paired instrument
| Definition | Of a comparison, made on the same rows or seeds for both arms. Pairing helps exactly when the two arms covary. Chapter 0 section 0.9. |
|---|---|
| Example | Scoring both arms on the same 40 documents pairs the comparison, and the difference’s variance drops when the arms covary. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id paired, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | readscope/SPEC.md:806-857, readscope/calibration/records/c11c-operator-drift.json, lean/DataMiningAsObservation/Bootstrap.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- Of a comparison, made on the same rows or the same seeds for both arms, so that the difference is scored row by row. The variance of the difference is the sum of the variances less twice the covariance, so pairing helps exactly when the two arms covary.
- The paired null at rank two read 0.385 against 0.572 on fourteen of sixteen cells, and the encoder comparisons carry a paired bootstrap interval on each relation.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 0 section 0.9 and chapter 8 section 8.4 of Data Mining as
Observation, with the paired null in
readscope/SPEC.md:806-857.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 8 section 8.4 | C-11c paired null, rank 2 positional 0.385 vs null 0.572, 0.615 vs 0.224, 14 of 16 cells, scope 16 cells one 3B model 192 positions | readscope/SPEC.md:806-857;
readscope/calibration/records/c11c-operator-drift.json |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Bootstrap.lean,
theorems mean_sub, var_sub,
paired_lt_iff, cov_comm, 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, 4, 6, 8, 11, 12.
Related
bootstrap; confidence interval; seed; standard error; control.
See also
Book equations stated beside the entry’s terms, not defining it: 0.18, 8.2, 0.29.
Ledger rows that cite the entry’s records without naming it: NEG-14, GO-B-Llama, GO-B-Llama-rematch.
Sources-table rows that share a record with the entry without naming it: chapter 11 section 11.8, chapter 12 section 12.4.
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.