The Observation Theory EncyclopediaFrom TSKAboutBy kindBy chapterBy Lean fileLedgerProvenance

paired instrument

DefinitionOf 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.
ExampleScoring both arms on the same 40 documents pairs the comparison, and the difference’s variance drops when the arms covary.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id paired, kind instrument.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • 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.
Prior artnone recorded
Evidencereadscope/SPEC.md:806-857, readscope/calibration/records/c11c-operator-drift.json, lean/DataMiningAsObservation/Bootstrap.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
00.51estimatesame rows, two arms
The same rows or seeds in both arms.

Equation

none

Conditions

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.

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