# How to test a directional hypothesis using ANOVA?

Everything I have read has indicated that when performing ANOVA, the null and alternative hypothesis are always the following:

• $H_0$: There is no difference in the means,
• $H_a$: There is a difference in the means.

But if I have a treatment and I expect, based on past experience or literature, that this treatment would perform better than the other, can the hypothesis with ANOVA ever be:

• $H_0$: A would equal or worse than B,
• $H_a$: A would be better than B?

I realize the above can be tested with a one-tailed $t$-test, but is the same hypothesis correct/possible for ANOVA, or is it a statistical no no?

-
It's correct and reasonable, but ANOVA looks at square of the effect, so you have to go back to the one-sided t-test. But with two treatments, the t-test and ANOVA are the same thing; the ANOVA F statistic is just $t^2$.