{
  "aliases": [
    "Simpson reversal"
  ],
  "status": "shipping",
  "advantages": [],
  "limitations": [],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-10-20",
  "slug": "simpsons-paradox",
  "term": "Simpson's paradox",
  "definition": "Simpson's paradox is a change or reversal in an association when subgroup results are combined or separated.",
  "note": "Combining strata can change the comparison because the groups being compared contribute different proportions to those strata. Conditioning is not automatically the right interpretation: Simpson's 1951 examples emphasize that the meaning of the classifications matters. [simpson1951]\n\nIn Hesela's invented drive-exposure example, cohort A has higher AFR in both age bands (2% versus 1%, and 6% versus 5%) but lower pooled AFR (2.4% versus 4.6%). A supplies 90% of its exposure in the younger band; B supplies 90% in the older band. These are fixed arithmetic inputs, not evidence about a vendor. Shared 50/50 exposure weights give 4% for A and 3% for B. [hesela-composition]\n\nKeep failures, drive-days, age boundaries and reference weights visible. An aggregate describes its own composition; standardization changes the comparison target and does not establish causation or remove unmeasured differences. [hesela-composition]",
  "related": [
    "afr",
    "drive-day",
    "direct-standardization"
  ],
  "citations": [
    {
      "id": "simpson1951",
      "title": "E. H. Simpson (1951): The Interpretation of Interaction in Contingency Tables, JRSS B 13(2), 238-241, sections 8-11",
      "url": "https://math.bme.hu/~marib/bsmeur/simpson.pdf",
      "accessed": "2026-10-20"
    },
    {
      "id": "hesela-composition",
      "title": "Hesela: AFR, fleet composition and common-weight comparison (synthetic example)",
      "url": "https://hesela.com/analyses/afr-rate-not-probability/#composition",
      "accessed": "2026-10-20"
    }
  ]
}