Inference for low- and high-dimensional multigroup repeated measures designs with unequal covariance matrices

2015 ◽  
Vol 58 (4) ◽  
pp. 810-830 ◽  
Author(s):  
Martin Happ ◽  
Solomon W. Harrar ◽  
Arne C. Bathke
Keyword(s):  
Repeated Measures ◽  
Covariance Matrices ◽  
High Dimensional ◽  
Repeated Measures Designs

Nonparametric Tests for Analyzing Interactions Among Intra-Block Ranks in Multiple Group Repeated Measures Designs

2000 ◽  
Vol 25 (1) ◽  
pp. 20-59 ◽  
Author(s):  
T. Mark Beasley
Keyword(s):  
Repeated Measures ◽  
Profile Analysis ◽  
Nonparametric Tests ◽  
Covariance Matrices ◽  
Statistical Properties ◽  
Multivariate Approach ◽  
Omnibus Test ◽  
Multiple Group ◽  
Multiple Groups ◽  
Repeated Measures Designs

This study developed an extension of the Hollander and Sethuraman (1978) statistic (B2 ) for testing discordance among intra-block rankings of K elements for multiple groups (J ≥ 2) of raters. B2 was demonstrated to be equivalent to the Pillai-Bartlett trace (V ) from a multivariate profile analysis performed on the ranks such that B2 = V (N - 1) Results confirmed the utility of B2 as an omnibus test of interaction (i.e., discordance) among intra-block ranks and demonstrated that it was more powerful than the multivariate approach to ranked data suggested by Serlin and Marascuilo (1983) . An extension of the Friedman (1937) two-way ANOVA for intra-block ranks was also developed. The adequacy of these procedures for testing interactions in multiple group repeated measures designs was investigated. The Friedman model demonstrated adequate statistical properties only when covariance matrices were spherical. Results also demonstrated that the Hollander-Sethuraman model was useful in testing interaction contrasts.

scholarly journals Analysis of high-dimensional one group repeated measures designs

Statistics ◽  
2015 ◽  
Vol 49 (6) ◽  
pp. 1243-1261 ◽  
Author(s):  
Markus Pauly ◽  
David Ellenberger ◽  
Edgar Brunner
Keyword(s):  
Repeated Measures ◽  
High Dimensional ◽  
Repeated Measures Designs

Power Comparisons of Eight Tests for Sphericity in Repeated Measures Designs

1992 ◽  
Vol 17 (3) ◽  
pp. 233-249 ◽  
Author(s):  
John E. Cornell ◽  
Dean M. Young ◽  
Samuel L. Seaman ◽  
Roger E. Kirk
Keyword(s):  
Repeated Measures ◽  
Covariance Matrices ◽  
Block Designs ◽  
Sample Covariance Matrices ◽  
Large Samples ◽  
Sample Covariance ◽  
Invariant Test ◽  
Power Comparisons ◽  
Repeated Measures Designs ◽  
Randomized Block Designs

A Monte Carlo simulation was conducted to investigate the relative power of eight tests for sphericity in randomized block designs. Box’s (1954) epsilon values º = .35, .55, .75, .80, .85, .90, .95, and 1.00 were used to quantify departures from sphericity for rank-1 population covariance matrices of dimension p = 3, 5, 7, and 9. Sample covariance matrices were generated for samples of size n = 10, 15, 20, and 30. The locally best invariant test demonstrated substantial power to detect departures from sphericity—regardless of p— for both small and large samples for rank-1 alternatives. Recommendations are made regarding the use of preliminary tests.

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