On Fisher's Method of Combining p‐Values

The problem of combining p‐values from independent experiments is discussed. It is shown that Fisher's solution to the problem can be derived from a “weight‐free” method that has been suggested for the purpose of ranking vector observations (Biometrics 19: 85–97, 1963). The method implies that the value p = 0.37 is a critical one: p‐values below 0.37 suggest that the null hypothesis is more likely to be false, whereas p‐values above 0.37 suggest that it is more likely to be true.