Simpson's paradox concept
| Definition | A reversal of a comparison when groups are combined, which the book reads as an aggregation quotient. Chapter 5. Also Simpson. |
|---|---|
| Example | A treatment better in both the young and the old can be worse overall when the two groups are mixed unequally. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id simpsons-paradox, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Simpson.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A pooled rate is the size-weighted mean of the group rates, so pooling is a quotient that declares the group labels irrelevant, and it can reverse a comparison that holds in every group when the groups have different sizes under the two arms.
- With equal group sizes under both arms the pooled comparison agrees with a comparison that holds in every group. The book’s answer is the min-over-strata verdict, which never pools.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
TSK chapter 5 on objective measures, as chapter 5 section 5.5 of Data Mining as Observation reads it, an aggregation quotient.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 5 section 5.1 to 5.3, 5.5 | support, confidence, lift, the Apriori principle, FP-growth, closed and maximal itemsets, objective measures, Simpson’s paradox, cross-support | TSK 2e chapter 5 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Simpson.lean,
theorems pooled_eq_weighted, reversal,
no_reversal_of_equal_sizes, at observation-data-mining
f3914f0; what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation primer S, chapters 5.
Related
quotient; min-over-strata; abstention; deployment mismatch.
See also
Book equations stated beside the entry’s terms, not defining it: 10.7.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.