Test the Overall Significance of p-values by Using Joint Tail Probability of Ordered p-values as Test Statistic

Fisher’s combined probability test is the most commonly used method to test the overall significance of a set independent p-values. However, it is very obviously that Fisher’s statistic is more sensitive to smaller p-values than to larger p-value and a small p-value may overrule the other p-values and decide the test result. This is, in some cases, viewed as a flaw. In order to overcome this flaw and improve the power of the test, the joint tail probability of a set p-values is proposed as a new statistic to combine and make an overall test of the p-values. Through the development of a method and a practical application, this study reveals that the new method has plausible properties and more power.