The analysis of repeated measurements: a comparison of mixed-model satterthwaite f tests and a nonpooled adjusted degrees of freedom multivariate test

Bibliography

• Akaike , H. 1974 . A new look at the statistical model identification . IEEE Transaction on Automatic Control , AC-19 : 716 – 723 .
   Web of Science ®Google Scholar
• Algina , J. and Keselman , H.J. 1997 . Testing repeated measures hypotheses when covariances are heterogeneous: Revisiting the robustness of the Welch-James test . Multivariate Behavioral Research , 325 : 255 – 274 .
   Google Scholar
• Algina , J. and Keselman , H.J. 1998 . A power comparison of the Welch-James and Improved General Approximation tests in the split-plot design . Journal of Educational and Behavioral Statistics , 23 : 152 – 169 .
   Web of Science ®Google Scholar
• Algina , J. and Oshima , T.C. 1994 . Type I error rates for Huynh's general approximation and improved general approximation tests . British Journal of Mathematical and Statistical Psychology , 47 : 151 – 165 .
   Web of Science ®Google Scholar
• Algina , J. and Oshima , T.C. 1995 . An improved general approximation test for the main effect in a split plot design . British Journal of Mathematical and Statistical Psychology , 48 : 149 – 160 .
   Web of Science ®Google Scholar
• Bradley , J.V. 1978 . Robustness? . British Journal of Mathematical and Statistical Psychology , 31 : 144 – 152 .
   Web of Science ®Google Scholar
• Brown , M.B. and Forsythe , A.B. 1974 . The small sample behavior of some statistics which test the equality of several means . Technometrics , l6 : 129 – 132 .
   Google Scholar
• Bryk , A.S. and Raudenbush , S.W. 1992 . Hierarchial linear models , Newbury Park, CA : Sage Publications, Inc .
   Google Scholar
• Fai , A.H.T. and Cornelius , P.L. 1996 . Approximate F-tests of multiple degree of freedom hypotheses in genarlized least squares analyses of unbalanced split-plot experiments . Journal of Statistical Computation and Simulation , 54 : 363 – 378 .
   Web of Science ®Google Scholar
• Giesbrecht , F.G. and Burns , J.C. 1985 . Two-stage analysis based on a mixed model: Large-sample asymptotic theory and small-sample simulations results . Biometrics , 41 : 477 – 486 .
   Web of Science ®Google Scholar
• Greenhouse , S.W. and Geisser , S. 1959 . On methods in the analysis of profile data . Psychometrika , 24 : 95 – 112 .
   Web of Science ®Google Scholar
• Huynh , H. 1978 . Some approximate tests for repeated measurement designs . Psychometrika , 43 : 161 – 175 .
   Web of Science ®Google Scholar
• Huynh , H. and Feldt , L. 1970 . Conditions under which mean square ratios in repeated measurements designs have exact F distributions . Journal of the American Statistical Association , 65 : 1582 – 1589 .
   Google Scholar
• Huynh , H. and Feldt , L.S. 1976 . Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs . Journal of Educational Statistics , 1 : 69 – 82 .
   Google Scholar
• James , G.S. 1951 . The comparison of several groups of observations when the ratios of the population variances are unknown . Biometrika , 38 : 324 – 329 .
   Web of Science ®Google Scholar
• James , G.S. 1954 . Tests of linear hypotheses in univariate and multivariate analysis when the ratios of the population variances are unknown . Biometrika , 41 : 19 – 43 .
   Web of Science ®Google Scholar
• Jennrich , R.I. and Schluchter , M.D. 1986 . Unbalanced repeated -measures models with structured covariance matrices . Biometrics , 42 : 805 – 820 .
   PubMed Web of Science ®Google Scholar
• Johansen , S. 1980 . The Welch-James approximation of the distribution of the residual sum of squares in weighted linear regression . Biometrika , 67 : 85 – 92 .
   Web of Science ®Google Scholar
• Johnson , M.F. , Ramberg , J.S. and Wang , C. 1982 . The Johnson translation system in Monte Carlo studies . Communications in Statistics-Simulation and Computation , 11 : 521 – 525 .
   Web of Science ®Google Scholar
• Keselman , H.J. , Algina , J. , Kowalchuk , R.K. and Wolfinger , R.D. 1999 . A comparison of recent approaches to the analysis of repeated measurements . British Journal of Mathematical and Statistical Psychology , 52 : 63 – 78 .
   Web of Science ®Google Scholar
• Keselman , H.J. , Algina , J. , Kowalchuk , R.K. and Wolfinger , R.D. 1998 . A comparison of two approaches for selecting covariance structures in the analysis of repeated measurements . Communications in Statistics -Computation and Simulation , 27 : 591 – 604 .
   Web of Science ®Google Scholar
• Keselman , H.J. , Carriere , K.C. and Lix , L.M. 1993 . Testing repeated measures hypotheses when covariance matrices are heterogeneous . Journal of Educational Statistics , 18 : 305 – 319 .
   Google Scholar
• 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. , Keselman , J.C. and Levin , J.R. 1998 . Statistical practices of Educational Researchers: An analysis of their ANOVA, MANOVA and ANCOVA analyses . Review of Educational Research , 68 ( 3 ) : 350 – 386 .
   Web of Science ®Google Scholar
• Keselman , J.C. and Keselman , H.J. 1990 . Analysing unbalanced repeated measures designs . British Journal of Mathematical and Statistical Psychology , 43 ( 3 ) : 265 – 282 .
   Google Scholar
• Khuri , A.I. , Mathew , T. and Sinha , B.K. 1998 . Statistical tests for mixed linear models , New York : Wiley .
   Google Scholar
• Kowalchuk , R.K. , Lix , L.M. and Keselman , H.J. . The analysis of repeated measures designs . Paper presented at the Annual Meeting of the Psychometric Society . 1996 , Banff, Alberta.
   Google Scholar
• Littell , R.C. , Milliken , G.A. , Stroup , W.W. and Wolfinger , R.D. 1996 . SAS system for mixed models , Cary, NC : SAS Institute .
   Google Scholar
• Little , R.J.A. 1994 . A class of pattern-mixture models for normal incomplete data . Biometrics , 81 : 471 – 483 .
   Google Scholar
• Little , R.J.A. 1995 . Modeling the drop-out mechanism in repeated measures studies . Journal of the American Statistical Association , 90 : 1112 – 1121 .
   Web of Science ®Google Scholar
• Lix , L.M. and Keselman , H.J. 1995 . Approximate degrees of freedom tests: A unified perspective on testing for mean equality . Psychological Bulletin , 117 : 547 – 560 .
   Web of Science ®Google Scholar
• Mclean , R.A. and Sanders , W.L. . Approximating degrees of freedom for standard errors in mixed linear models . Proceedings of the Statistical Computing Section. American Statistical Association . New Orleans. pp. 50 – 59 .
   Google Scholar
• Mendoza , J.L. 1980 . A Significance test for multisample sphericity . Psychometrika , 45 : 495 – 498 .
   Web of Science ®Google Scholar
• Micceri , T. 1989 . The unicorn, the normal curve, and other improbable creatures . Psychological Bulletin , 105 : 156 – 166 .
   Web of Science ®Google Scholar
• Rogan , J.C. , Keselman , H.J. and Mendoza , J.L. 1979 . Analysis of repeated measurements . British Journal of Mathematical and Statistical Psychology , 32 : 269 – 286 .
   Web of Science ®Google Scholar
• Rouanet , H. and Lepine , D. 1970 . Comparison between treatments in a repeated measures design: ANOVA and multivariate methods . British Journal of Mathematical and Statistical Psychology , 23 : 147 – 163 .
   Web of Science ®Google Scholar
• SAS Institute . 1989 . SAS/IML sowtware: Usage and reference , Cary, NC : Author . Version 6
   Google Scholar
• SAS Institute . 1996 . SAS/STATSoftware: Changes and Enhancements through Release 6.11 , Cary, NC : Author .
   Google Scholar
• Satterthwaite , F.E. 1941 . Synthesis of variance . Psychometrika , 6 : 309 – 316 .
   Web of Science ®Google Scholar
• Sawilowsky , S.S. and Blair , R.C. 1992 . A more realistic look at the robustness and Type II error probabilities of the t test to departures from population normality . Psychological Bulletin , 111 : 352 – 360 .
   Web of Science ®Google Scholar
• Schwarz , G. 1978 . Estimating the dimension of a model . Annals of Statistics , 6 : 461 – 464 .
   Web of Science ®Google Scholar
• Welch , B.L. 1938 . The significance of the difference between two means when the population variances are unequal . Biometrika , 29 : 350 – 362 .
   Web of Science ®Google Scholar
• Welch , B.L. 1947 . The generalization of Students' problems when several different population variances are involved . Biometrika , 34 : 28 – 35 .
   PubMed Web of Science ®Google Scholar
• Welch , B.L. 1951 . On the comparison of several mean values: An alternative approach . Biometrika , 38 : 330 – 336 .
   Web of Science ®Google Scholar
• Wilcox , R.R. 1994 . A one-way random effects model for trimmed means . Psychometrika , 59 : 289 – 306 .
   Web of Science ®Google Scholar
• Wolfinger , R. 1993 . Covariance structure selection in general mixed models . Communication in Statistics-Simulation , 22 : 1079 – 1106 .
   Web of Science ®Google Scholar
• Wolfinger , R.D. 1996 . Heterogeneous variance-covariance structures for repeated measurements . Journal of Agricultural, Biological, and Environmental Statistics , 1 : 205 – 230 .
   Google Scholar
• Wright , S.P. . Adjusted F tests for repeated measures with the MIXED procedure . Proceedings of the Twentieth Annual SAS Users Group International Conference . Cary, NC.
   Google Scholar