Comparing the regression slopes of independent groups

British Journal of Mathematical and Statistical Psychology

Volumn 63, Issue 2, 2010, Pages 319-340

  Ng, Marie ^a   Wilcox, Rand R ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYSIS OF VARIANCE; ARTICLE; COMPUTER PROGRAM; COMPUTER SIMULATION; HUMAN; INFORMATION PROCESSING; MATHEMATICAL COMPUTING; PSYCHOLOGY; PSYCHOMETRY; REGRESSION ANALYSIS; REPRODUCIBILITY; SOCIOLOGY; STATISTICAL MODEL; STATISTICS;

ANALYSIS OF VARIANCE; COMPUTER SIMULATION; DATA COLLECTION; HUMANS; MATHEMATICAL COMPUTING; MODELS, STATISTICAL; PSYCHOLOGY; PSYCHOMETRICS; REGRESSION ANALYSIS; REPRODUCIBILITY OF RESULTS; SOCIAL SCIENCES; SOFTWARE;

EID: 77953637651     PISSN: 00071102     EISSN: None     Source Type: Journal    
DOI: 10.1348/000711009X456845     Document Type: Article

References (37)

1. Aguinis, H., & Pierce, C. A. (1998). Heterogeneity of error variance and the assessment of moderating effects of categorical variable: A conceptual review. Organizational Research Methods, 1, 296-314.
2. Alexander, R. A., & DeShon, R. P. (1994). Effect of error variance heterogeneity on the power of tests for regression slope differences. Psychological Bulletin, 2, 308-314.
3. Alexander, R. A., & Govern, D. M. (1994). A new and simpler approximation for ANOVA under variance heterogeneity. Journal of Educational Statistics, 19, 91-101.
4. 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.
5. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. London: Erlbaum.
6. Cribari-Neto, F. (2004). Asymptotic inference under heteroscedasticity of unknown form. Computational Statistics & Data Analysis, 45, 215-233.
7. Cribari-Neto, F., Souza, T. C., & Vasconcellos, A. L. P. (2007). Inference under heteroskedasticity and leveraged data. Communication in Statistics - Theory and Methods, 36, 1877-1888.
8. Davidson, R., & Flachaire, E. (2000). The wild bootstrap, tamed at last. Econometric Society World Congress 2000 Contributed Papers 1413.
9. Davidson, R., & MacKinnon, J. G. (1993). Estimation and inference in econometrics. New York: Oxford University Press.
10. Dawson, J. F., & Richter, A. W. (2006). Probing three-way interactions in moderated multiple regression: Development and application of a slope difference test. Journal of Applied Psychology, 91, 917-926.
11. Dietz, E. J. (1987). A comparison of robust estimators in simple linear regression. Communications in Statistics - Simulation and Computation, 16, 1209-1227.
12. Dietz, E. J. (1989). Teaching regression in a nonparametric statistic course. American Statistician, 43, 35-40.
13. Godfrey, L. G. (2006). Tests for regression models with heteroscedasticity of unknown form. Computational Statistics & Data Analysis, 50, 2715-2733.
14. Hall, P. (1986). On the number of bootstrap simulations required to construct a confidence interval. Annals of Statistics, 14, 1453-1462.
15. Hall, P. (1992). The bootstrap and Edgeworth expansion. New York: Springer.
16. Hall, P., & Wilson, S. R. (1991). Two guidelines for bootstrap hypothesis testing. Biometrics, 47, 757-762.
17. Hayes, A. F., & Cai, L. (2007). Using heteroscedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation. Behavior Research Methods, 39, 709-722.
18. Hinkley, D. V. (1977). Jackknifing in unbalanced situations. Technometrics, 19, 285-292.
19. Huber, P. J. (1967). The behavior of maximum likelihood estimation under nonstandard conditions. In L. M. Le Cam & J. Neyman (Eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press.
20. Huber, P. J. (1973). Robust regression: Asymptotics, conjectures, and Monte Carlo. Annuals of Statistics, 1, 799-821.
21. James, G. S. (1951). The comparison of several groups of observations when the ratios of population variances are unknown. Biometrika, 38, 324-329.
22. Long, J. S., & Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. American Statistician, 54, 217-224.
23. MacKinnon, J. G., & White, H. (1985). Some heteroscedasticity consistent covariance matrix estimators with improved finite sample properties. Journal of Econometrics, 29, 305-325.
24. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2006). Introduction to linear regression analysis. Hoboken, NJ: Wiley.
25. Morris, J. H., Sherman, J. D., & Mansfield, E. R. (1986). Failures to detect moderating effects with ordinary least squares-moderated multiple regression: Some reasons and a remedy. Psychological Bulletin, 99, 282-288.
26. Ng, M. (2006). A comparative study of six heteroscedastic robust approaches for testing single regression coefficient. Unpublished technical report, Department of Psychology, University of Southern California.
27. Ng, M., & Wilcox, R. R. (2008). Testing the slope of a regression model with a dummy variable. Unpublished technical report, Department of Psychology, University of Southern California.
28. Ng, M., & Wilcox, R. R. (2008). Level robust methods based on the least squares regression estimator. Journal of Modern Applied Statistical Methods.
29. Overton, R. C. (2001). Moderated multiple regression for interaction involving categorical variables: A statistical control for heterogeneous variance across two groups. Psychological Methods, 6, 218-233.
30. Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall's tau. Journal of the American Statistical Association, 63, 1379-1389.
31. Theil, H. (1950). A rank invariant method for linear and polynomial regression analysis. Indagationes Mathematicae, 12, 85-91.
32. Welch, B. L. (1938). The significance of the difference between two means when the population variances are unequal. Biometrika, 29, 350-362.
33. White, H. (1980). A heteroskedastic-consistent covariance matrix estimator and a direct test of heteroscedasticity. Econometrica, 48, 817-838.
34. Wilcox, R. R. (1996). Confidence intervals for the slope of a regression line when the error term has nonconstant variance. Computational Statistics & Data Analysis, 22, 89-98.
35. Wilcox, R. R. (1998). A note on the Theil-Sen regression estimator when the regressor is random and the error term is heteroscedastic. Biometrical Journal, 40, 261-268.
36. Wilcox, R. R. (2003). Power: Basics, practical problems, and possible solutions. In I. B. Weiner, J. A. Schinka, &W. F. Velicer (Eds.), Handbook of psychology - Researchmethods in psychology (Vol. 2, pp. 65-86). Hoboken, NJ: Wiley.
37. Wilcox, R. R. (2005). Introduction to robust estimation and hypothesis testing. San Diego, CA: Academic Press.