. Annals of Mathematical Statistics, 40, 610-618.
29. Quade, D. (1967). Rank analysis of covariance. Journal of the American Statistical Association, 62, 1187-1200.
30. Regeth, R. A., & Stine, W. W. (1998). Comparing means from nonnormal distributions: The bisquare-weighted analysis of variance. Behavior Research Methods, Instruments, & Computers, 30, 707-712.
31. Salter, K. C., & Fawcett, R. F. (1993). The ART test of interaction: A robust and powerful rank test of interaction in factorial models. Communications in Statistics: Computation and Simulation, 22, 137-153.
32. SAS Institute, Inc. (1995). SAS User's Guide: Statistics, 5th ed. N.C.: SAS Institute.
33. Sawilowsky, S. S., Blair, R. C., & Higgins, J. J. (1989). An investigation of the Type I error and power properties of the rank transform procedure in factorial ANOVA. Journal of Educational Statistics, 14, 255-267.
34. Seaman, S., Algina, J., & Olejnik, S. F. (1985). Type I error probabilities and power of the rank and parametric ANCOVA procedures. Journal of Educational Statistics, 10, 345-367.
35. Stephenson, W. R., & Jacobson, D. (1988). A comparison of non-parametric analysis of covariance techniques. Communication in Statistics: Computation and Simulation, 26, 605-618.
36. Thompson, G. L. (1991). A note on the rank transform for interactions. Biometrika, 78, 697-701.
37. Visual Numerics. (1994). MSL Math/Library: FORTRAN subroutines for mathematical applications, Volume II. Houston, TX: Author.
38. Winer, B. J., Brown, D. R., & Michels, K. M. (1991). Statistical principles in experimental designs (3rd). NY: McGraw-Hill.