The present paper is concerned with the power function of the classical tests associated with the normal distribution. Proofs of Hsu, Simaika, and Wald are simplified in a general manner applicable to other tests involving the normal distribution. The set theoretic structure of several tests is characterized. A simple proof of the stringency of the classical test of a linear hypothesis is given.
"The Power of the Classical Tests Associated with the Normal Distribution." Ann. Math. Statist. 20 (4) 540 - 551, December, 1949. https://doi.org/10.1214/aoms/1177729946