The problem is that of testing for a change of the mean in a sequence of independent normal random variables with the same variance. Well-known tests such as likelihood ratio tests, tests based upon cusums of recursive residuals, Pettitt’s test and the Chernoff-Zacks’ statistic are investigated again through their approximate power. For a given level, the computation of the thresholds and of the power functions is done using approximations of boundary crossing probabilities, as in

*D. Siegmund*’s preceding works, see e.g.: Sequential analysis. Tests and confidence intervals (1985;

Zbl 0573.62071). The approximation is much better than with the classical asymptotic theory and some numerical results are given; the conclusion about the comparison of the tests are unsurprising.