Binomial funnel control limits (source code)

= Binomial funnel control limits
{title2=$p_0\pm z_{1-\alpha/2}\sqrt{p_0(1-p_0)/n}$}

The displayed pointwise <control limits> follow from the <normal approximation> to an observed <binomial proportion>. Clip plotted limits to the probability range. Their nominal coverage is approximate and can be poor for small expected counts; exact binomial tails give a discrete alternative. Pointwise coverage does not provide simultaneous coverage of all hospitals; use <Bonferroni correction> or another <familywise error rate> procedure when that is the required guarantee.