The efficiency of a family of tests is defined. Methods for evaluating the efficiency are discussed. The asymptotic efficiency is obtained for certain families of tests under assumptions which imply that the sample size is large.
Wassily Hoeffding. Joan Raup Rosenblatt. "The Efficiency of Tests." Ann. Math. Statist. 26 (1) 52 - 63, March, 1955. https://doi.org/10.1214/aoms/1177728592