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Multivariate tests for non-additivity

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Abstract

A full bivariate generalization of the Anscombe-Tukey one degree of freedom for univariate non-additivity is presented, and is compared to other proposals. Higher dimensional extensions follow directly. In general, k(k+1)/2 degrees of freedom can be allocated to assessing non-additivity in k dimensions. Hence coordinate-wise additivity is necessary but not sufficient for multivariate additivity.

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Authors and Affiliations

  1. Department of Basic and Clinical Research, Research Institute of Scripps Clinic, 10666 North Torrey Pines Road, 92037, La Jolla, California

    James A. Koziol

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  1. James A. Koziol
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Koziol, J.A. Multivariate tests for non-additivity. Statistical Papers 30, 27–37 (1989). https://doi.org/10.1007/BF02924306

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  • DOI: https://doi.org/10.1007/BF02924306

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