Abstract Combining p-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are difficult to combine. For simple null hypotheses, given any non-parametric combination method which has a monotone increasing acceptance region, there exists a problem for which this method is most powerful against some alternative. Starting from this perspective and recasting each method of combining p-values as a likelihood ratio test, we present theoretical results for some of the standard combiners which provide guidance about how a powerful combiner might be chosen in practice. In this paper we consider the problem of combining independent tests as for testing a simple hypothesis in case of log-normal distribution. We study the six free-distribution combination test producers namely; Fisher, logistic, sum of p-values, inverse normal, Tippett’s method, and maximum of p-values. Moreover, we studying the behavior of these tests via the exact Bahadur slope. The limits of the ratios of every pair of these slopes are discussed as the parameter and As the maximum of p-values is better than all other methods, followed in decreasing order by the inverse normal, logistic, the sum of p-values, Fisher, and Tippett’s procedure. Whereas, the worst method the sum of p-values and the other methods remain the same, since they have the same limit. In the end, a numerical study to investigate these comparisons behavior in different values of It will be shown that the inverse normal method is the best method followed by the logistic method, the Fisher method and the sum of p-values method.
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