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

Volumn 65, Issue 1, 1996, Pages 57-71

  Hsiung, Tung Hsing ^a   Olejnik, Stephen ^b  

^a National Taiwan Taitung Teachers College   (United States)

^b UNIVERSITY OF GEORGIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030354996     PISSN: 00220973     EISSN: 19400683     Source Type: Journal    
DOI: 10.1080/00220973.1996.9943463     Document Type: Article

References (22)

1. Brown, M. B., & Forsythe, A. B. (1974). The small sample behavior of some statistics which test the equality of several means. Technometrics, 16, 129-132.
2. Fleishman, A. I. (1978). A method for simulating nonnormal distributions. Psychometrika, 43, 521-532.
3. 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.
4. Holland, B. S., & Copenhaver, M. D. (1987). An improved sequentially rejective Bonferroni test procedure. Biometrics, 43, 417-423.
5. Hsiung, T., & Olejnik, S. (1993, April). Contrast analyses for the additive nonorthogonal two-factor design in the unequal variance case. Paper presented at the annual meeting of the American Educational Research Association, Atlanta, GA.
6. Hsiung, T., Olejnik, S., & Huberty, C. (1994). Comment on a Wilcox test statistic for comparing means when variances are unequal. Journal of Educational Statistics, 19, 111-118.
7. Hsiung, T., Olejnik, S., & Oshima, T. C. (1994). A SAS/IML program for applying the James second-order test in two-factor fixed-effect ANOVA models. Educational and Psychological Measurement, 54, 696-698.
8. James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika, 38, 324-329.
9. Keppel, G. (1991). Design and analysis: A researcher's handbook (3rd ed.). Englewood Cliffs, NJ: Prentice Hall.
10. Keselman, H. J., & Rogan, J. C. (1978). A comparison of the modified Tukey and Scheffe methods of multiple comparisons for pairwise contrasts. Journal of the American Statistical Association, 73, 47-52.
11. Lix, L. M., & Keselman, H. J. (1994). Approximate degrees of freedom tests: A unified perspective on testing for mean equality. Manuscript submitted for publication.
12. Maxwell, S. E., & Delaney, H. D. (1990). Designing experiments and analyzing data: A model comparison perspective. Belmont, CA: Wadsworth.
13. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156-166.
14. Milligan, G. W., Wong, D. S., & Thompson P. A. (1987). Robustness properties of nonorthogonal analysis of variance. Psychological Bulletin, 101, 464-470.
15. Oshima, T. C., & Algina, J. (1992a). Type 1 error rates for James's second-order test and Wilcox's Hm test under heteroscedasticity and nonnormality. British Journal of Mathematical and Statistical Psychology, 45, 225-263.
16. Oshima, T. C., & Algina, J. (1992b). A SAS program for testing the hypothesis of the equal means under heteroscedasticity: James's second-order test. Educational and Psychological Measurement, 52, 117-118.
17. SAS Institute Inc. (1989). SAS/IML software: Usage and reference. Version 6 (1st ed.). Cary, NC: Author.
18. Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330-336.
19. Wilcox, R. R. (1987). New designs in analysis of variance. Annual Review of Psychology, 38, 29-60.
20. Wilcox, R. R. (1988). A new alternative to the ANOVA F and on James's second-order method. British Journal of Mathematical and Statistical Psychology, 41, 109-117.
21. Wilcox, R. R. (1989). Adjusting for unequal variances when comparing means in one-way and twoway fixed effects ANOVA methods. Journal of Educational Statistics, 14, 269-278.
22. Wilcox, R. R., Charlin, V. L., & Thompson, K. L. (1986). New Monte Carlo results on the robustness of the ANOVA F, W, and F statistics. Communication in Statistics-Simulation and Computation, 15, 933-943.