Weighted simplex procedures for determining boundary points and constants for the univariate and multivariate power methods

Journal of Educational and Behavioral Statistics

Volumn 25, Issue 4, 2000, Pages 417-436

  Headrick, Todd C ^a   Sawilowsky, Shlomo S ^b  

^a SOUTHERN ILLINOIS UNIVERSITY   (United States)

^b WAYNE STATE UNIVERSITY   (United States)

Author keywords

Kurtosis; Nonnormal distributions; Power method; Skew; Weighted simplex procedure

Indexed keywords

EID: 0034555580     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/10769986025004417     Document Type: Article

References (34)

1. Arrow, K. J., & Enthoven, A. C. (1961). Quasi-Concave programming. Econometrica, 29(4), 779-800.
2. Blair, R. C. (1981). A reaction to "Consequences of failure to meet assumptions underlying the fixed effects analysis of variance and covariance." Review of Educational Research, 51(4), 499-507.
3. Blair, R. C., & Higgins, J. J. (1980). A comparison of the power of Wilcoxon's rank-sum statistic to that of Student's t statistic under various non-normal distributions. Journal of Educational Statistics. 1980, 5(4), 309-335.
4. Boneau, C. A. (1962). A comparison of the power of the U and t tests. Psychological Review, 69(3), 246-256.
5. Bradley, D. R., & Fleisher, C. L. (1994). Generating multivariate data from nonnormal distributions: Mihal and Barrett revisited. Behavior Research Methods, Instruments, & Computers, 26(2), 156-166.
6. Bradley, J. V. (1968). Distribution free statistical tests. Engelwood Cliffs, NJ: Prentice-Hall, 1968.
7. Bradley, J. V. (1982). The insidious L-shaped distribution. Bulletin of the Psychonomic Society, 20(2), 85-88.
8. Chiang, A. C. (1984). Fundamental Methods of Mathematical Economics (3rd ed.). New York: McGraw-Hill.
9. Devroye, L. (1986). Non-uniform random variate generation. New York: Springer-Verlag.
10. Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532.
11. Glass, G. V., Peckham, P. D., & Sanders, J. R. (1972). Consequences of failure to meet assumptions underlying the fixed effects analysis of variance and covariance. Review of Educational Research, 42, 237-288.
12. Habib, A. R., & Harwell, M. R. (1989). An empirical study of the type I error rate and power of some selected normal theory and nonparametric tests of the independence of two sets of variables. Communications in Statistics: Computation and Simulation, 18(2), 793-826.
13. Harwell, M. R., & Serlin, R. C. (1988). An experimental study of a proposed test of nonparametric analysis of covariance. Psychological Bulletin, 104(2), 268-281.
14. Harwell, M. R., & Serlin, R. C. (1989). A nonparametric test statistic for the general linear model. Journal of Educational Statistics, 14(4), 351-371.
15. Harwell, M. R., & Serlin, R. C. (1997). An empirical study of five multivariate tests for the single-factor repeated measures model. Communications in Statistics: Compulation and Simulation, 26(2), 605-618.
16. Headrick, T. C. (1997). Type I error and power of the rank transform analysis of covariance (ANCOVA) in a 3 × 4 factorial layout. Unpublished doctoral dissertation, Wayne State University, Detroit, MI.
17. Headrick, T. C., & Sawilowsky, S. S. (1999, January). The best test for interaction in factorial ANOVA and ANCOVA. The University of Florida Statistics Symposium on Selected Topics in Nonparametric Methods, Gainesville, FL.
18. Headrick, T. C., & Sawilowsky, S. S. (1999). Simulating correlated multivariate nonnormal distributions: Extending the Fleishman power method. Psychometrika, 64, 25-35.
19. Hodges, J. L., & Lehmann, E. L. (1956). The efficiency of some nonparametric competitors of the t-test. Annals of Mathematical Statistics, 27, 324-335.
20. Kendall, M., & Stuart, A. (1977). The advanced theory of statistics (4th ed.). New York: Macmillan.
21. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156-166.
22. Olejnik, S. F., & Algina, J. (1984). Parametric ANCOVA and the rank transform ANCOVA when the data are conditionally non-normal and heteroscedastic. Journal of Educational Statistics, 9(2), 129-150.
23. Olejnik, S. F., & Algina, J. (1987). An analysis of statistical power for parametric ANCOVA and rank transform ANCOVA. Communications in Statistics: Theory and Method, 16(7), 1923-1949.
24. Pearson, E. S., & Please, N. W. (1975). Relation between the shape of population distribution and the robustness of four simple test statistics. Biometrika, 63, 223-241.
25. Price, W. L. (1979). A weighted simplex procedure for the solution of simultaneous nonlinear equations, Journal of the Institute of Mathematics and its Applications, 24, 1-8.
26. Price, W. L., & Dowson, M. (1979). Algorithm 107: A weighted simplex procedure for the solution of simultaneous nonlinear equations. The Computer Journal, 22, 222-223.
27. Ramberg, J. S., & Schmeiser, B.W. (1974). An approximate method for generating asymmetric random variables. Communications of the ACM, 17, 78-82.
28. Rhee, K. (1993). A FORTRAN solution for evaluating the coefficients of the power method for nonnormal transformation. Educational and Psychological Measurement, 53, 107-109.
29. Sawilowsky, S. S., & Blair, R. C. (1992). A more realistic look at the robustness and type I error properties of the t-test to departures from population normality. Psychological Bulletin, 111(2), 352-360.
30. Scheffe, H. (1959). The analysis of variance. New York: John Wiley & Sons.
31. Seamen, S., Algina, J., & Olejnik, S. F. (1985). Type I error probabilities and power of the rank and parametric ANCOVA procedures. Journal of Educational Statistics. 10(4), 345-367.
32. Tadikamalla, P. R. (1980). On simulating nonnormal distributions. Psychometrika, 45, 273-279.
33. Tukey, J. W. (1960). The practical relationship between the common transformation of percentages of counts and of amounts (Technical Report 36). Princeton, NJ: Princeton University, Statistical Techniques Research Group.
34. Visual Numerics, Inc. (1994). IMSL Math/Library: FORTRAN subroutines for mathematical applications, Volume II. Houston, TX: Author.