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A Multivariate Extension of Friedman's χ2r-Test

Thomas M. Gerig
Journal of the American Statistical Association
Vol. 64, No. 328 (Dec., 1969), pp. 1595-1608
DOI: 10.2307/2286091
Stable URL: http://www.jstor.org/stable/2286091
Page Count: 14
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A Multivariate Extension of Friedman's χ2r-Test
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Abstract

This paper deals with a multivariate extension of Friedman's χ2r-test. A rank permutation distribution and the large sample properties of the criterion are studied. The asymptotic relative efficiency (A.R.E.) for a sequence of translation alternatives is studied and bounds are given for certain special cases. It is shown that, under specified conditions, the A.R.E. of this test with respect to the likelihood ratio test is largest when the block dispersion matrices differ and can be greater than unity when the differences are large.

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