I am using Fisher's combined test to fuse several different independent tests. I have a problem understanding the results in some cases.
Example: Let's say I run two different tests, both with the hypothesis that mu is smaller than 0. Let's say that n is identical and the two samples have the same calculated variance. However, let's assume that one test yielded an average that is $1.5$ and the other is $-1.5$. I will get two complementing p-vals (e.g., $0.995$ & $0.005$). Interestingly, combining the two brings about a significant $p$-value in the Fisher test: $p=0.0175$.
This is weird because I could have chosen the exact opposite test $(\mu>0)$ and sampled results - and still get $p=0.0175$. It's almost as if the Fisher test does not take the direction of the hypothesis into account.
Can anyone explain this?