# 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?

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## 1 Answer

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 $t^2$.

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ANOVA's F test is a generalization of the two sample t-test to cases with more than 2 treatments. –  suncoolsu Oct 1 '11 at 1:46
@suncoolsu - yes, but I thought it was clear that he was thinking anova in the case of 2 treatments. –  Karl Oct 1 '11 at 2:10
Dr. Broman, I was just adding to your statement (nothing else) –  suncoolsu Oct 1 '11 at 2:13
@suncoolsu - Ah yes; no worries; and please just "Karl" –  Karl Oct 1 '11 at 2:17
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