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.
Cited by¶
12 citations across 12 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.
- 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.
- 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.
- Among mild patients: A recovers 81 of 87 (93%), B recovers 234 of 270 (87%) — A wins.
- 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.
- 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.
Domain-specific¶
Mechanisms¶
- Aggregation Bias Audit
- It does reverse: the flagship hospital looks worse than a community clinic on the raw pooled rate, but within every severity tier it does better — a Simpson-style reversal
This sourceFormalizes Simpson’s paradox as a reversal between pooled and conditionally stratified comparisons.
- It does reverse: the flagship hospital looks worse than a community clinic on the raw pooled rate, but within every severity tier it does better — a Simpson-style reversal
- Cumulative Volume Cohort Analysis
- Aggregating cohorts carelessly invites Simpson's paradox — a decline visible within every subgroup can reverse or vanish once the groups are pooled.
This sourceDefines Simpson's paradox as a reversal in the pooled comparison despite the same-direction comparison within each conditioned subgroup.
- Aggregating cohorts carelessly invites Simpson's paradox — a decline visible within every subgroup can reverse or vanish once the groups are pooled.
- Drill-Down Root Signal Review
- Its failure mode is that disaggregation is not causation, and a naïve drill can reverse itself — Simpson's paradox
This sourceFormalizes Simpson’s paradox, in which an unconditional association can reverse under each level of a conditioning variable.
- Its failure mode is that disaggregation is not causation, and a naïve drill can reverse itself — Simpson's paradox
- Executive-Level Summary
- Its failure mode is that a summary which compresses without disclosing can hide a subgroup reversal — a case where the aggregate points one way while an important segment points the opposite, the situation named by Simpson's paradox.
This sourceFormalizes Simpson's paradox as a reversal between aggregate and subgroup-conditioned comparisons.
- Its failure mode is that a summary which compresses without disclosing can hide a subgroup reversal — a case where the aggregate points one way while an important segment points the opposite, the situation named by Simpson's paradox.
- Gradient Dashboard
- A citywide average can look perfectly flat even as one district's exposure climbs — the classic shape of Simpson's paradox, where a trend visible in every subgroup disappears once the subgroups are pooled.
This sourceShows how a trend present within conditioned subgroups can disappear or reverse when the groups are aggregated.
- A citywide average can look perfectly flat even as one district's exposure climbs — the classic shape of Simpson's paradox, where a trend visible in every subgroup disappears once the subgroups are pooled.
- Group-Stratified Validation
- Its strength is defeating the specific illusion that an aggregate creates: a pooled metric can look excellent while reversing inside subgroups, and only disaggregation exposes it.
This sourceFormalizes Simpson’s paradox as a reversal between pooled and conditionally stratified comparisons.
- Its strength is defeating the specific illusion that an aggregate creates: a pooled metric can look excellent while reversing inside subgroups, and only disaggregation exposes it.
- Local / Global Analysis
- The canonical case is Simpson's paradox, where a trend present in every subgroup disappears or flips when the groups are combined.
This sourceAnalyzes Simpson's paradox, in which subgroup associations can disappear or reverse after aggregation.
- The canonical case is Simpson's paradox, where a trend present in every subgroup disappears or flips when the groups are combined.
- Multi-Level Model Check
- The relationship reverses when the level of aggregation changes.
This sourceShows that an association can reverse between conditioned subgroups and the corresponding aggregated population.
- The relationship reverses when the level of aggregation changes.
Verification¶
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