The effects of nonnormality on parametric, nonparametric, and model comparison approaches to pairwise comparisons

Educational and Psychological Measurement

Volumn 63, Issue 4, 2003, Pages 615-635

  Cribbie, Robert A ^a   Keselman, H J ^b  

^a UNIVERSITY OF YORK   (United Kingdom)

^b UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Multiple comparison procedures; Pairwise comparisons

Indexed keywords

EID: 0041569846     PISSN: 00131644     EISSN: None     Source Type: Journal    
DOI: 10.1177/0013164403251283     Document Type: Article

References (39)

1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, AC-19, 716-723.
2. Boneau, C. A. (1960). The effects of violations of assumptions underlying the t test. Psychological Bulletin, 57, 49-64.
3. Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152.
4. Cressie, N. A. C., & Whitford, H. J. (1986). How to use the two sample t-test. Biometrical Journal, 28, 131-148.
5. Cribbie, R. A., & Keselman, H. J. (in press). Pairwise multiple comparisons: A model testing approach versus stepwise procedures. British Journal of Mathematical and Statistical Psychology.
6. Dayton, C. M. (1998). Information criteria for the paired-comparisons problem. The American Statistician, 52, 144-151.
7. Dunnett, C. W. (1980). Pairwise multiple comparisons in the unequal variance case. Journal of the American Statistical Association, 75, 796-800.
8. Einot, I., & Gabriel, K. R. (1975). A study of the powers of several methods of multiple comparisons. Journal of the American Statistical Association, 70, 574-583.
9. Gibbons, J. D., & Chakraborti, S. (1991). Comparisons of the Mann-Whitney, Student's t, and alternate t tests for means of normal distributions. Journal of Experimental Education, 59, 259-267.
10. Hayter, A. J. (1986). The maximum family wise error rate of Fisher's least significant difference test. Journal of the American Statistical Association, 81, 1000-1004.
11. Hoaglin, D. C. (1985). Summarizing shape numerically: The g- and h- distributions. In D. Hoaglin, F. Mosteller, & J. Tukey (Eds.), Exploring data tables, trends, and shapes (pp. 461 513). NewYork: Wiley.
12. Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika, 75, 383-386.
13. Keselman, H. J., Huberty, C. J., et al. (1998). Statistical practices of educational researchers: An analysis of their ANOVA, MANOVA, and ANCOVA analyses. Review of Educational Research, 68, 350-386.
14. Keselman, H. J., Lix, L. M., & Kowalchuk, R. K. (1998). Multiple comparison procedures for trimmed means. Psychological Methods, 3, 123-141.
15. Kromrey, J. D., & La Rocca, M. A. (1995). Power and Type I error rates of new pairwise multiple comparison procedures under heterogeneous variances. Journal of Experimental Education, 63, 343-362.
16. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156-166.
17. Miller, J. (1988). A warning about median reaction time. Journal of Experimental Psychology: Human Perception and Performance, 14, 539-543.
18. Mudholkar, A., Mudholkar, G. S., & Srivastava, D. K. (1991). A construction and appraisal of pooled trimmed-t statistics. Communications in Statistics: Theory and Methods, 20, 1345-1359.
19. Penfield, D. A. (1994). Choosing a two-sample location test. Journal of Experimental Education, 62, 343-360.
20. Ryan, T. A. (1960). Significance tests for multiple comparison of proportions, variances, and other statistics. Psychological Bulletin, 57, 318-328.
21. SAS Institute. (1999a). SAS/IML user's guide, Version 8. Cary, NC: Author.
22. SAS Institute. (1999b). SAS/STAT user's guide, Version 7-1. Cary, NC: Author.
23. Sawilowsky, S. S., & Blair, R. C. (1992). A more realistic look at the robustness and Type II error probabilities of the t test to departures from population normality. Psychological Bulletin, 111, 352-360.
24. Seaman, M. A., Levin, J. R., & Serlin, R. C. (1991). New developments in pairwise multiple comparisons: Some powerful and practicable procedures. Psychological Bulletin, 110, 577-586.
25. Sprent, P. (1993). Applied nonparametric statistical methods (2nd ed.). London: Chapman & Hall.
26. Toothaker, L. E. (1991). Multiple comparisons for researchers. Newbury Park, CA: Sage.
27. Tukey, J. W. (1953). The problem of multiple comparisons. Unpublished manuscript, Princeton University, Department of Statistics.
28. Tukey, J. W. (1960). A survey of sampling from contaminated distributions. In I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, & H. B. Mann (Eds.), Contributions to probabilities and statistics. Stanford, CA: Stanford University Press.
29. Welch, B. L. (1938). The significance of the difference between two means when population variances are unequal. Biometrika, 38, 330-336.
30. Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330-336.
31. Welsch, R. E. (1977). Stepwise multiple comparison procedures. Journal of the American Statistical Association, 72, 566-575.
32. Westfall, P. H., Tobias, R. D., Rom, D., Wolfinger, R. D., & Hochberg, Y. (1999). Multiple comparisons and multiple tests using the SAS system. Gary, NC: SAS Institute.
33. Wilcox, R. R. (1990). Comparing the means of two independent groups. Biometrics Journal, 32, 771-780.
34. Wilcox, R. R. (1995). ANOVA: The practical importance of heteroscedastic methods, using trimmed means versus means, and designing simulation studies. British Journal of Mathematical and Statistical Psychology, 48, 99-114.
35. Wilcox, R. R. (1997). Three multiple comparison procedures for trimmed means. Biometrical Journal, 37, 643-656.
36. Yuen, K. K. (1974). The two-sample trimmed / for unequal population variances. Biometrika, 61, 165-170.
37. Zhou, X., Gao, S., & Hui, S. L. (1997). Methods for comparing the means of two independent log-normal samples. Biometrics, 53, 1129-1135.
38. Zimmerman, D. W. (1996). A note on homogeneity of variance of scores and ranks. Journal of Experimental Education, 64, 351-362.
39. Zumbo, B. D., & Coulombe, D. (1997). Investigation of the robust rank-order test for non-normal populations with unequal variances: The case of reaction time. Canadian Journal of Experimental Psychology, 51, 139-150.