Approximate power for repeated-measures anova lacking sphericity

Journal of the American Statistical Association

Volumn 84, Issue 406, 1989, Pages 549-555

  Muller, Keith E ^a   Barton, Curtis N ^b  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b CENTER FOR DRUG EVALUATION AND RESEARCH   (United States)

Author keywords

Equicorrelation; Error rates; Noncentral chi square; Noncentral pseudo Wishart; Noncentral Wishart; Sample size

Indexed keywords

EID: 0041986427     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1989.10478802     Document Type: Article

References (24)

1. Anderson, T. W. (1984), An Introduction to Multivariate Statistical Analysis (2nd ed.), New York: John Wiley.
2. Box, G. E. P. (1954a), “Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I: Effects of Inequality of Variance in the One-Way Classification,” The Annals of Mathematical Statistics, 25, 290–302.
3. —— (1954b), “Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, II: Effects of Inequality of Variance and of Correlation Between Errors in the Two-Way Classification,” The Annals of Mathematical Statistics, 25, 484–498.
4. Collier, R. O., Jr., Baker, F. B., Mandeville, G. K., and 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.
5. Davidson, M. L. (1972), “Univariate Versus Multivariate Tests in Repeated Measures Experiments,” Psychological Bulletin, 77, 446–452.
6. 2Random Variables” (Algorithm AS 155), Applied Statistics, 29, 323–333.
7. Fujikoshi, Y. (1978), “Asymptotic Expansions for the Distributions of Some Functions of the Latent Roots of Matrices in Three Situations,” Journal of Multivariate Analysis, 8, 63–72.
8. Geisser, S., and Greenhouse, S. W. (1958), “An Extension of Box’s Results on the Use of the F Distribution in Multivariate Analysis,” The Annals of Mathematical Statistics, 29, 885–891.
9. Graybill, F. A. (1976), Theory and Applications of the Linear Model, North Scituate, MA: Duxbury Press.
10. Greenhouse, S. W., and Geisser, S. (1959), “On Methods in the Analysis of Profile Data,” Psychometrika, 24, 95–112.
11. Huynh, H., and Feldt, L. S. (1970), “Conditions Under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distribution,” Journal of the American Statistical Association, 65, 1582–1589.
12. Johnson, N. L., and Kotz, S. (1970), Continuous Univariate Distributions—2, Boston: Houghton Mifflin.
13. Keselman, H. J., Rogan, J. C., Mendoza, J. L., and Breen, J. L. (1980), “Testing the Validity Conditions of Repeated Measures F Tests,” Psychological Bulletin, 87, 479–481.
14. Mathai, A. M. (1980), “Moments of the Trace of a Noncentral Wishart Matrix,” Communications in Statistics, Part A—Theory and Methods, 9, 795–801.
15. Maxwell, S. E., and Arvey, R. D. (1982), “Small Sample Profile Analysis With Many Variables,” Psychological Bulletin, 92, 778–785.
16. Mendoza, J. L., Toothaker, L. E., and Crain, B. R. (1976), “Necessary and Sufficient Conditions for F Ratios in the L × J × K Factorial Design With Two Repeated Factors,” Journal of the American Statistical Association, 71, 992–993.
17. Mendoza, J. L., Toothaker, L. E., and Nicewander, W. A. (1974), “A Monte Carlo Comparison of the Univariate and Multivariate Methods for the Groups by Trials Repeated-Measures Design,” Multivariate Behavioral Research, 9, 165–177.
18. Morrison, D. F. (1976), Multivariate Statistical Methods (2nd ed.), New York: McGraw-Hill.
19. Muller, K. E., and Peterson, B. L. (1984), “Practical Methods for Computing Power in Testing the Multivariate General Linear Hypothesis,” Computational Statistics and Data Analysis, 2, 143–158.
20. Satterthwaite, F. E. (1941), “Synthesis of Variance,” Psychometrika, 6, 309–316.
21. Searle, S. R. (1971), Linear Models, New York: John Wiley.
22. Serfling, R. J. (1980), Approximate Theorems of Mathematical Statistics, New York: John Wiley.
23. Timm, N. H. (1975), Multivariate Analysis, Monterey, CA: Brooks/Cole.
24. Wang, C. M. (1983), “On the Analysis of Multivariate Repeated Measures Designs,” Communications in Statistics—Theory and Methods, 12, 1647–1659.