Stepwise and Simultaneous Multiple Comparison Procedures of Repeated Measures’ Means

1994 ◽  
Vol 19 (2) ◽  
pp. 127-162 ◽  
Author(s):  
H. J. Keselman
Keyword(s):  
Repeated Measures ◽  
Type I Error ◽  
Multiple Comparison ◽  
Multivariate Normality ◽  
Type I ◽  
Stepwise Procedures ◽  
Multiple Comparison Procedures ◽  
Multisample Sphericity

Stepwise multiple comparison procedures (MCPs) for repeated measures’ means based on the methods of Hayter (1986) , Hochberg (1988) , Peritz (1970) , Ryan (1960) - Welsch (1977a) , Shaffer (1979 , 1986) , and Welsch (1977a) were compared for their overall familywise rates of Type I error when multisample sphericity and multivariate normality were not satisfied. Robust stepwise procedures were identified by Keselman, Keselman, and Shaffer (1991) with respect to three definitions of power. On average, Welsh’s (1977a) step-up procedure was found to be the most powerful MCP.

Repeated Measures Multiple Comparison Procedures: Effects of Violating Multisample Sphericity in Unbalanced Designs

1988 ◽  
Vol 13 (3) ◽  
pp. 215-226 ◽  
Author(s):  
H. J. Keselman ◽  
Joanne C. Keselman
Keyword(s):  
Repeated Measures ◽  
Type I Error ◽  
Multiple Comparison ◽  
Type I ◽  
Type I Errors ◽  
Unbalanced Designs ◽  
Bonferroni Procedure ◽  
Weighted Means ◽  
Multiple Comparison Procedures ◽  
Multisample Sphericity

Two Tukey multiple comparison procedures as well as a Bonferroni and multivariate approach were compared for their rates of Type I error and any-pairs power when multisample sphericity was not satisfied and the design was unbalanced. Pairwise comparisons of unweighted and weighted repeated measures means were computed. Results indicated that heterogenous covariance matrices in combination with unequal group sizes resulted in substantially inflated rates of Type I error for all MCPs involving comparisons of unweighted means. For tests of weighted means, both the Bonferroni and a multivariate critical value limited the number of Type I errors; however, the Bonferroni procedure provided a more powerful test, particularly when the number of repeated measures treatment levels was large.

Improved Repeated Measures Stepwise Multiple Comparison Procedures

1995 ◽  
Vol 20 (1) ◽  
pp. 83-99 ◽  
Author(s):  
H. J. Keselman ◽  
Lisa M. Lix
Keyword(s):  
Repeated Measures ◽  
Degrees Of Freedom ◽  
Type I Error ◽  
Multiple Comparison ◽  
Type I ◽  
Test Statistics ◽  
Type I Errors ◽  
Multiple Comparison Procedures ◽  
Pairwise Contrasts ◽  
Pairwise Test

Approximate degrees of freedom omnibus and pairwise test statistics of Johansen (1980) and Keselman, Keselman, and Shaffer (1991) , respectively, were used with numerous stepwise multiple comparison procedures (MCPs) to perform pairwise contrasts on repeated measures means. The MCPs were compared for their overall familywise rates of Type I error and for their sensitivity to detect true pairwise differences among means when multisample sphericity and multivariate normality assumptions were not satisfied. Results indicated that multiple range procedures which were modified according to the method described by Duncan (1957) were always robust with respect to Type I errors and were at least as powerful as the unmodified range procedures, and could result in increases in power as large as 22%. Overall, the Welsch (1977a) step-up, Peritz-Duncan ( Peritz, 1970 ), and Ryan-Welsch-Duncan ( Ryan, 1960 ; Welsch, 1977a ) multiple range procedures were found to be most powerful.

scholarly journals Multiple Comparisons Using Composite Likelihood in Clustered Data

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Mahdis Azadbakhsh ◽  
Xin Gao ◽  
Hanna Jankowski
Keyword(s):  
Type I Error ◽  
Clustered Data ◽  
Likelihood Estimation ◽  
Good Control ◽  
Multiple Hypothesis Testing ◽  
Composite Likelihood ◽  
Multiple Comparison ◽  
Likelihood Method ◽  
Type I ◽  
Multiple Comparison Procedures

AbstractWe study the problem of multiple hypothesis testing for correlated clustered data. As the existing multiple comparison procedures based on maximum likelihood estimation could be computationally intensive, we propose to construct multiple comparison procedures based on composite likelihood method. The new test statistics account for the correlation structure within the clusters and are computationally convenient to compute. Simulation studies show that the composite likelihood based procedures maintain good control of the familywise type I error rate in the presence of intra-cluster correlation, whereas ignoring the correlation leads to erratic performance.

The Quest for α: Developments in Multiple Comparison Procedures in the Quarter Century Since

1996 ◽  
Vol 66 (3) ◽  
pp. 269-306 ◽  
Author(s):  
Gregory R. Hancock ◽  
Alan J. Klockars
Keyword(s):  
Type I Error ◽  
Reference Group ◽  
Error Rates ◽  
Multiple Comparison ◽  
Type I ◽  
Quarter Century ◽  
Homogeneity Of Variance ◽  
Current Article ◽  
Post Hoc ◽  
Multiple Comparison Procedures

In a highly regarded work, Games (1971) presented state-of-the-art multiple comparison procedures (MCPs) for a variety of research scenarios and sought to bring order to the seemingly chaotic array of MCPs being used at that time. The current article is a sequel of sorts, placing Games’s insights in the context of many of the major developments in simultaneous and sequential inference since his article’s publication. Specifically, we address the common MCP scenarios of orthogonal contrasts, nonorthogonal contrasts, comparisons against a reference group, all possible pairwise comparisons, and exploratory post hoc contrasts, all under the assumed conditions of independent scores, normality, and homogeneity of variance. In addition, discussions of the philosophical issues surrounding the control of Type I error rates are presented.

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