I have a bunch of independent p-values and now I want to combine them using the Fisher's method. Each of the individual p-values is coming from a one-sided test. I am just a little bit confused about the "side" of the Fisher's method test, i.e. when I calculate the Fisher's method p-value in R, I use:
1 - pchisq( -2*sum(log(p-values)), df)
df = 2*length(p-values).
Is this a one-sided test? It should be because when the test statistic
-2*sum(log(p-values)) is much smaller than
df, then the Fisher's p-value is close to 1. There should be a problem here, right? How shall I (or should I?) reject the null if my test statistic is very small? I am just uncomfortable with the "close-to-1" p-values.
By the way, I use the method for testing model goodness-of-fit, and a small p-value is to indicate model lack-of-fit.