I have a dataset which has the following numbers:
Case + Case -
Intervention + 20 23
Intervention - 0 110
The two tailed p value for Fisher's Exact test is 0.0448. Therefore the null hypothesis can be rejected. However, the one tailed p value is 0.03.
Can I claim significance that the intervention is associated with the cases? One opinion I have received is that I cannot, as 2x0.03 > 0.05.
Then I am in the situation that I can reject the null hypothesis, but cannot accept any other?
Patrick
For the data you posted I don't get the p-values you stated.
Note that for Fisher's test, Pr(|OR|>1) ≠ 2*Pr(OR1).
Oh, sorry, the data should read:
Case + Case -
Intervention + 20 110
Intervention - 0 23
The test, as you performed it, is not to "accept a hypothesis". It is only to "reject the null". The one-sided cases still are used to just "reject the null", but the rejection is done only for a particular sign of the estimate. If the sign is not in the "right direction", you don't reject the null, so you don't interpret the results. This makes sense if the direction of the effect must be in a certain direction, and if your data would suggest a change in the opposite direction, it is clear that this observation must be due to some unlucky circumstance (unfortunate sampling).
If the intervention can have a positive or a negative effect, then you should be interested to interpret the sign of the observed OR, that is, if it is above or below 1 (as either result can possibly be due to the intervention). Thus, I think you would only look at the two-sided test.
Rejecting the null with p 1.
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