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**Testing of multivariate repeated measures data with block exchangeable covariance structure.**
*(English)*
Zbl 1404.62062

Summary: 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 \(pq +1\) 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 \(pq \times pq\) dimensional unknown unstructured variance-covariance matrix. Some simulation studies are performed to compare the power of the new \(D^2\) test and the existing \(BT^2\) test. The performance of the proposed \(D^2\) test is demonstrated with the two medical data sets.

### MSC:

62H15 | Hypothesis testing in multivariate analysis |

62H12 | Estimation in multivariate analysis |

62H10 | Multivariate distribution of statistics |

62E17 | Approximations to statistical distributions (nonasymptotic) |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

### Keywords:

\(BT^2\) statistic; \(D^2\) statistic; Hotelling’s \(T^2\) statistic; Lawley-Hotelling trace distribution
Full Text:
DOI

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