Comparing treatment and control groups on multiple outcomes: Robust procedures for testing a directional alternative hypothesis

Educational and Psychological Measurement

Volumn 69, Issue 2, 2009, Pages 198-215

  Lix, Lisa M ^a   Deering, Kathleen N ^b   Fouladi, Rachel T ^c   Manivong, Phongsack ^d  

^a UNIVERSITY OF SASKATCHEWAN   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c SIMON FRASER UNIVERSITY   (Canada)

^d UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Likelihood ratio test; Multivariate; Nonnormality; Positive orthant hypothesis; T test; Variance heterogeneity

Indexed keywords

EID: 62849102042     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164408322027     Document Type: Article

References (47)

1. Andrews, D.W.K. (2000). Inconsistency of the bootstrap when a parameter is on the boundary of the parameter space. Econometrica, 68, 399-405.
2. Berkovits, I., Hancock, G.R., & Nevitt, J. (2000). Bootstrap resampling approaches for repeated measures designs: Relative robustness to sphericity and normality violations. Educational and Psychological Measurement, 60, 877-892.
3. Blair, R.C., & Sawilowsky, S. (1993). Comparison of two tests useful in situations where treatment is expected to increase variability relative to controls. Statistics in Medicine, 12, 2233-2243.
4. Bradley, J.V. (1978). Robustness ? British Journal of Mathematical and Statistical Psychology, 31, 144-152.
5. Brownie, C., Boos, D.D., & Hughes-Oliver, J. (1990). Modifying the t and ANOVA F tests when treatment is expected to increase variability relative to controls. Biometrics, 46, 259-266.
6. Carpenter, J., & Bithell, J. (2000). Bootstrap confidence intervals: When, which, what? A practical guide for medical statisticians. Statistics in Medicine, 19, 1141-1164.
7. Christensen, W.F., & Rencher, A.C. (1997). A comparison of Type I error rates and power levels for seven solutions to the multivariate Behrens-Fisher problem. Communications in Statistics: Simulation and Computation, 26, 1251-1273.
8. Efron, B., & Tibshirani, R.J. (1993). An introduction to the bootstrap. New York: Chapman & Hall.
9. Field, C., & Genton, M.G. (2006). The multivariate g-and-h distribution. Technometrics, 48, 104-111.
10. Fouladi, R.T., & Yockey, R.D. (2002). Type I error control of two-group multivariate tests on means under conditions of heterogeneous correlation structure and varied multivariate distributions. Communications in Statistics: Simulation and Computation, 31, 375-400.
11. Harwell, M.R., Rubinstein, E.N., Hayes, W.S., & Olds, C.C. (1992). Summarizing Monte Carlo results in methodological research: The one- and two-factor fixed effects ANOVA cases. Journal of Educational and Behavioral Statistics, 17, 315-339.
12. Holland, J.M., Neimeyer, R.A., Currier, J.M., & Berman, J.S. (2007). The efficacy of personal construct therapy: A comprehensive review. Journal of Clinical Psychology, 63, 93-107.
13. Horton, N.J., & Lipsitz, S.R. (2001). Multiple imputation in practice: Comparison of software packages for regression models with missing variables. The American Statistician, 55, 244-254.
14. Hotelling, H. (1931). The generalization of Student's ratio. Annals of Mathematical Statistics, 2, 360-378.
15. Huang, P., Tilley, B.C., Woolson, R.F., & Lipsitz, S. (2005). Adjusting O'Brien's test to control Type I error for the generalized nonparametric Behrens-Fisher problem. Biometrics, 61, 532-539.
16. Huber, P.J. (1981). Robust statistics. New York: John Wiley.
17. Johansen, S. (1980). The Welch-James approximation to the distribution of the residual sum of squares in a weighted linear regression. Biometrika, 67, 85-92.
18. Keefe, F.J., Dunsmore, J., & Burnett, R. (1992). Behavioral and cognitive-behavioral approaches to chronic pain: Recent advances and future directions. Journal of Consulting and Clinical Psychology, 60, 528-536.
19. Kim, S.J. (1992). A practical solution to the multivariate Behrens-Fisher problem. Biometrika, 79, 171-176.
20. Kudo, A. (1963). A multivariate analogue of the one-sided test. Biometrika, 50, 403-418.
21. Lix, L.M., & Fouladi, R. (2007). Robust step-down tests for multivariate independent group designs. British Journal of Mathematical and Statistical Psychology, 60, 245-265.
22. Lix, L.M., Keselman, H.J., & Hinds, A. (2005). Robust tests for the multivariate Behrens-Fisher problem. Computer Methods and Programs in Biomedicine, 77, 129-139.
23. Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156-166.
24. Minhajuddin, A.T.M., Frawley, W.H., Schucany, W.R., & Woodward, W.A. (2007). Bootstrap tests for multivariate directional alternatives. Journal of Statistical Planning and Inference, 137, 2302-2315.
25. Mudholkar, G.S., Kost, J., & Subbaiah, P. (2001). Robust tests for the significance of orthant restricted mean vector. Communications in Statistics: Theory and Methods, 30, 1789-1810.
26. Mudholkar, G.S., & Srivastava, D.K. (2000). A class of robust stepwise alternatives to Hotelling's T2 tests. Journal of Applied Statistics, 27, 599-619.
27. Nel, D.G., & van der Merwe, C.A. (1986). A solution to the multivariate Behrens-Fisher problem. Communications in Statistics: Simulation and Computation, 15, 3719-3735.
28. Perlman, M.D. (1969). One-sided testing problems in multivariate analysis. Annals of Mathematical Statistics, 40, 549-567.
29. Pocock, S.J., Geller, N.L., & Tsiatis, A.A. (1987). The analysis of multiple endpoints in clinical trials. Biometrics, 43, 487-498.
30. Roy, S.N. (1958). Step down procedure in multivariate analysis. Annals of Mathematical Statistics, 29, 1177-1187.
31. Roy, S.N., & Bargman, R.E. (1958). Tests of multiple independence and the associated confidence bounds. Annals of Mathematical Statistics, 29, 491-503.
32. Sankoh, A.J., Huque, M.F., Russell, H.K., & D' Agostino, S. (1999). Global two-group multiple endpoint adjustment methods applied to clinical trials. Drug Information Journal, 33, 119-140.
33. SAS Institute. (2004). SAS/IML user's guide, version 9. Cary, NC: Author.
34. Schafer, J.L., & Graham, J.W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147-177.
35. Sen, P.K. (1983). A Fisherian detour of the step-down procedure. In P. K. Sen (Ed.), Contributions to statistics (pp. 367-377). Amsterdam: North-Holland.
36. Srivastava, D.K., & Mudholkar, G.S. (2001). Trimmed T2: A robust analog of Hotelling's T2. Journal of Statistical Planning and Inference, 97, 343-358.
37. Stevens, J.P. (1973). Step-down analysis and simultaneous confidence intervals in MANOVA. Multivariate Behavioral Research, 8, 391-402.
38. Tamhane, A.C., & Logan, B.R. (2002). Accurate critical constants for the one-sided approximate likelihood ratio test of a normal mean vector when the covariance matrix is estimated. Biometrics, 58, 650-656.
39. Tamhane, A.C., & Logan, B.R. (2003). Multiple endpoints: An overview and new developments (Tech. Rep. No. 43). Milwaukee: Medical College of Wisconsin, Division of Biostatistics.
40. Tang, D., Gnecco, C., & Geller, N.L. (1989). An approximate likelihood ratio test for a normal mean vector with nonnegative components with application to clinical trials. Biometrika, 76, 577-583.
41. Weisz, J.R., Doss, A.J., & Hawley, K.M. (2005). Youth psychotherapy outcome research: A review and critique of the evidence base. Annual Review of Psychology, 56, 337-363.
42. Welch, B.L. (1938). The significance of the difference between two means when the population variances are unequal. Biometrika, 29, 350-362.
43. Westfall, P.H., & Young, S.S. (1993). Resampling based multiple testing. New York: John Wiley.
44. Wilcox, R.R. (1995). Simulation results on solutions to the multivariate Behrens-Fisher problem via trimmed means. The Statistician, 44, 213-225.
45. Yao, Y. (1965). An approximate degrees of freedom solution to the multivariate Behrens-Fisher problem. Biometrika, 52, 139-147.
46. Yuen, K.K. (1974). The two-sample trimmed t for unequal population variances. Biometrika, 61, 165-170.
47. Yuen, K.K., & Dixon, W.J. (1973). The approximate behavior and performance of the two-sample trimmed t. Biometrika, 60, 369-374.