Using Johnson's transformation and robust estimators with heteroscedastic test statistics: An examination of the effects of non-normality and heterogeneity in the non-orthogonal two-way ANOVA design

British Journal of Mathematical and Statistical Psychology

Volumn 54, Issue 1, 2001, Pages 79-94

  Wei Ming, Luh ^a   Jiin Huarng, Guo ^b  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b DEPARTMENT OF ELECTRONIC ENGINEERING   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035345080     PISSN: 00071102     EISSN: None     Source Type: Journal    
DOI: 10.1348/000711001159438     Document Type: Article

References (37)

1. Alexander, R. A., & Govern, D. M. (1994). A new and simpler approximation and ANOVA under variance heterogeneity. Journal of Educational Statistics, 19, 91-101.
2. Algina, J., & Olejnik, S. F. (1984). Implementing the Welch-James procedure with factorial designs. Educational and Psychological Measurement, 44, 39-48.
3. Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152.
4. Coombs, W. T., Algina, J., & Oltman, D. O. (1996). Univariate and multivariate omnibus hypothesis tests selected to control Type I error rates when population variances are not necessarily equal. Review of Educational Research, 66, 137-179.
5. Harwell, M. R., Rubinstein, E. N., Hayes, W. S., & Olds, C. C. (1992). Summarizing Monte Carlo results in methodological research: The one-and two-factor fixed-effects ANOVA cases. Journal of Educational Statistics, 17, 297-313.
6. Hoaglin, D. C. (1985). Summarizing shape numerically: the g-and-h distributions. In D. C. Hoaglin, F. Mosteller, and J. W. Tukey (Eds.), Exploring data tables, trends, and shapes. New York: Wiley.
7. Hoyle, M. H. (1973). Transformations: An introduction and a bibliography. International Statistical Review, 41, 203-223.
8. Hsiung, T., & Olejnik, S. (1996). Type I error rates and statistical power for the James second-order test and the univariate F test in two-way fixed effects ANOVA models under heteroscedasticity and/ or nonnormality. Journal of Experimental Education, 65, 57-71.
9. James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika, 38, 324-329.
10. Johansen, S. (1980). The Welch-James approximation to the distribution of the residual sum of squares in a weighted linear regression. Biometrika, 67, 85-92.
11. Johnson, N. J. (1978). Modified t tests and confidence intervals for asymmetrical populations. Journal of the American Statistical Association, 73, 536-544.
12. Keselman, H. J., Carriere, K. C., & Lix, L. M. (1995). Robust and powerful nonorthogonal analyses. Psychometrika, 60, 395-418.
13. Keselman, H. J., Carriere, K. C., & Lix, L. M. (1996). Errata to 'Robust and powerful nonorthogonal analyses'. Psychometrika, 61, 191.
14. Keselman, H. J., Kowalchuk, R. K., & Lix, L. M. (1998). Robust nonorthogonal analyses revisited: An update based on trimmed means. Psychometrika, 63, 145-163.
15. Keselman, H. J., Lix, L. M., & Kowalchuk, R. K. (1998). Multiple comparison procedures for trimmed means. Psychological Methods, 3, 123-141.
16. Kirk, R. E. (1995). Experimental design: Procedures for the behavioral sciences, 3rd edition. Pacific Grove, CA: Brooks/Cole.
17. Lix, L. M., & Keselman, H. J. (1995). Approximate degrees of freedom tests: A unified perspective on testing for mean equality. Psychological Bulletin, 117, 547-560.
18. Luh, W. M. (1999). Developing trimmed mean test statistics for two-way fixed effects ANOVA models under variance heterogeneity and non-normality. Journal of Experimental Education, 67, 243-264.
19. Luh, W. M., & Guo, J. H. (1999). A powerful transformation trimmed mean method for one-way fixed effects ANOVA model under non-normality and inequality of variances. British Journal of Mathematical and Statistical Psychology, 52, 303-320.
20. Martinez, J., & Iglewicz, B. (1984). Some properties of the Tukey g and h family of distributions. Communications in Statistics: Theory and Methods, 13, 353-369.
21. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156-166.
22. Milligan, G. W., Wong, D. S., & Thompson, P. A. (1987). Robustness properties of nonorthogonal analysis of variance. Psychological Bulletin, 101, 464-470.
23. Oshima, T. C., & Algina, J. (1992). Type I error rates for James's second-order test and Wilcoxs Hm test under heteroscedasticity and non-normality. British Journal of Mathematical and Statistical Psychology, 45, 255-263.
24. Rosenberger, J. L., & Gasko, M. (1983). Comparing location estimators: Trimmed means, medians and trimean. In D. Hoaglin, F. Mosteller, & J. Tukey (Eds.), Understanding robust and exploratory data analysis. New York: Wiley.
25. SAS Institute, Inc. (1985). SAS/IML user's guide for personal computers, version 6 edition. Cary, NC: SAS.
26. SAS Institute, Inc. (1996). SAS Basic software, version 6.12 edition. Cary, NC: SAS.
27. Staudte, R. G., & Sheather, S. J. (1990). Robust estimation and testing. New York: Wiley.
28. Sutton, C. D. (1993). Computer-intensive methods for tests about the mean of an asymmetrical distribution. Journal of the American Statistical Association, 88, 802-810.
29. Tukey, J. W., & McLaughlin, D. H. (1963). Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/Winsorization I. Sankhyā, A, 25, 331-352.
30. Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330-336.
31. Wilcox, R. R. (1989). Adjusting for unequal variances when comparing means in one-way and two-way fixed effects ANOVA models. Journal of Educational Statistics, 14, 269-278.
32. Wilcox, R. R. (1994a). Some results on the Tukey-McLaughlin and Yuen methods for trimmed means when distributions are skewed. Biometrical Journal, 36, 259-273.
33. Wilcox, R. R. (1994b). A one-way random effects model for trimmed means. Psychometrika, 59, 289-306.
34. Wilcox, R. R. (1995). ANOVA: A paradigm for low power and misleading measures of effect size? Review of Educational Research, 65, 51-77.
35. Wilcox, R. R. (1996). Statistics for the social sciences. San Diego, CA: Academic Press.
36. Wilcox, R. R. (1997). A bootstrap modification of the Alexander-Govern ANOVA method, plus comments on comparing trimmed means. Educational and Psychological Measurement, 57, 655-665.
37. Yuen, K. K., & Dixon, W. J. (1973). The approximate behaviour and performance of the two-sample trimmed t. Biometrika, 60, 369-374.