If I have some data*, and want to test the hypothesis that it has a given mean $\mu_0$, I know of the possibility of using a one-sample t-test. Here, $\mu_0=0$ could be the null-hypothesis of a treatment having no effect, for example. (*let’s assume the data is normally distributed around its mean)
Now, suppose I now have several such datasets, and am interested in the question “Which of these groups have a mean different to $\mu_0$”. I could run several of these t-tests against $\mu_0$, but then I increase Type-I errors due to the multiple comparisons. A Bonferroni correction seems like a valid but very inelegant and too conservative solution.
I learned of the ANOVA as a generalization of the two-sample t-tests to compare their means, but here the question is different: “Do any two of these groups have different means?”
My question is: are there any generalizations of one-sample t-tests that control for multiple comparisons, other than a Bonferroni correction?