Testing of multivariate repeated measures data with block exchangeable covariance structure

• Published in: Test (Madrid, Spain) Vol. 27; no. 2; pp. 360 - 378
• Main Authors: Žežula, Ivan, Klein, Daniel, Roy, Anuradha
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018; Springer Nature B.V
• Subjects: Covariance matrix; Economics; Finance; Hypothesis testing; Insurance; Management; Mathematics and Statistics; Multivariate analysis; Original Paper; Sampling; Statistical Theory and Methods; Statistics; Statistics for Business; Within-subjects design; 62H15; statistic; Lawley–Hotelling trace distribution; Hotelling’s; 62H10; 62H12; 62E17
• ISSN: 1133-0686; 1863-8260
• DOI: 10.1007/s11749-017-0549-z

A new hypothesis testing of equality of mean vectors in two populations using D 2 statistic for multivariate repeated measures data on q response variables at p sites or time points in a block exchangeable covariance matrix setting is proposed. The minimum sample size needed for our new test is only q + 1 , unlike p q + 1 in Hotelling’s T 2 test. The new test is very efficient in small sample scenario, when the number of observations is not adequate to estimate the p q × p q dimensional unknown unstructured variance–covariance matrix. Some simulation studies are performed to compare the power of the new D 2 test and the existing B T 2 test. The performance of the proposed D 2 test is demonstrated with the two medical data sets.