{
  "schema": "vedokrok.public-item.v1",
  "release_id": "MHC-RPUB-20260920-75ad787a",
  "url": "/knowledge/subtract-the-overlap-before-combining-counts",
  "id": "MHC-D-RESEARCH-0257",
  "version": "0.1.0",
  "title": "Subtract the overlap before combining counts",
  "summary": "Two category totals do not necessarily describe two different crowds.",
  "kind": "protocol",
  "body": "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.",
  "limits": [
    "More than two overlapping groups require fuller reconciliation; subtracting only one overlap is insufficient."
  ],
  "topics": [
    "union-numerical-reasoning"
  ],
  "intents": [],
  "source_ids": [
    "RS-A805F8FC957ACEF5"
  ],
  "evidence": [
    {
      "claim": "The size of a union equals the two group counts added together minus their overlap.",
      "source_id": "RS-A805F8FC957ACEF5",
      "role": "supports",
      "note": "The overlap must use the same identities, period and eligibility definition as the two groups.",
      "locator": "Addition rule applied to finite counts"
    }
  ],
  "use_when": [
    "People, cases or items can appear in more than one category."
  ],
  "avoid_when": [
    "More than two overlapping groups require fuller reconciliation; subtracting only one overlap is insufficient."
  ],
  "example": "Eighteen people attended one session, twelve attended another and five attended both: twenty-five different people attended at least one.",
  "check": "The combined result counts each eligible identity once.",
  "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."
  ],
  "sources": [
    {
      "id": "RS-A805F8FC957ACEF5",
      "title": "Introductory Statistics 2e, 3.3: Two Basic Rules of Probability",
      "url": "https://openstax.org/books/introductory-statistics-2e/pages/3-3-two-basic-rules-of-probability"
    }
  ],
  "relations": [
    {
      "from": "MHC-D-RESEARCH-0257",
      "to": "MHC-D-RESEARCH-0244",
      "type": "useful_with",
      "url": "/knowledge/ask-what-the-percentage-is-a-percentage-of"
    }
  ],
  "collections": [
    {
      "id": "RC-D976097B2A42D9AC",
      "title": "Make the numbers answer the right question",
      "url": "/collections/make-the-numbers-answer-the-right-question"
    }
  ]
}