4
$\begingroup$

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?

$\endgroup$
3
$\begingroup$

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 $t^2$.

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.