What is the Wilson interval?
The Wilson interval is a method for calculating the plausible range around a measured rate that stays sensible even when the rate is small or the sample is limited, unlike the textbook formula most people default to.
Most people compute a margin of error with a simple formula built for rates near 50%. That formula breaks down at the edges: apply it to a citation rate of 4% from a modest sample and it can produce a lower bound below zero, which is meaningless for a rate that can't go negative. The Wilson interval is a different calculation that adjusts for exactly this, producing a range that stays within 0 and 100% and behaves reasonably even with a small sample or a rate near either extreme.
This matters for AI visibility because most of the rates involved, citation rates, mention rates, block rates, sit low, often under 20%, which is precisely where the simple formula misleads. A reported range of "12%, plus or minus 15 points" using the naive method is a sign the underlying math wasn't suited to the number it was applied to.
The Wilson interval isn't a fancier way to make a number look more scientific, it's the version of the calculation that's actually valid for the kind of low, sample-limited rate that AI visibility measurement produces constantly.
Related
- Confidence bandA confidence band is the range around a measured score that reflects how much of the number is sampling noise rather than signal.
- Margin of errorA margin of error is the range around a measured number, such as a citation rate, within which the true value probably falls given the sample it came from.
- Sample sizeSample size is the number of prompts, queries, or pages included in a single measurement, and it sets how much random noise a result carries.
- Sampling varianceSampling variance is the run-to-run variation you get from asking a language model the same question more than once.
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