Alternative procedures for testing regression slope homogeneity when group error variances are unequal

Psychological Methods

Volumn 1, Issue 3, 1996, Pages 261-277

  DeShon, Richard P ^a   Alexander, Ralph A ^b  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b UNIVERSITY OF AKRON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000239286     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/1082-989X.1.3.261     Document Type: Article

References (48)

1. Adichie, J. N. (1974). Rank score comparison of several regression parameters. The Annals of Statistics, 2, 396-402.
2. Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, CA: Sage.
3. Alexander, R. A., & DeShon, R. P. (1994). The effect of error variance heterogeneity on the power of tests for regression slope differences. Psychological Bulletin, 115, 308-314.
4. Alexander, R. A., & Govern, D. M. (1994). A new and simpler approximation for ANOVA under variance heterogeneity. Journal of Educational Statistics, 19, 91-101.
5. Aspin, A. A. (1948). An examination and further development of a formula arising in the problem of comparing two mean values. Biometrika, 35, 88-96.
6. Atiquallah, M. (1964). The robustness of the covariance analysis of a one-way classification. Biometrika, 51, 365-372.
7. Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Society, A160, 268-282.
8. Box, G. E. P., & Watson, G. S. (1962). Robustness for non-normality of regression tests. Biometrika, 49, 93-106.
9. Bradley, J. C. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152.
10. 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.
11. Cochran, W. G. (1957). Analysis of covariance: Its nature and uses. Biometrics, 13, 261-281.
12. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
13. Conover, W. J., & Iman, R. L. (1982). Analysis of covariance using the rank transformation. Biometrics, 38, 715-724.
14. DeShon, R. P., & Alexander, R. A. (1994). A generalization of James' second-order approximation to the test for regression slope equality. Educational and Psychological Measurement, 54, 328-335.
15. Dijkstra, J. B., & Werter, P. S. (1981). Testing the equality of several means when the population variances are unequal. Communications in Statistics. Part B: Simulation and Computation, 10, 557-569.
16. Dretzke, B. J., Levin, J. R., & Serlin, R. C. (1982). Testing for regression homogeneity under variance heterogeneity. Psychological Bulletin, 91, 376-383.
17. Games, P. A., Winkler, H. B., & Probert, D. A. (1972). Robust tests for homogeneity of variance. Educational and Psychological Measurement, 32, 887-909.
18. Gartside, P. S. (1972). A study of methods for comparing several variances. Journal of the American Statistical Association, 67, 342-346.
19. Hartley, H. O., & Harris, D. L. (1963). Monte Carlo computations in normal correlation problems. Journal of the Association for Computing Machinery, 10, 302-306.
20. Hill, G. W. (1970). Algorithm 395: Student's-t distribution. Communications of the ACM, 13, 617-619.
21. Hollander, M. (1970). A distribution-free test for parallelism. Journal of the American Statistical Association, 65, 387-394.
22. Hsu, L. M. (1993). Using Cohen's tables to determine the maximum power attainable in two-sample tests when one sample is limited in size. Journal of Applied Psychology, 78, 303-305.
23. Huitema, B. E. (1980). The analysis of covariance and alternatives. New York: Wiley.
24. Humphreys, L. G. (1986). An analysis and evaluation of test and item bias in the prediction context. Journal of Applied Psychology, 71, 327-333.
25. James, G. S. (1951). The comparison of several groups of observations when the ratios of population variances is unknown. Biometrika, 38, 324-329.
26. Johnson, M. E. (1987). Multivariate statistical simulation. New York: Wiley.
27. Johnson, M. E., Ramberg, J. S., & Wang, C. (1982). The Johnson translation system in Monte Carlo studies. Communications in Statistics. Part B: Simulation and Computation. 11, 521-525.
28. Johnson, N. L. (1949). Bivariate distributions based on simple translation systems. Biometrika, 36, 297-304.
29. Johnson, N. L., & Kotz, S. (1972). Continuous multivariate distributions. New York: Wiley.
30. Kendall, M., & Stuart, A. (1979). The advanced theory of statistics (Vol. II, 4th ed.) London: Charles Griffin.
31. Layard, M. W. J. (1973). Robust large-sample tests for homogeneity of variances. Journal of the American Statistical Association, 68, 195-198.
32. Lo, L. C., Simkin, M. G., & Worthley, R. G. (1978). A small-sample comparison of rank score tests for parallelism of several regression lines. Journal of the American Statistical Association, 73, 666-669.
33. Maxwell, S. E., & Delaney, H. D. (1993). Bivariate median splits and spurious statistical significance. Psychological Bulletin, 113, 181-190.
34. McClelland, G. H., & Judd, C. M. (1993). Statistical difficulties of detecting interactions and moderator effects. Psychological Bulletin, 114, 376-390.
35. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156-166.
36. Noether, G. E. (1981). Comment on "Rank transformations as a bridge between parametric and nonparametric statistics." The American Statistician, 35, 129-130.
37. 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, 129-149.
38. Olejnik, S. F., & Algina, J. (1987). An analysis of statistical power for parametric ANCOVA and rank transform ANCOVA. Communications in Statistics. Part A: Theory and Methods, 16, 1923-1949.
39. m test under heteroscedasticity and non-normality. British Journal of Mathematical and Statistical Psychology, 45, 255-263.
40. Potthoff, R. F. (1974). A non-parametric test of whether two simple regression lines are parallel. The Annals of Statistics, 2, 295-310.
41. Sen, P. K. (1969). On a class of rank order tests for the parallelism of several regression lines. The Annals of Mathematical Statistics, 40, 1668-1683.
42. Smit, C. F. (1979). An empirical comparison of several test for parallelism of regression lines. Communications in Statistics. Part B: Simulation and Computation, 8, 61-74.
43. Tabatabai, M. A., & Tan, W. Y. (1985). Some comparative studies on testing parallelism of several straight lines under heteroscedastic variances. Communications in Statistics. Part B: Simulation and Computation, 14, 837-844.
44. Welch, B. L. (1938). The significance of the difference between two means when the population variances are unequal. Biometrika, 29, 350-362.
45. Wightman, L. F., & Muller, D. G. (1990). An analysis of differential validity and differential prediction for Black, Mexican American, Hispanic, and White law school students (Report No. SAC-90-03). Newtown, PA: Law School Admission Services, Inc.
46. Wilcox, R. R. (1987). New designs in analysis of variance. Annual Review of Psychology, 38, 29-60.
47. Wilcox, R. R. (1988). A new alternative to the ANOVA F and new results on James' second-order method. British Journal of Mathematical and Statistical Psychology, 41, 109-117.
48. Wilcox, R. R. (1989). Adjusting for unequal variances when comparing means in one-way and two-way fixed effects ANOVA models. Journal of Educational Statistics, 14, 269-278.