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John J. Gart, Robert E. Tarone, N. E. Day, D. P. Byar, The Relation between Score Tests and Approximate UMPU Tests in Exponential Models Common in Biometry, Biometrics, Vol. 39, No. 3 (Sep., 1983), pp. 781-786
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Gart et al. (1983) studied this question.
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