The problem of approximating the power and significance levels of repeated significance tests (RST) and modified repeated significance tests (MRST) is considered. The method due to Siegmund in the special case of normal observations with known variance is generalized. The main advantages that are claimed for this method are two-fold. First, it can be used to approximate the power of RSTs. Second, it can also be used to approximate the power and significance levels of MRSTs. Numerical and Monte Carlo results are also given for the repeated $t$-test.
"Repeated Significance Tests for Exponential Families." Ann. Statist. 16 (4) 1643 - 1666, December, 1988. https://doi.org/10.1214/aos/1176351059