An accurate test for homogeneity of odds ratios based on Cochran's Q-statistic

Background: A frequently used statistic for testing homogeneity in a meta-analysis of K independent studies is Cochran's Q. For a standard test of homogeneity the Q statistic is referred to a chi-square distribution with K - 1 degrees of freedom. For the situation in which the effects of the studies are logarithms of odds ratios, the chi-square distribution is much too conservative for moderate size studies, although it may be asymptotically correct as the individual studies become large. Methods: Using a mixture of theoretical results and simulations, we provide formulas to estimate the shape and scale parameters of a gamma distribution to t the distribution of Q. Results: Simulation studies show that the gamma distribution is a good approximation to the distribution for Q. Conclusions: : Use of the gamma distribution instead of the chi-square distribution for Q should eliminate inaccurate inferences in assessing homogeneity in a meta-analysis. (A computer program for implementing this test is provided.) This hypothesis test is competitive with the Breslow-Day test both in accuracy of level and in power

The neutron and its role in cosmology and particle physics

Experiments with cold and ultracold neutrons have reached a level of precision such that problems far beyond the scale of the present Standard Model of particle physics become accessible to experimental investigation. Due to the close links between particle physics and cosmology, these studies also permit a deep look into the very first instances of our universe. First addressed in this article, both in theory and experiment, is the problem of baryogenesis ... The question how baryogenesis could have happened is open to experimental tests, and it turns out that this problem can be curbed by the very stringent limits on an electric dipole moment of the neutron, a quantity that also has deep implications for particle physics. Then we discuss the recent spectacular observation of neutron quantization in the earth's gravitational field and of resonance transitions between such gravitational energy states. These measurements, together with new evaluations of neutron scattering data, set new constraints on deviations from Newton's gravitational law at the picometer scale. Such deviations are predicted in modern theories with extra-dimensions that propose unification of the Planck scale with the scale of the Standard Model ... Another main topic is the weak-interaction parameters in various fields of physics and astrophysics that must all be derived from measured neutron decay data. Up to now, about 10 different neutron decay observables have been measured, much more than needed in the electroweak Standard Model. This allows various precise tests for new physics beyond the Standard Model, competing with or surpassing similar tests at high-energy. The review ends with a discussion of neutron and nuclear data required in the synthesis of the elements during the "first three minutes" and later on in stellar nucleosynthesis.Comment: 91 pages, 30 figures, accepted by Reviews of Modern Physic

Asymptotics of guarded weights of evidence

A test at a significance level a yields a decision which can be quantified by assigning the value 1 if the null hypothesis is rejected and 0 otherwise. The theory of guarded weights of evidence for the alternative (Blyth and Staudte, 1995. Statist. Probab. Lett. 23, 45–52) generalizes the usual Neyman–Pearson theory by considering L2 norm risk. The result is a weight of evidence for the alternative which preserves the bound a on the risk of making a type I error and which takes values between 0 and 1. In this paper we establish, under quite general conditions, the asymptotic convergence of guarded weights of evidence. Both fixed and local alternatives are considered. These results are then applied to yield a consistency theorem, a version of the central limit theorem for guarded weights of evidence and an asymptotic result for guarded weights of evidence based on the F-statistic which in turn is applied to one-way ANOVA

Erratum to:On the moments of Cochran's Q statistic under the null hypothesis, with application to the meta-analysis of risk difference (Res Syn Meth., (2011), 2, (254-270), 10.1002/jrsm.54)

This article was published in Volume 2, Issue 4, December 2011 of Research Synthesis Methods (Kulinskaya et al.1). Supporting information files were added. The online version of this article has been corrected