Exact power for normal location alternatives is obtained for the bivariate sign tests of Blumen [1] and Hodges [5]. A recursive scheme, used in conjunction with a computer, permits comparison of the two tests for sample sizes $n = 8(1)12$. Efficiency values relative to Hotelling's bivariate T² test are also obtained for the test of Hodges. Slight power differences are noted for the sign tests along with surprisingly high power when compared with the T².
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Jerome Klotz (1964) studied this question.
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