On Simpson's Paradox and the Sure-Thing Principle.

Blyth, C. R. (1972). On Simpson's Paradox and the Sure-Thing Principle. Journal of the American Statistical Association, 67(338), 364-366.

Type

Journal article

Intellectual base

Primary research

Year

1972

DOI

10.1080/01621459.1972.10482387

Link

https://doi.org/10.1080/01621459.1972.10482387

Cited from

mathematics, statistics_experimental_design

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Partition Dependence of Aggregates
  • This is not measurement error or a bad sample — it is the intrinsic consequence of the partition, demonstrable by the algebra of conditional expectations: the marginal association is a severity-weighted blend of the conditional associations plus a term driven entirely by how treatment and outcome each vary between the pooled groups.

    This sourceFormal treatment showing the marginal association as a weighted blend of conditionals, with the between-group term driving reversal.

• Simpson–Yule Effect
  • Among mild patients: A recovers 81 of 87 (93%), B recovers 234 of 270 (87%) — A wins.

    This sourceClassic exposition giving the two-stratum construction in which the within-stratum winner reverses on pooling; the canonical formal statement of the aggregation reversal.

• Simpson's Paradox
  • A cluster of cousin patterns travels with it and should be flagged wherever it appears — Yule–Simpson reversal in two-way tables, Lord's paradox in change scores, collider and M-bias as the over-conditioning opposite, Berkson's paradox as selection-induced association — all sharing the family resemblance that aggregation and conditioning choices carry causal commitments.

    This sourceIntroduces the modern name 'Simpson's paradox' and situates it among related amalgamation/reversal anomalies in contingency tables.

Domain-specific

• Sure-thing principle
  • … observable transfers from A canonical instance directly demonstrates that the conditioning event and its complement exhaust the relevant states and the same pairwise preference holds in both. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, or implementation..

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