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

1988 ◽  
Vol 13 (3) ◽  
pp. 215 ◽  
Author(s):  
H. J. Keselman ◽  
Joanne C. Keselman
Keyword(s):  
Repeated Measures ◽  
Multiple Comparison ◽  
Unbalanced Designs ◽  
Multiple Comparison Procedures ◽  
Multisample Sphericity

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.

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.

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.

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