Comparison of aligned Friedman rank and parametric methods for testing interactions in split-plot designs

Computational Statistics and Data Analysis

Volumn 42, Issue 4, 2003, Pages 569-593

  Beasley, T Mark ^a   Zumbo, Bruno D ^b  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Aligned ranks; Friedman ranks; Interaction tests; Repeated measures; Split plot design

Indexed keywords

DATA REDUCTION; ERROR ANALYSIS; MATHEMATICAL MODELS;

PARAMETRIC METHODS;

STATISTICAL METHODS;

STATISTICAL ANALYSIS;

EID: 0037471439     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(02)00147-0     Document Type: Article

References (66)

1. Agresti, A., Pendergast, J., 1986. Comparing mean ranks for repeated measures data. Comm. Statist. Theory Methods 15, 1417-1433.
2. Akritas, M.G., 1990. The rank transform method on some two factor designs. J. Amer. Statist. Assoc. 85, 73-78.
3. Akritas, M.G., Arnold, S.F., 1994. Fully non-parametric hypotheses for factorial designs, I: multivariate repeated-measures designs. J. Amer. Statist. Assoc. 89, 336-343.
4. Akritas, M.G., Arnold, S.F., Brunner, E., 1997. Nonparametric hypotheses and rank statistics for unbalanced factorial designs. J. Amer. Statist. Assoc. 92, 258-265.
5. Algina, J., Keselman, H.J., 1998. A power comparison of the Welch James and improved general approximation tests in the split plot design. J. Educ. Behav. Statist. 23, 152-169.
6. Algina, J., Oshima, T.C., 1994. Type I error rates for Huynh's general approximation and improved general approximation tests. British J. Math. Statist. Psych. 47, 151-165.
7. Allison, D.B., Neale, M.C., Zannolli, R., Schork, N.J., Amos, C.I., Blangero, J., 1999. Testing the robustness of the likelihood-ratio test in a variance-component quantitative-trait loci-mapping procedure. Am. J. Hum. Genet. 65, 531-544.
8. Beasley, T.M., 1994. CORRMTX: generating correlated data matrices in SAS/IML. Appl. Psych. Measure. 18, 95.
9. Beasley, T.M., 2000. Nonparametric tests for analyzing interactions among intra-block ranks in multiple group repeated measures designs. J. Educ. Behav. Statist. 25, 20-59.
10. Beasley, T.M., 2002. Multivariate aligned rank test for interactions in multiple group repeated measures designs. Multiv. Behav. Res. 37, 197-226.
11. Beasley, T.M., Zumbo, B.D., 1998. Rank transformation and df-correction procedures for split-plot designs. Paper presented at the Meeting of the American Educational Research Association, San Diego, CA.
12. Beasley, T.M., Zumbo, B.D., 2002. Aligned rank tests for interactions in split-plot designs: distributional assumptions and stochastic homogeneity. Manuscript submitted for publication.
13. Beckett, J., Schucany, W.R., 1979. Concordance among categorized groups of judges. J. Educ. Statist. 4, 125-137.
14. Blair, R.C. Sawilowsky, S.S., Higgins, J.J., 1987. Limitations of the rank transform statistic in test for interactions. Comm. Statist. Simulation Comput. 16, 1133-1145.
15. Boik, R.J., 1993. The analysis of two-factor interactions in fixed effects linear models. J. Educ. Statist. 18, 1-40.
16. Box, G.E.P., 1954. Some theorems on quadratic forms applied in the study of analysis of variance problems, I: effect of inequality of variance in the one-way classification. Ann. Math. Statist. 25, 290-302.
17. Bradley, J.V., 1978. Robustness?. British J. Math. Statist. Psych. 31, 144-152.
18. Brunner, E., Langer, F., 2000. Nonparametric analysis of ordered categorical data in designs with longitudinal observations and small sample sizes. Biometrical J. 42, 663-675.
19. Cliff, N., 1996. Answering ordinal questions with ordinal data using ordinal statistics. Multiv. Behav. Res. 31, 331-350.
20. Conover, W.J., Iman, R.L., 1981. Rank transformations as a bridge between parametric and non-parametric statistics. Amer. Statist. 35, 124-133.
21. Fleishman, A.I., 1978. A method for simulating non-normal distributions. Psychometrika 43, 521-532.
22. Friedman, M., 1937. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Amer. Statist. Assoc. 32, 675-701.
23. Greenhouse, S.W., Geisser, S., 1959. On methods in the analysis of profile data. Psychometrika 24, 95-112.
24. Harwell, M.R., Serlin, R.C., 1994. A Monte Carlo study of the Friedman test and some competitors in the single factor, repeated measures design with unequal covariances. Comput. Statist. Data Anal. 17, 35-49.
25. Harwell, M.R., Serlin, R.C., 1997. An empirical study of five multivariate tests for the single-factor repeated measures model. Comm. Statist. Simulation Comput. 26, 605-618.
26. Headrick, T.C., Rotou, O., 2001. An investigation of the rank transformation in multiple regression. Comput. Statist. Data Anal. 38, 203-215.
27. Headrick, T.C., Sawilowsky, S.S., 1999. Simulating correlated multivariate nonnormal distributions: extending the Fleishman power method. Psychometrika 64, 25-35.
28. Headrick, T.C., Sawilowsky, S.S., 2000. Properties of the rank transformation in factorial analysis of covariance. Comm. Statist. Simulation Comput. 29, 1059-1088.
29. Headrick, T.C., Vineyard, G., 2001. An empirical investigation of four tests of interaction in the context of factorial analysis of covaraince. Multiv. Linear Regress. View 27, 3-15.
30. Hettmansperger, T.P., 1984. Statistical Inference Based on Ranks. Wiley, New York.
31. Higgins, J.J., Tashtoush, S., 1994. An aligned rank transform test for interaction. Nonlinear World 1, 201-211.
32. Hollander, M., Sethuraman, J., 1978. Testing for agreement between two groups of judges. Biometrika 65, 403-411.
33. Hollander, M., Wolfe, D.A., 1973. Nonparametric Statistical Methods. Wiley, New York.
34. Hora, S.C., Conover, W.J., 1984. The F-statistic in the two-way layout with rank-score transformed data. J. Amer. Statist. Assoc. 79, 668-673.
35. Hotelling, H., 1951. A generalized T-test and measure of multivariate dispersion. Proceedings of the Second Berkeley Symposium in Mathematics, Statistics and Probability, Vol. 2, pp. 23-41.
36. Huynh, H., 1978. Some approximate tests for repeated measurement designs. Psychometrika 43, 161-175.
37. Huynh, H., Feldt, L.S., 1970. Conditions under which mean squares ratios in repeated measurements designs have exact F-distributions. J. Amer. Statist. Assoc. 65, 1582-1585.
38. Huynh, H., Feldt, L.S., 1976. Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. J. Educ. Statist. 1, 69-82.
39. Kaiser, H.F., Dickman, K., 1962. Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika 27, 179-182.
40. Keselman, H.J., Algina, J., 1996. The analysis of higher-order repeated measures designs. In: Thompson, B. (Ed.), Advances in Social Science Methodology, Vol. 4. JAI Press, Greenwich, CT, pp. 45-70.
41. Keselman, H.J., Huberty, C.J, Lix, L.M., Olejnik, S., Cribbie, R.A., Donahue, B., Kowalchuk, R.K., Lowman, L.L., Petoskey, M.D., Levin, J.R., Keselman, J.C., 1998. Statistical practices of educational researchers: an analysis of their ANOVA, MANOVA, and ANCOVA analyses. Rev. Educ. Res. 68, 350-386.
42. Klockars, A.J., Hancock, G.R. (2000). Scheffé's more powerful F-protected post hoc procedure. J. Educ. Behav. Statist. 25, 13-19.
43. Koch, G.G., 1969. Some aspects of the statistical analysis of "split-plot" experiments in completely randomized layouts. J. Amer. Statist. Assoc. 64, 485-506.
44. Koch, G.G., Amara, I.A. Stokes, M.E. Gillings, D.B., 1980. Some views on parametric and non-parametric analysis for repeated measurements and selected bibliography. Internat. Statist. Rev. 48, 249-265.
45. Lecoutre, B., 1991. A correction for the e approximate test in repeated measures designs with two or more independent groups. J. Educ. Statist. 16, 371-372.
46. Lynch, M., Walsh, B., 1998. Genetics and Analysis of Quantitative Traits. Sinauer, Sunderland, MA.
47. Marascuilo, L.A., 1966. Large-sample multiple comparisons. Psych. Bull. 65, 280-290.
48. Marascuilo, L.A., McSweeney, M., 1967. Nonparametric and post hoc comparisons for trend. Psych Bull. 67, 401-412.
49. Marascuilo, L.A., McSweeney, M., 1977. Nonparametric and Distribution-Free Methods for the Social Sciences. Brooks-Cole, Monterey, CA.
50. Micceri, T., 1989. The unicorn, the normal curve, and other improbable creatures. Psych. Bull. 105, 156-166.
51. Randles, R.H., Wolfe, D.A., 1979. Introduction to the Theory of Non-Parametric Statistics. Wiley, New York.
52. Rasmussen, J.L., 1989. Parametric and non-parametric analysis of groups by trials design under variance-covariance inhomogeneity. British J. Math. Statist. Psych. 42, 91-102.
53. Rasmussen, J.L. Heumann, K.A., Heumann, M.T., Botzum, M., 1989. Univariate and multivariate groups by trials analysis under violation of variance-covariance and normality assumptions. Multiv. Behav. Res. 24, 93-105.
54. Salter, K.C., Fawcett, R.F., 1993. The ART test of interaction: a robust and powerful test of interaction in factorial models. Comm. Statist. Simulation Comput. 22, 137-153.
55. SAS Institute, 2001. SAS/IML user's guide (Release 8.2). Cary, NC.
56. Scheffé, H., 1959. The Analysis of Variance. Wiley, New York.
57. Serlin, R.C., Harwell, M.R., 2001. A review of non-parametric test for complex experimental designs in educational research. Paper presented at the American Educational Research Association, Seattle, WA.
58. Sheehan-Holt, J., 1998. MANOVA simultaneous test procedures: the power and robustness of restricted multivariate contrasts. Educ Psych. Measure. 58, 861-881.
59. Thompson, G.L., 1991. A note on the rank transform for interactions. Biometrika 78, 697-701.
60. Thompson, G.L., 1993. A correction note on the rank transform for interactions. Biometrika 80, 711.
61. Toothaker, L.E., Newman, D., 1994. A. Nonparametric competitors to the two way ANOVA. J. Educ. Behav. Statist. 19, 237-273.
62. Vargha, A., Delaney, H.D., 1998. The Kruskal-Wallis test and stochastic homogeneity. J. Educ. Behav. Statist. 23, 170-192.
63. Wilcox, R., 1993. Robustness in ANOVA. In E. Edwards (Ed.), Applied Analysis of Variance in the Behavioral Sciences. Marcel Dekker, New York, pp. 345-374.
64. Winer, B.J., Brown, D.R., Michels, K.M., 1991. Statistical Principles in Experimental Design, 3rd Edition. McGraw-Hill, New York.
65. Zimmerman, D., Zumbo, B.D., 1993. Relative power of the Wilcoxon test, the Friedman test, and the repeated-measures ANOVA on ranks. J. Experiment. Educ. 62, 75-86.
66. Zumbo, B.D., Coulombe, D., 1997. Investigation of the robust rank-order test for non-normal populations with unequal variances: the case of reaction time. Canad. J. Experiment. Psych. 51, 139-149.