Related papers: Annotated Bibliography of Some Papers on Combining…
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. A diverse range of p-value combination…
We review the methods to combine several measurements, in the form of parameter values or $p$-values.
The two-trials rule in drug regulation requires statistically significant results from two pivotal trials to demonstrate efficacy. However, it is unclear how the effect estimates from both trials should be combined to quantify the drug…
This paper is meant as a contribution to the often debated subject of how to combine data which appear to be in mutual disagreement. As a practical example, the epsilon-prime/epsilon determinations have been considered.
The problem of combining p-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily…
We introduce the notion of p*-values (p*-variables), which generalizes p-values (p-variables) in several senses. The new notion has four natural interpretations: operational, probabilistic, Bayesian, and frequentist. A main example of a…
Fisher's method prescribes a way to combine p-values from multiple experiments into a single p-value. However, the original method can only determine a combined p-value analytically if all constituent p-values are weighted equally. Here we…
For Poisson distribution $Pois(n, \lambda)$ with $\lambda \gg 1$, $n \gg 1$ we propose to determine significance as $S = \frac{n_{obs}-\lambda}{\sqrt{\lambda}}$. The significance $S$ coincides up to sign with often used significance. For…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
Statistical significance of both the original and the replication study is a commonly used criterion to assess replication attempts, also known as the two-trials rule in drug development. However, replication studies are sometimes conducted…
This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of p-values without making any assumptions about their dependence structure. An old result by…
The customary use of P-values in scientific research has been attacked as being ill-conceived, and the utility of P-values has been derided. This paper reviews common misconceptions about P-values and their alleged deficits as indices of…
Testing effect size homogeneity is an essential part when conducting a meta-analysis. Comparative studies of effect size homogeneity tests in case of binary outcomes are found in the literature, but no test has come out as an absolute…
The effects of the experiment itself upon the obtained results and, especially, the influence of a large number of experiments are extensively discussed in the literature. We show that the important factor that stands at the basis of these…
Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…
Methods of merging several p-values into a single p-value are important in their own right and widely used in multiple hypothesis testing. This paper is the first to systematically study the admissibility (in Wald's sense) of p-merging…
P-value functions are modern statistical tools that unify effect estimation and hypothesis testing and can provide alternative point and interval estimates compared to standard meta-analysis methods, using any of the many $p$-value…
Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there…
As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant…
For a given testing problem, let $U_1,...,U_n$ be individually valid and conditionally on the data i.i.d.\ P-variables (often called P-values). For example, the data could come in groups, and each $U_i$ could be based on subsampling just…