A comparison of data analysis strategies for testing omnibus effects in higher-order repeated measures designs

Multivariate Behavioral Research

Volumn 37, Issue 3, 2002, Pages 331-357

  Keselman, H J ^a   Algina, James ^c   Kowalchuk, Rhonda K ^b  

^a UNIVERSITY OF MANITOBA   (Canada)

^b UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036400744     PISSN: 00273171     EISSN: None     Source Type: Journal    
DOI: 10.1207/S15327906MBR3703_2     Document Type: Review

References (73)

1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transaction on Automatic Control, AC-19, 716-723.
2. Algina, J. (1994). Some alternative approximate tests for a split plot design. Multivariate Behavioral Research, 29, 365-384.
3. Algina, J. (1997). Generalization of improved general approximation tests to split-plot designs with multiple between-subjects factors and/or multiple within-subjects factors. British Journal of Mathematical and Statistical Psychology, 50, 243-252.
4. Algina, J. & Keselman, H. J. (1997). Testing repeated measures hypotheses when covariance matrices are heterogeneous: Revisiting the robustness of the Welch-James test. Multivariate Behavioral Research, 32, 255-274.
5. Algina, J. & Keselman, H. J. (1998). A power comparison of the Welch-James and Improved General Approximation tests in the split-plot design. Journal of Educational and Behavioral Statistics, 23, 152-169.
6. Algina, J. & Oshima, T. C. (1994). Type I error rates for Huynh's general approximation and improved general approximation tests. British Journal of Mathematical and Statistical Psychology, 47, 151-165.
7. Algina, J. & Oshima, T. C. (1995). An improved general approximation test for the main effect in a split-plot design. British Journal of Mathematical and Statistical Psychology, 48, 149-160.
8. Barcikowski, R. S. & Robey, R. R. (1984). Decisions in single group repeated measures analysis: Statistical tests and three computer packages. The American Statistician, 38, 148-150.
9. Boik, R. J. (1997). Analysis of repeated measures under second-stage sphericity: An empirical Bayes approach. Journal of Educational and Behavioral Statistics, 22, 155-192.
10. Collier, R. O., Jr., Baker, F. B., Mandeville, G. K., & Hayes, T. F. (1967). Estimates of test size for several test procedures based on conventional variance ratios in the repeated measures design. Psychometrika, 32, 339-353.
11. 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.
12. Greenhouse, S. W. & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24, 95-112.
13. Harville, D. A. & Jeske, D. R. (1992). Mean squared error of estimation or prediction under a general linear model. JASA, 87, 724-731.
14. Hedeker, D. & Gibbons, R. D. (1997). Application of random-effects pattern-mixture models for missing data in longitudinal studies. Psychological Methods, 2, 64-78.
15. Hertzog, C. & Rovine, M. (1985). Repeated-measures analysis of variance in developmental research: Selected issues. Child Development, 56, 787-809.
16. Huynh, H. (1978). Some approximate tests for repeated measurement designs. Psychometrika, 43, 161-175.
17. Huynh, H. & Feldt, L. (1970). Conditions under which mean square ratios in repeated measurements designs have exact F distributions. Journal of the American Statistical Association, 65, 1582-1589.
18. Huynh, H. & Feldt, L. S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of Educational Statistics, 1, 69-82.
19. James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika, 38, 324-329.
20. James, G. S. (1954). Tests of linear hypotheses in univariate and multivariate analysis when the ratios of the population variances are unknown. Biometrika, 41, 19-43.
21. Jennings, J. R. (1987). Editorial policy on analyses of variance with repeated measures. Psychophysiology, 24, 474-475.
22. Jennrich, R. L. and Schluchter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics, 42, 805-820.
23. 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.
24. Kenward, M. G. & Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihhod. Biometrics, 53, 983-997.
25. Keselman, H. J. & Algina, J. (1996). The analysis of higher-order repeated measures designs. In B. Thompson's (Ed.), Advances in social science methodology (Vol 4), Greenwich, CT: JAI Press.
26. Keselman, H. J., Algina, J., Kowalchuk, R. K., & Wolfinger, R. D. (1998). A comparison of two approaches for selecting covariance structures in the analysis of repeated measurements. Communications in Statistics-Simulation and Computation, 27, 591-604.
27. Keselman, H. J., Algina, J., Kowalchuk, R. K., & Wolfinger, R. D. (1999a). A comparison of recent approaches to the analysis of repeated measurements. British Journal of Mathematical and Statistical Psychology, 52, 63-78.
28. Keselman, H. J., Algina, J., Kowalchuk, R. K., & Wolfinger, R. D. (1999b). The analysis of repeated measurements: A comparison of mixed-model Satterthwaite F tests and a nonpooled adjusted degrees of freedom multivariate test. Communications in Statistics-Theory and Methods, 28(12), 2967-2999.
29. Keselman, H. J., Carriere, K. C., & Lix, L. M. (1993). Testing repeated measures hypotheses when covariance matrices are heterogeneous. Journal of Educational Statistics, 18, 305-319.
30. Keselman, H. J., Huberty, C. J., Lix, L. M., Olejnik, S., Cribbie, R. A., Donahue, B., Kowalchuk, R. K., Lowman, L. L., Petoskey, M. D., Keselman, J. C., & Levin, J. R. (1998). Statistical practices of educational researchers: An analysis of their ANOVA, MANOVA and ANCOVA analyses. Review of Educational Research, 68(3), 350-386.
31. Keselman, H. J. & Keselman, J. C. (1988). Comparing repeated measures means in factorial designs. Psychophysiology, 25, 612-618.
32. Keselman, H. J. & Keselman, J. C. (1993). Analysis of repeated measurements. In L. K. Edwards (Ed.), Applied analysis of variance in behavioral science (pp. 105-145). New York: Marcel Dekker.
33. Keselman, H. J., Keselman, J. C., & Lix, L. M. (1995). The analysis of repeated measurements: Univariate tests, multivariate tests, or both? British Journal of Mathematical and Statistical Psychology, 48, 319-338.
34. Keselman, H. J., Keselman, J. C., & Shaffer, J. P. (1991). Multiple pairwise comparisons of repeated measures means under violations of multisample sphericity. Psychological Bulletin, 110, 162-170.
35. Keselman, H. J., Kowalchuk, R. K., Algina, J., Lix, L. M., & Wilcox, R. R. (2000). Testing treatment effects in repeated measures designs: Trimmed means and bootstrapping. British Journal of Mathematical and Statistical Psychology, 53, 175-191.
36. Keselman, H. J., Kowalchuk, R. K., & Boik, R. J. (2000). An examination of the robustness of the Empirical Bayes and other approaches for testing main and interaction effects in repeated measures designs. British Journal of Mathematical and Statistical Psychology, 53, 51-67.
37. Keselman, H. J., Wilcox, R. R., & Lix, L. M. (in press). A generally robust approach to hypothesis testing in independent and correlated groups designs. Psychophysiology.
38. Keselman, J. C. & Keselman, H. J. (1990). Analysing unbalanced repeated measures designs. British Journal of Mathematical and Statistical Psychology, 43, 265-282.
39. Keselman, J. C., Lix, L. M., & Keselman, H. J. (1996). The analysis of repeated measuremenmts: A quantitative research synthesis. British Journal of Mathematical and Statistical Psychology, 49, 275-298.
40. Kirk, R. E. (1995). Experimental design: Procedures for the behavioral sciences (3rd Ed). Belmont, CA: Brooks/Cole.
41. Kowalchuk, R. K. & Keselman, H. J. (2001, April). The analysis of repeated measurements with mixed-model Kenward-Roger's adjusted F-tests, Paper presented at the annual meeting of The American Educational Research Association, Seattle.
42. Kowalchuk, R. K. & Keselman, H. J. (in press). Mixed-model pairwise multiple comparisons of repeated measures means. Psychological Methods.
43. Lecoutre, B. (1991). A correction for the ∈̃ approximate test in repeated measures designs with two or more independent groups. Journal of Educational Statistics, 16, 371-372.
44. Littell, R. C., Milliken, G. A., Stroup, W. W., & Wolfinger, R. D. (1996). SAS system for mixed models. Cary, NC: SAS Institute.
45. Little, R. J. A. (1995). Modeling the drop-out mechanism in repeated-measures studies. Journal of the American Statistical Association, 90, 1112-1121.
46. Little, R. J. A. & Rubin, D. B. (1987). Statistical analysis with missing data. New York: Wiley.
47. 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.
48. Lix, L. M., & Keselman, H. J. (1996). Interaction contrasts in repeated measures designs. British Journal of Mathematical and Statistical Psychology, 49, 147-162.
49. Maxwell, S. E., & Delaney, H. D. (2000). Designing experiments and analyzing data: A model comparison perspective. Mahwah, NJ: Erlbaum.
50. McCall, R. B. & Appelbaum, M. I. (1973). Bias in the analysis of repeated-measures designs: Some alternative approaches. Child Development, 44, 401-415.
51. Mendoza, J. L. (1980). A significance test for multisample sphericity. Psychometrika, 45, 495-498.
52. Miller, J. (1988). A warning about median reaction time. Journal of Experimental Psychology: Human Perception and Performance, 14, 539-543.
53. Norušis, M. J. (1993). SPSS for Windows, Advanced Statistics, Release 6.0. Chicago, IL: SPSS, Inc.
54. Olson, C. L. (1974). Comparative robustness of six tests in multivariate analysis of variance. Journal of the American Statistical Association, 69, 894-908.
55. Overall, J. E., Ahn, C., Shivakumar, C., & Kalburgi, Y. (1999). Problematic formulations of SAS Proc Mixed models for repeated measurements. Journal of Biopharmaceutical Statistics, 9, 189-216.
56. Overall, J. E. & Doyle, S. R. (1994). Estimating sample sizes for repeated measurement designs. Controlled Clinical Trials, 15, 100-123.
57. Quintana, S. M. & Maxwell, S. E. (1994). A Monte Carlo comparison of seven ∈-adjustment procedures in repeated measures designs with small sample sizes. Journal of Educational Statistics, 19, 57-71.
58. Rogan, J. C., Keselman, H. J., & Mendoza, J. L. (1979). Analysis of repeated measurements. British Journal of Mathematical and Statistical Psychology, 32, 269-286.
59. Rouanet, H. & Lepine, D. (1970). Comparison between treatments in a repeated measures design: ANOVA and multivariate methods. British Journal of Mathematical and Statistical Psychology, 23, 147-163.
60. Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581-592.
61. SAS Institute. (1999a). SAS/IML: User's Guide, Version 8. Cary, NC: Author.
62. SAS Institute. (1999b). SAS/STAT User's Guide, Version 8, Volumes 1-3. Cary, NC: Author.
63. Schafer, J. L. (1997). Analysis of incomplete multivariate data. New York: Chapman and Hall.
64. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
65. Tukey, J. W. (1960). A survey of sampling from contaminated normal distributions. In I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, & H. B. Mann (Eds.), Contributions to probability and statistics (pp. 448-485). Stanford, CA: Stanford University Press.
66. Wang-Clow, F., Lange, M., Laird, N. M., & Ware, J. H. (1995). A simulation study of estimators for rates of change in longitudinal studies with attrition. Statistics in Medicine, 14, 283-297.
67. Welch, B. L. (1947). The generalization of students' problems when several different population variances are involved. Biometrika, 34, 28-35.
68. Welch, B. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330-336.
69. Wilcox, R. R. (1987). New designs in analysis of variance. Annual Review of Psychology, 38, 29-60.
70. Wolfinger, R. D. (1996). Heterogeneous variance-covariance structures for repeated measures. Journal of Agricultural, Biological, and Environmental Statistics, 1, 205-230.
71. Wu, M. C. & Bailey, K. R. (1989). Estimation and comparison of changes in the presence of informative right censoring: Conditional linear model. Biometrics, 45, 939-955.
72. Wright, S. P. & Wolfinger, R. D. (1996, October). Repeated measures analysis using mixed models: Some simulation results. Paper presented at the Conference on Modelling Longitudinal and Spatially Correlated Data: Methods, Applications, and Future Directions, Nantucket, MA.
73. 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.