Combining p-values and random p-values

Combining independent tests is a key-problem in Meta Analysis and one way of doing it is to use the reported p-values, which can be regarded as independent standard uniform observations under the common null hypothesis. Therefore, the problem of combining independent tests is closely tied to testing the uniformity of the p-values. Continuing the investigation initiated by Gomes et al. (2009), we present two simulation studies. In the first one we study the behaviour of pseudo-p-values, augmenting the sample of p-values using an auxiliary Beta(1, q), q ∈ [0.5, 3], population; q = 3, namely, favors the generation of values close to zero, needed for an overall rejection of the null hypothesis. In the second case we study the behaviour of pseudo-p-values when these are internally generated, using an extension of the family of densities fX_m, m ∈ [-2, 0), introduced in Gomes et al. (2009), so that slopes m ∈ [0, 2] are included. The results of the first study are by far better than those reported in Gomes et al. (2009), the proportion of rejections of the combined uniformity test increases with the number of pseudo-p-values. The results of the second study also show an increase of the power with data augmentation, specially when m > -1.