Let's say I want to answer the question if smokers vs nonsmokers have different levels of Gene A. This seems like an obvious two-sided test. However, if I have multiple studies and I want to combine their p-values using Fisher's method, I now am confused how to accomplish this since Fisher's method is one-sided.
For example, let's say I am using a Wilcoxon Two-Sample rank sum test, and achieve the following results from 4 studies:
- Study 1: Smokers have higher Gene A, p = 0.02
- Study 2: Smokers have higher Gene A, p = 0.04
- Study 3: Smokers have lower Gene A, p = 0.02
- Study 2: Smokers have lower Gene A, p = 0.04
Because these are two-sided probabilities, I could not simply use Fisher's method on these p-values (would lose directionality), so instead I could calculate new p-values using a one-sided Wilcoxon test.
Testing the hypothesis that Gene A is greater in smokers, the data may instead look like this:
- Study 1: Testing if Smokers have higher Gene A, p = 0.01
- Study 2: Testing if Smokers have higher Gene A, p = 0.02
- Study 3: Testing if Smokers have higher Gene A, p = 0.99
- Study 2: Testing if Smokers have higher Gene A, p = 0.99
If I tried to use Fisher's method I get Χ2 = 17.07459, df =8, p = 0.029. This is not the result I would expect, as I would expect the p-values to "cancel" out to a large extent.
Regardless of that, this requires me to have a notion of the appropriate direction to construct my Wilcoxon test, when in in reality I want a "two-sided" approach--I do not know if it will be greater or lower.
Is there a way to generate a two-sided combined p-value (ie one that I could construct from a set of 4 one-sided p values in one direction, and 4 corresponding one-sided p values in the other direction)?