This paper examines the loss of power when using tests based on the assumption that the variable being sampled has a "complete" normal distribution when in fact the distribution is a "truncated" one. The cases considered here are for small sample sizes and "symmetric" truncation, while the hypothesis considered is the one-sided testing for the mean of a normal distribution. Some tables are computed and it appears that an appreciable loss occurs only in the size of the test. The loss in power is found to decrease very rapidly with the distance of the alternative value of the mean from the one tested and also with the distance of the truncation from the mean.
"Truncation and Tests of Hypotheses." Ann. Math. Statist. 30 (1) 230 - 238, March, 1959. https://doi.org/10.1214/aoms/1177706378