diff --git a/docs/what_combine_does/statistical_tests.md b/docs/what_combine_does/statistical_tests.md index 3a50d152c5d..d0b33396b27 100644 --- a/docs/what_combine_does/statistical_tests.md +++ b/docs/what_combine_does/statistical_tests.md @@ -225,31 +225,6 @@ Where $p_{\mu}$ is the usual probability of observing the observed value of the Using the $\mathrm{CL}_{s}$ criterion fixes the issue of setting limits much stricter than the experimental sensitivity, because for values of $\mu$ to which the experiment is not sensitive the distribution of the test statistic under the signal hypothesis is nearly the same as under the background hypothesis. Therefore, given the use of opposite tails in the p-value definition, $p_{\mu} \approx 1-p_{b}$, and the ratio approaches 1. - - Note that this means that a limit set using the $\mathrm{CL}_{s}$ criterion at a given $\mathrm{CL}$ will exclude the true parameter value $\mu$ with a frequency less than the nominal rate of $1-\mathrm{CL}$. The actual frequency at which it is excluded depends on the sensitivity of the experiment to that parameter value.