A comparison of tests of the Wilks-Lawley hypothesis in multivariate analysis

Mikhail, N. N.

doi:10.1093/biomet/52.1-2.149

Cited by 23 publications

(3 citation statements)

References 13 publications

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“…Now, some detailed comparison may be made with the table of approximate powers given by Mikhail (1965) for test of hypothesis (ii) based on three criteria. Now, some detailed comparison may be made with the table of approximate powers given by Mikhail (1965) for test of hypothesis (ii) based on three criteria.…”

Section: Power Comparisonsmentioning

confidence: 99%

“…Now, some detailed comparison may be made with the table of approximate powers given by Mikhail (1965) for test of hypothesis (ii) based on three criteria. However, in connexion with the approximate powers (Mikhail, 1965), it should be pointed out that the second moment of U(P) obtained by Khatri & Pillai (1967) does not reduce to that given by Mikhail (1965) for p = 2, even after taking into account that his definitions of the criteria are in terms of the sums of product matrices and not the sample covariance matrices as stated in his paper. However, in connexion with the approximate powers (Mikhail, 1965), it should be pointed out that the second moment of U(P) obtained by Khatri & Pillai (1967) does not reduce to that given by Mikhail (1965) for p = 2, even after taking into account that his definitions of the criteria are in terms of the sums of product matrices and not the sample covariance matrices as stated in his paper.…”

Section: Power Comparisonsmentioning

confidence: 99%

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Power Comparisons of Tests of Two Multivariate Hypotheses Based on Four Criteria

Pillai¹,

Jayachandran²

1967

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika.

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Section: Power Comparisonsmentioning

confidence: 99%

Section: Power Comparisonsmentioning

confidence: 99%

Power Comparisons of Tests of Two Multivariate Hypotheses Based on Four Criteria

Pillai¹,

Jayachandran²

1967

Biometrika

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“…Such a choice provides greater complexity to the use of the multivariate GLM in neuroimaging when using contrasts that produce non-exact F values. Though these tests have been compared numerous times in the statistical literature ( Ito, 1962 , Lee, 1971 , Mikhail, 1965 , Olson, 1974 , Pillai and Jayachandran, 1967 ), we sought to briefly investigate their behaviour when applied to real neuroimaging data. To do this, we used the C matrix from the main effect of condition contrast detailed earlier with A = I k .…”

Section: Comparisons Between the Multivariate Test Statisticsmentioning

confidence: 99%

Multivariate and repeated measures (MRM): A new toolbox for dependent and multimodal group-level neuroimaging data

et al. 2016

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Repeated measurements and multimodal data are common in neuroimaging research. Despite this, conventional approaches to group level analysis ignore these repeated measurements in favour of multiple between-subject models using contrasts of interest. This approach has a number of drawbacks as certain designs and comparisons of interest are either not possible or complex to implement. Unfortunately, even when attempting to analyse group level data within a repeated-measures framework, the methods implemented in popular software packages make potentially unrealistic assumptions about the covariance structure across the brain. In this paper, we describe how this issue can be addressed in a simple and efficient manner using the multivariate form of the familiar general linear model (GLM), as implemented in a new MATLAB toolbox. This multivariate framework is discussed, paying particular attention to methods of inference by permutation. Comparisons with existing approaches and software packages for dependent group-level neuroimaging data are made. We also demonstrate how this method is easily adapted for dependency at the group level when multiple modalities of imaging are collected from the same individuals. Follow-up of these multimodal models using linear discriminant functions (LDA) is also discussed, with applications to future studies wishing to integrate multiple scanning techniques into investigating populations of interest.

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Lambda Criterion, Wilks'

Dasgupta

2005

Encyclopedia of Biostatistics

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A comparison of tests of the Wilks-Lawley hypothesis in multivariate analysis

Cited by 23 publications

References 13 publications

Power Comparisons of Tests of Two Multivariate Hypotheses Based on Four Criteria

Power Comparisons of Tests of Two Multivariate Hypotheses Based on Four Criteria

Multivariate and repeated measures (MRM): A new toolbox for dependent and multimodal group-level neuroimaging data

Lambda Criterion, Wilks'

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