Kendall correlation concept
| Definition | The fraction of item pairs two rankings order the same way, minus the fraction they order differently. Equation 0.15. Also Kendall, rank correlation, rank agreement. |
|---|---|
| Example | Rankings (1, 2, 3) and (1, 3, 2) agree on two pairs and disagree on one, Kendall tau one third. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id kendall-correlation, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.15. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Kendall.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.15.
\[\tau=\frac{\#\{\text{concordant pairs}\}-\#\{\text{discordant pairs}\}}{n(n-1)/2}.\]
Conditions
- The fraction of item pairs two rankings order the same way minus the fraction they order differently. It lies between minus one and one, it is one when no pair disagrees, and since it depends only on the orderings a strictly increasing transform of either score leaves it unchanged.
- It is the rank-agreement statistic the rank certificate bounds from below, and a floor on it is a floor on the consumer’s rankings, not on any distance.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Kendall, a new measure of rank correlation, 1938, as chapter 0 section 0.9 states it, and the rank certificate’s statistic in readscope and openvector-bench.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Kendall.lean,
theorems not_both, card_add_le,
tau_mem, concordant_comp,
discordant_comp, tau_comp,
discordant_self, 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 0, 1, 8, 11.
Related
rank certificate; rank-faithful; Monotone Invariance Theorem; recall at k.
See also
Book equations stated beside the entry’s terms, not defining it: 11.2.
Ledger rows that cite the entry’s records without naming it: GO-B-Llama, GO-B-Llama-rematch.
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.