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Okay, this might seem like a stupid question and it sure feels that way. And I have probably just lost myself by overthinking it or something, but here goes:

In Cohrans C-test you take the ratio between the largest variance in a set of populations divided by the sum of all variances. This ratio is the test statistic for which you can look up tabulated p-values, and reject or accept $H_0$. This comes straight from examples from a book (A.J. Underwood, Experiments in ecology).

$H_0 = $The populations variances are equal
$H_1 =$ The variances are heterogeneous
$\text{If: } P_{observed} < P_{critical} \rightarrow \text{Accept } H_0 $

In an ANOVA the $H_0$ is that the two (or whatever number) compared populations have equal variances, thus being the logical opposite of $H_1$ (that at least two means significantly differ). According to my course and a lot of examples:
$\text{If: }P_{observed} < P_{critical} \rightarrow Reject \space H_0. $

This doesn't make sense at all, so please tell me where I am wrong!

PS. I did try to look around the community for an answer, but I would like to have this specific issue explained. DS

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  • $\begingroup$ You might also find it useful to read the definition of p-value at Wikipedia (the definition is right at the start). $\endgroup$ – Glen_b May 21 '13 at 12:02
  • $\begingroup$ Yeah I did, but you know how it is when you sit with a problem too long, or with something that you know that you know, but still can't do it. Anyway, my eyes were opened =) $\endgroup$ – Zewz May 21 '13 at 15:06
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You've got a couple things confused. First, we never *accept $H_0$", we either reject it or fail to reject it.

Second, if you want to word it in terms of P, then the procedure is always:

If $P_{\text{observed}} < P_{\text{critical}}$ then reject $H_0$, otherwise, fail to reject.

but if you word it in terms of test statistics then it's the other way round, e.g. for an F (which would be used in ANOVA)

If $F_{\text{observed}} > F_{\text{critical}}$ then reject $H_0$, otherwise, fail to reject.

this is because the probability of getting a particular test statistic, given that $H_0$ is true, declines as the test statistic gets farther from 0.

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  • $\begingroup$ Alright, so I lost myself among the difference of test statistics and P-values. Thanks for the answer, a real life(mind?)-saver! $\endgroup$ – Zewz May 21 '13 at 11:07

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