Testing treatment effects in repeated measures designs: an update for psychophysiological researchers.

In 1987, Jennings enumerated data analysis procedures that authors must follow for analyzing effects in repeated measures designs when submitting papers to Psychophysiology. These prescriptions were intended to counteract the effects of nonspherical data, a condition know to produce biased tests of significance. Since this editorial policy was established, additional refinements to the analysis of these designs have appeared in print in a number of sources that are not likely to be routinely read by psychophysiological researchers. Accordingly, this paper includes additional procedures not previously enumerated in the editorial policy that can be used to analyze repeated measurements. Furthermore, I indicate how numerical solutions can easily be obtained.

[1]  H. Hotelling The Generalization of Student’s Ratio , 1931 .

[2]  S. S. Wilks CERTAIN GENERALIZATIONS IN THE ANALYSIS OF VARIANCE , 1932 .

[3]  R Fisher,et al.  Design of Experiments , 1936 .

[4]  D. Lawley A GENERALIZATION OF FISHER'S z TEST , 1938 .

[5]  B. L. Welch THE SIGNIFICANCE OF THE DIFFERENCE BETWEEN TWO MEANS WHEN THE POPULATION VARIANCES ARE UNEQUAL , 1938 .

[6]  M. Bartlett A note on tests of significance in multivariate analysis , 1939, Mathematical Proceedings of the Cambridge Philosophical Society.

[7]  F. E. Satterthwaite Synthesis of variance , 1941 .

[8]  Satterthwaite Fe An approximate distribution of estimates of variance components. , 1946 .

[9]  F. E. Satterthwaite An approximate distribution of estimates of variance components. , 1946, Biometrics.

[10]  Welch Bl THE GENERALIZATION OF ‘STUDENT'S’ PROBLEM WHEN SEVERAL DIFFERENT POPULATION VARLANCES ARE INVOLVED , 1947 .

[11]  L. S. Kogan Analysis of variance; repeated measurements. , 1948, Psychological bulletin.

[12]  J. Baron,et al.  Analysis of Variance: Repeated-Measures , 1948 .

[13]  H. Hotelling A Generalized T Test and Measure of Multivariate Dispersion , 1951 .

[14]  B. L. Welch ON THE COMPARISON OF SEVERAL MEAN VALUES: AN ALTERNATIVE APPROACH , 1951 .

[15]  G. S. James THE COMPARISON OF SEVERAL GROUPS OF OBSERVATIONS WHEN THE RATIOS OF THE POPULATION VARIANCES ARE UNKNOWN , 1951 .

[16]  S. N. Roy On a Heuristic Method of Test Construction and its use in Multivariate Analysis , 1953 .

[17]  G. Box 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 , 1954 .

[18]  G. S. James TESTS OF LINEAR HYPOTHESES IN UNIVERIATE AND MULTIVARIATE ANALYSIS WHEN THE RATIOS OF THE POPULATION VARIANCES ARE UNKNOWN , 1954 .

[19]  K. Pillai Some New Test Criteria in Multivariate Analysis , 1955 .

[20]  S. Geisser,et al.  On methods in the analysis of profile data , 1959 .

[21]  F B Baker,et al.  Estimates of test size for several test procedures based on conventional variance ratios in the repeated measures design , 1967, Psychometrika.

[22]  R. Kirk Experimental Design: Procedures for the Behavioral Sciences , 1970 .

[23]  H. Rouanet,et al.  COMPARISON BETWEEN TREATMENTS IN A REPEATED‐MEASUREMENT DESIGN: ANOVA AND MULTIVARIATE METHODS , 1970 .

[24]  H. Huynh,et al.  Conditions under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions , 1970 .

[25]  Michael L. Davidson Univariate versus multivariate tests in repeated-measures experiments. , 1972 .

[26]  H. Akaike A new look at the statistical model identification , 1974 .

[27]  Chester L. Olson,et al.  Comparative Robustness of Six Tests in Multivariate Analysis of Variance , 1974 .

[28]  J. F. Howell,et al.  Pairwise Multiple Comparison Procedures with Unequal N’s and/or Variances: A Monte Carlo Study , 1976 .

[29]  Necessary and Sufficient Conditions for F Ratios in the L × J × K Factorial Design with Two Repeated Factors , 1976 .

[30]  H. Huynh,et al.  Estimation of the Box Correction for Degrees of Freedom from Sample Data in Randomized Block and Split-Plot Designs , 1976 .

[31]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[32]  K. Ruben Gabriel,et al.  Type IV Errors and Analysis of Simple Effects , 1978 .

[33]  Huynh Huynh,et al.  Some approximate tests for repeated measurement designs , 1978 .

[34]  Juliet Popper Shaffer,et al.  Comparison of Means: An F Test Followed by a Modified Multiple Range Procedure , 1979 .

[35]  Jorge L. Mendoza,et al.  Analysis of repeated measurements. , 1979 .

[36]  H J Keselman,et al.  Repeated measures F tests and psychophysiological research: controlling the number of false positives. , 1980, Psychophysiology.

[37]  Jorge L. Mendoza,et al.  A significance test for multisample sphericity , 1980 .

[38]  Scott E. Maxwell,et al.  Pairwise Multiple Comparisons in Repeated Measures Designs , 1980 .

[39]  S. Johansen,et al.  The Welch - James approximation to the distribution of the residual sum of squares in a weighted lin , 1980 .

[40]  A. Hayter The Maximum Familywise Error Rate of Fisher's Least Significant Difference Test , 1986 .

[41]  J. Shaffer Modified Sequentially Rejective Multiple Test Procedures , 1986 .

[42]  J. Richard Jennings,et al.  Editorial Policy on Analyses of Variance With Repeated Measures , 1987 .

[43]  John C. W. Rayner,et al.  Welch's approximate solution for the Behrens-Fisher problem , 1987 .

[44]  J. Thayer,et al.  The continuing problem of false positives in repeated measures ANOVA in psychophysiology: a multivariate solution. , 1987, Psychophysiology.

[45]  Y. Hochberg A sharper Bonferroni procedure for multiple tests of significance , 1988 .

[46]  H. Keselman,et al.  Repeated Measures Multiple Comparison Procedures: Effects of Violating Multisample Sphericity in Unbalanced Designs , 1988 .

[47]  Keith E. Muller,et al.  Approximate Power for Repeated-Measures ANOVA Lacking Sphericity , 1989 .

[48]  A. Tamhane,et al.  Multiple Comparison Procedures , 1989 .

[49]  Scott E. Maxwell,et al.  Designing Experiments and Analyzing Data: A Model Comparison Perspective , 1990 .

[50]  H. J. Keselman,et al.  Analysing unbalanced repeated measures designs , 1990 .

[51]  Juliet Popper Shaffer,et al.  Multiple pairwise comparisons of repeated measures means under violation of multisample sphericity , 1991 .

[52]  L. Toothaker Multiple Comparisons for Researchers , 1991 .

[53]  Joel R. Levin,et al.  New developments in pairwise multiple comparisons : some powerful and practicable procedures , 1991 .

[54]  B. Lecoutre A Correction for the ε̃ Approximate Test in Repeated Measures Designs With Two or More Independent Groups , 1991 .

[55]  K. Muller,et al.  Power Calculations for General Linear Multivariate Models Including Repeated Measures Applications. , 1992, Journal of the American Statistical Association.

[56]  Scott E. Maxwell,et al.  Designing Experiments and Analyzing Data , 1992 .

[57]  Lisa M. Lix,et al.  Testing Repeated Measures Hypotheses When Covariance Matrices are Heterogeneous , 1993 .

[58]  Robert J. Boik,et al.  The Analysis of Two-Factor Interactions in Fixed Effects Linear Models , 1993 .

[59]  Keith E. Muller,et al.  Unified power analysis for t-tests through multivariate hypotheses. , 1993 .

[60]  Marija J. Norusis,et al.  SPSS for Windows, Advanced Statistics, release 6.0 , 1993 .

[61]  J. Overall,et al.  Estimating sample sizes for repeated measurement designs. , 1994, Controlled clinical trials.

[62]  Some Alternative Approximate Tests for a Split Plot Design. , 1994, Multivariate behavioral research.

[63]  H. J. Keselman,et al.  Stepwise and Simultaneous Multiple Comparison Procedures of Repeated Measures’ Means , 1994 .

[64]  Roger E. Kirk,et al.  Experimental design: Procedures for the behavioral sciences (3rd ed.). , 1995 .

[65]  H. Keselman,et al.  Approximate degrees of freedom tests: A unified perspective on testing for mean equality. , 1995 .

[66]  THE ANALYSIS OF REPEATED MEASUREMENTS : UNIVARIATE TESTS, MULTIVARIATE TESTS, OR BOTH ? , 1995 .

[67]  R. Littell SAS System for Mixed Models , 1996 .

[68]  H. Keselman,et al.  Interaction contrasts in repeated measures designs. , 1996 .

[69]  Generalization of Improved General Approximation tests to split‐plot designs with multiple between‐subjects factors and/or multiple within‐subjects factors , 1997 .

[70]  H. Keselman,et al.  Detecting repeated measures effects with univariate and multivariate statistics , 1997 .

[71]  Russell D. Wolfinger,et al.  A comparison of two approaches for selecting covariance structures in the analysis of repeated measurements , 1998 .

[72]  A Power Comparison of the Welch-James and Improved General Approximation Tests in the Split-Plot Design , 1998 .

[73]  H. Keselman,et al.  A comparison of recent approaches to the analysis of repeated measurements , 1999 .