Medical College of Wisconsin
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Accurate critical constants for the one-sided approximate likelihood ratio test of a normal mean vector when the covariance matrix is estimated. Biometrics 2002 Sep;58(3):650-6 PMID: 12230000

Pubmed ID



Tang, Gnecco, and Geller (1989, Biometrika 76, 577-583) proposed an approximate likelihood ratio (ALR) test of the null hypothesis that a normal mean vector equals a null vector against the alternative that all of its components are nonnegative with at least one strictly positive. This test is useful for comparing a treatment group with a control group on multiple endpoints, and the data from the two groups are assumed to follow multivariate normal distributions with different mean vectors and a common covariance matrix (the homoscedastic case). Tang et al. derived the test statistic and its null distribution assuming a known covariance matrix. In practice, when the covariance matrix is estimated, the critical constants tabulated by Tang et al. result in a highly liberal test. To deal with this problem, we derive an accurate small-sample approximation to the null distribution of the ALR test statistic by using the moment matching method. The proposed approximation is then extended to the heteroscedastic case. The accuracy of both the approximations is verified by simulations. A real data example is given to illustrate the use of the approximations.

Author List

Tamhane AC, Logan BR


Brent R. Logan PhD Director, Professor in the Institute for Health and Equity department at Medical College of Wisconsin


2-s2.0-0036714878   13 Citations

MESH terms used to index this publication - Major topics in bold

Blood Transfusion, Autologous
Chi-Square Distribution
Clinical Trials as Topic
Coronary Artery Bypass
Likelihood Functions
Models, Statistical
Postoperative Complications
jenkins-FCD Prod-321 98992d628744e349846c2f62ac68f241d7e1ea70