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

• You might also find it useful to read the definition of p-value at Wikipedia (the definition is right at the start). – Glen_b -Reinstate Monica May 21 '13 at 12:02
• 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 =) – Zewz May 21 '13 at 15:06

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.

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