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sampling instrument

DefinitionChoosing which rows to read. The standard error of a sample mean falls as one over the square root of the sample size. Chapter 2 section 2.7.
ExampleReading 350000 of 2391361 rows is a 15 percent sample, and its mean has standard error the spread over the square root of 350000.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id sampling, kind instrument.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • Choosing which rows to read. A sample’s mean lies between its smallest and largest row, the standard error of the mean falls as one over the square root of the sample size, and a sample too thin to score is abstained on rather than averaged in.
  • Sampling and aggregation are design choices that decide what the reader can see, and the first strata run read 350000 of 2391361 rows and abstained on the strata with two rows and one.
Prior artnone recorded
Evidencelean/DataMiningAsObservation/StandardError.lean, lean/DataMiningAsObservation/Ensemble.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
00.51estimaten = 4n = 16n = 64n = 256the interval shrinks as one over root n
Which rows to read, and the standard error of the mean of those read.

Equation

none

Conditions

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Chapter 2 section 2.7 of Data Mining as Observation, with the first strata run’s sample in turboquant-pro/docs/STRATA_RFC.md:24-98.

Measurements

none

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/StandardError.lean, theorems se_pos, se_quarter, se_antitone, se_tendsto_zero, thousand_folds, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

lean/DataMiningAsObservation/Ensemble.lean, theorems average_between, sq_average_le, average_const, 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, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14.

Related

standard error; aggregation; bootstrap; seed; stratification.

See also

Book equations stated beside the entry’s terms, not defining it: 0.18, 8.2, 2.1.

Ledger rows that cite the entry’s records without naming it: NEG-14.

Sources-table rows that share a record with the entry without naming it: chapter 4 section 4.7, chapter 8 section 8.1, chapter 10 section 10.4.

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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