Fig 2. Combining functions’ rejection regions.

Rejection regions at significance level 0.15 for the Tippett (blue, dashed), Liptak (green, dotted) and Fisher (red, continuous) functions in combining two independent p-values. The rejection regions are the areas below the respective lines. The Tippett function rejects the global null-hypothesis if at least one of the two partial tests is significant (violet and orange areas); in contrast, the Liptak function can reject the global null hypothesis if both partial tests are not significant, but their combination is (yellow area). However, the presence of a single, extremely high p-value will force the Liptak function to accept the global null hypothesis (orange areas). The Fisher function has an intermediate behavior between the previous two.