bar instrument

Definition	A threshold a statistic must reach, written down before the measurement. A bar discriminates only when the null fails it and the real system passes it, and a bar the null passes is vacuous. Chapter 8 section 8.3.
Example	A null scoring 0.30 and a system scoring 0.72 are separated by a bar at 0.55, and a bar at 0.25 is vacuous, since the null passes it.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `bar`, kind instrument.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 10.7.
Assumptions and scope	A threshold a statistic must reach, written down before the measurement. Passing a higher bar passes every lower one, a larger statistic passes every bar a smaller one passes, a bar discriminates exactly when it sits strictly above the null and at or below the real system, no bar discriminates when the null scores at least as high, and a bar the null passes is vacuous. A pass on eight cells at six parts in ten million against a bar of one in a hundred thousand was vacuous because the null cleared the bar too, which is where the anti-vacuity bar came from.
Prior art	none recorded
Evidence	`observation-theory-campaigns/experiments/PREREG-PF5-002.md:79-86`, `lean/DataMiningAsObservation/Bar.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

A bar discriminates when the null fails it and the system passes it.

Equation

Book equation 10.7.

\[\text{verdict}=\min_{i:\ n_i\ge n_{\min},\ |Q_i|\ge q_{\min}}\ \mathrm{score}_i,\qquad \text{ABSTAIN otherwise}.\]

Conditions

A threshold a statistic must reach, written down before the measurement. Passing a higher bar passes every lower one, a larger statistic passes every bar a smaller one passes, a bar discriminates exactly when it sits strictly above the null and at or below the real system, no bar discriminates when the null scores at least as high, and a bar the null passes is vacuous.
A pass on eight cells at six parts in ten million against a bar of one in a hundred thousand was vacuous because the null cleared the bar too, which is where the anti-vacuity bar came from.

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

Ledger

none

First stated

Chapter 8 section 8.3 of Data Mining as Observation, with the anti-vacuity bar quoted from observation-theory-campaigns/experiments/PREREG-PF5-002.md:79-86.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 8 section 8.3	anti-vacuity bar, quoted	`observation-theory-campaigns/experiments/PREREG-PF5-002.md:79-86`
chapter 9 section 9.2	the battery, three new templates, frozen ratios, code hash, bars at least 10 of 12 and the dimension ordering, eccentricity scope	`the-angular-observer/PREREG_RECOGNIZER_BATTERY.md:1-80`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

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 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14.

gate; vacuity threshold; null model; preregistration; verdict.

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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