A Monte Carlo study was conducted using SAS-IML to compare the multivariate analysis of variance (MANOVA) simultaneous test procedures (STPs) of 0, 'T, A, and V in terms of power and Type I error under various conditions including violations of MANOVA assumptions. The Type I error rates of moderately restricted contrasts in STPs were robust to violations of MANOVA assumptions such that the actual alpha remained below the nominal alpha. However, the power of the STPs was unacceptably low in moderately restricted contrasts under most conditions. For partially restricted contrasts, the power of the STPs was adequate for θ when the noncentrality structure was concentrated. When the noncentrality structure was diffuse, again θ had the highest power but decreased to a minimal level as the number of groups or variables increased.
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References
1.
Anderson, T. W. (1984).An introduction to multivariate statistical analysis (2nd ed.). New York: John Wiley.
2.
Andrews, D. F. , Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H., & Tukey, J. W. (1972). Robust estimates of location: Survey and advances. Princeton, NJ: Princeton University Press.
3.
Barcikowski, R. S. , & Elliott, R. (1991, October). Exploratory multivariate analysis of variance: Contrasts and variables. Paper presented at the annual meeting of the Mid-Western Educational Research Association, Chicago. (ERIC Document Reproduction Service No. ED 339 716)
4.
Barcikowski, R. S. , & Robey, R. (1992). Type I error and the number of iterations in Monte Carlo studies of robustness. British Journal of Mathematical and Statistical Psychology, 45, 283-288.
5.
Bartlett, M. S. (1939). A note on tests of significance in multivariate analysis. Proceedings of the Cambridge Philosophical Society, 35, 180-185.
6.
Belli, G. M. (1989, March). Parameters in MANOVA robustness studies: Comparability to empirical research. Paper presented at the annual meeting of the American Educational Research Association, San Francisco. (ERIC Document Reproduction Service No. ED 308 240)
7.
Bird, K. D. , & Hadzi-Pavlovic, D. (1983). Simultaneous test procedures and the choice of a test statistic in MANOVA. Psychological Bulletin, 93, 167-178.
8.
Bock, R. D. (1975). Multivariate statistical methods in behavioral research. New York: McGraw-Hill.
9.
Bray, J. H. , & Maxwell, S. E. (1985). Multivariate analysis of variance. Beverly Hills, CA: Sage.
10.
Camasso, M. J. , & Geismar, L. L. (1992). A multivariate approach to construct reliability and validity assessment: The case of family functioning. Social Work Research & Abstracts, 28, 16-26.
11.
Catell, R. B. (1973). Personality and mood by questionnaire. San Francisco: Jossey-Bass.
12.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum.
13.
Cronbach, L. J. , Gleser, G. C., Nanda, H., & Rajaratnam, N. (1972). The dependability of behavioral measurements. New York: John Wiley.
14.
Elliott, R. S. (1993). Contrast selection in post hoc multivariate analysis. Dissertation Abstracts International, 54, 1608A. (University Microfilms No. 95-36, 589)
15.
Emmons, N. J. , Stallings, W. M., & Layne, B. H. (1990, April). Statistical methods used in American Educational Research Journal, Journal of Educational Psychology, and Sociology of Education from 1972 through 1987. Paper presented at the annual meeting of the American Educational Research Association, Boston. (ERIC Document Reproduction Service No. ED 319 797)
16.
Fish, L. (1988). Why multivariate methods are usually vital. Measurement and Evaluation in Counseling and Development, 21, 130-137.
17.
Gabriel, K. R. (1968). Simultaneous test procedures in multivariate analysis of variance. Biometrika, 55, 489-504.
18.
Grimm, L. G. , & Yarnold, P. R. (Eds.). (1995). Reading and understanding multivariate statistics. Washington, DC: American Psychological Association.
19.
Harris, R. J. (1985). A primer of multivariate statistics (2nd ed.). Orlando, FL: Academic Press.
20.
Hotelling, H. (1931). The generalization of student's ratio. Annals of Mathematical Statistics, 2, 360-378.
21.
Huberty, C. J. , & Morris, J. D. (1989). Multivariate analysis versus multiple univariate analyses. Psychological Bulletin, 105, 302-308.
22.
Jöreskog, K. G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36, 109-133.
23.
Keppel, G. (1982). Design and analysis: A researcher's handbook (2nd ed.). Englewood Cliff, NJ: Prentice Hall.
24.
Korin, B. P. (1969). On testing the equality of k covariance matrices. Biometrika, 56, 216-218.
25.
(Corrections in Biometrika, 30, 467-469)
26.
Maxwell, S. E. (1992). Recent developments in MANOVA applications. In B. Thompson (Ed.), Advances in social science methodology (Vol. 2, pp. 137-168). Greenwich, CT: JAI.
27.
Olson, C. L. (1974). Comparative robustness of six tests in multivariate analysis of variance. Journal of the American Statistical Association, 69, 894-908.
28.
Olson, C. L. (1976). On choosing a test statistic in multivariate analysis of variance. Psychological Bulletin, 83, 579-586.
29.
Pillai, K.C.S. (1955). Some new test criteria in multivariate analysis. Annals of Mathematical Statistics, 26, 117-121.
30.
Roy, S. N. (1945). The individual sampling distribution of the maximum, the minimum, and any intermediate of the p-statistics on the null hypothesis. Sankhya, 7, 133-158.
31.
Roy, S. N. , & Bose, R. C. (1953). Simultaneous confidence interval estimation. Annals of Mathematical Statistics, 24, 513-536.
32.
SAS Institute . (1990). SAS/IML user's guide (Version 6.04). Cary, NC: Author.
33.
Schatzoff, M. (1966). Sensitivity comparisons among tests of the general linear hypothesis. Journal of the American Statistical Association, 61, 415-435.
34.
Scheffe, H. (1959). The analysis of variance. New York: John Wiley.
35.
Tatsuoka, M. M. (1988). Multivariate analysis (2nd ed.). New York: Macmillan.
36.
Thompson, B. (1986, November). Two reasons why multivariate methods are usually vital. Paper presented at the annual meeting of the Mid-South Educational Research Association, Memphis, TN. (ERIC Document Reproduction Service No. ED 367 687)
37.
Thompson, B. (1994, February). Why multivariate methods are usually vital in research: Some basic concepts. Paper presented as a featured speaker at the biennial meeting of the South-western Society for Research in Human Development, Austin, TX. (ERIC Document Reproduction Service No. ED 367 687)
38.
Wilks, S. S. (1932). Certain generalizations in the analysis of variance. Biometrika, 24, 471-494.
