Protocol
Subtract the overlap before combining counts
Two category totals do not necessarily describe two different crowds.
When it fits
- People, cases or items can appear in more than one category.
When to avoid it
- More than two overlapping groups require fuller reconciliation; subtracting only one overlap is insufficient.
Why it matters
To count the union of two groups, add their counts and subtract the overlap counted twice. Match identities and the observation period before combining them. A bigger total is not an improvement when it is made of repeated people.
Steps
- Define membership in each group for the same scope.
- Identify records or people that belong to both.
- Calculate A plus B minus the intersection, or count unique identities directly.
An example
Eighteen people attended one session, twelve attended another and five attended both: twenty-five different people attended at least one.
Check your result
The combined result counts each eligible identity once.
Keep this limit in mind
- More than two overlapping groups require fuller reconciliation; subtracting only one overlap is insufficient.
Connected ideas
Useful withAsk what the percentage is a percentage of
Evidence and sources
Supports
The size of a union equals the two group counts added together minus their overlap.
The overlap must use the same identities, period and eligibility definition as the two groups.
Introductory Statistics 2e, 3.3: Two Basic Rules of Probability · Addition rule applied to finite counts