[6gvONxR4sf7o]

Is the likelihood ratio test more general? I thought that one of the benefits of the usual NHST framework was that you only need the distribution of your stat under the null. With LRT don't you need the distribution under both the null and the alternative? How do you frame a null of mu = 0 against an alternative of mu != 0 with x ~ D_mu in this way?

[cygaril]

You don't necessarily need the distribution under the alternative to determine the values for which the likelihood ratio will be highest. In your example, the tails will be the areas of maximum likelihood for any (symmetric) alternative.

[6gvONxR4sf7o]

Huh, TIL. Thanks :)