Calculating standard error for funnel plots

Question

I'm a programmer, with a decent but not-expert knowledge of stats, and I'm working through these instructions for how to create funnel plots.

I know that there are better ready-made tools (e.g. R) for generating funnel plots, but these instructions are helping to understand the basics of funnel plots.

So, my question: Step 4 in the instructions refers to a 'special kind' of standard error. Why is it special?

And, can I validly copy the way standard error is calculated in these instructions to build a funnel plot for any dataset that includes raw population count and raw incident count?

Answer 1

Generally a variance for a mean of $n$ iid $X_i$s is ${\rm var}(X_i)/n$. Now since the $X_i$s are Bernoulli with success probability $p$, ${\rm var}(X_i)$ has a special form. It is $p(1-p)$. So each of the $23$ means have variance of the special form $p(1-p)/n$ and the standard error is the square root of that.

Answer 2

They call it "special" because the example in the tutorial deals with rates. More often funnel plots are drawn for values that come from normal distributions. In both cases you divide the standard deviation by the square root of the sample size, but in the case of normal distributions you take a different formula (mean squared deviation) to calculate it as in the case of rates (p(1-p)).