On combining significances. Some trivial examples

Abstract

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 experiments which measure the same quantities the natural but not unique rule for significance combining is $S_{comb}(S_1, S_2) = \frac{S_1\sigma_1+S_2\sigma_2}{\sqrt{\sigma^2_1+\sigma^2_2}}$, where $\sigma_1$ and $\sigma_2$ are variations. We also propose the rule for significances combining for the case with systematic errors.