A proportion with an interval, in short

Added a note to A proportion with an interval today, which is a good excuse to say the short version here.

A percentage without a denominator is not a finding. The Wilson interval behaves sensibly at small n, where the normal approximation falls apart.

What makes it a pattern rather than a tip is that the wrong version is the one you write naturally. It reads correctly, it runs, and it returns something. The failure is in the result, not in the execution — which means the only defence is recognising the shape before you are in it.

Two datasets on this site have the shape built in: ab-test-checkout and flight-delays. Both are small enough to run the broken version, see the number, then run the corrected one and see it change.

It lives under measuring because the arithmetic is fine and the interpretation is not, which is the harder failure to catch — nothing about the output looks wrong.

The long-form treatment is in the course (describing-a-column, uncertainty-and-sampling); the pattern page is the version to read at 4pm with a query open.

The pattern page has the version that holds and the version that looks right and is not, side by side. Reading them together is the point; either one alone is just code.