control instrument

Definition	A comparison arm that should not show the effect, run beside the arm that should. A control that passes the bar makes the bar vacuous. Chapter 8 section 8.4.
Example	The first smooth-field control read 2.804 and was controlling for nothing; the second attempt read 0.184.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `control`, kind instrument.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 8.3.
Assumptions and scope	A comparison arm that should not show the effect, run beside the arm that should. A control that passes the bar makes the bar vacuous, so a claim names its control and reports both, and an isotropic control collapses the flip because there is no direction to read. The first smooth-field control read 2.804 and was controlling for nothing, because the gradient it was compared against was piecewise constant, and the second attempt read 0.184.
Prior art	none recorded
Evidence	`geometric-observation/claims/LEDGER.md`, `geometric-observation/chapters/ch07_cost.md`, `lean/DataMiningAsObservation/NullModel.lean`, `lean/DataMiningAsObservation/Bar.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

An arm that should show no effect, run beside the one that should.

Equation

Book equation 8.3.

\[\Pr[\text{at least one of } m\text{ null tests passes}]=1-(1-\alpha)^{m},\qquad \alpha_{\mathrm{Bonferroni}}=\frac{\alpha}{m}.\]

Conditions

A comparison arm that should not show the effect, run beside the arm that should. A control that passes the bar makes the bar vacuous, so a claim names its control and reports both, and an isotropic control collapses the flip because there is no direction to read.
The first smooth-field control read 2.804 and was controlling for nothing, because the gradient it was compared against was piecewise constant, and the second attempt read 0.184.

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

Ledger

none

First stated

Chapter 8 section 8.4 of Data Mining as Observation, with the negative control in constraint-gap-measurements/notes/negative_control.md:1-50.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 4 section 4.2	GO-6, d 8 and r 4, output at or below surrogate at or below reconstruction at every rate, about 500 times, gap 0.41 to 0.005, isotropic control collapses	`geometric-observation/claims/LEDGER.md` row GO-6; `geometric-observation/chapters/ch07_cost.md`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/NullModel.lean, theorems card_pos_perm, scores_perm, stat_of_counts_const, excess_eq_zero_iff, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

lean/DataMiningAsObservation/Bar.lean, theorems passes_anti, passes_mono, discriminates_iff, no_bar_of_null_ge, exists_bar_of_lt, vacuous_of_null_passes, 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 2, 3, 4, 6, 7, 8, 9, 12, 13.

null model; bar; chance level; confound; isotropic.

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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