confound concept

Definition	A variable that moves with both the treatment and the outcome so that a measured difference cannot be attributed. Chapter 8 requires controls before a claim. Also control.
Example	A codebook change that arrived with a compression change moved 25 percent of the score on its own, so the comparison was confounded.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `confound`, kind concept.
Status	refutes or corrects [refuted]. Corrections: 1 item(s), see below.
Defining equation	Book equation 8.3.
Assumptions and scope	A variable that moves with both the treatment and the outcome. In the linear case the naive difference of group means is the treatment effect plus the confound’s effect times the difference of the confound’s means between the groups, so it equals the effect exactly when the confound is balanced or has no effect, and the bias can have either sign and any size. Controls come before claims. The twenty-five percent codebook confound in the flip’s early arms and the smooth-perturbation control that was withdrawn are the program’s cases, each carried in the ledger.
Prior art	none recorded
Evidence	`geometric-observation/claims/LEDGER.md:99`, `lean/DataMiningAsObservation/Confound.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

A variable that moves both arms of a comparison.

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 variable that moves with both the treatment and the outcome. In the linear case the naive difference of group means is the treatment effect plus the confound’s effect times the difference of the confound’s means between the groups, so it equals the effect exactly when the confound is balanced or has no effect, and the bias can have either sign and any size.
Controls come before claims. The twenty-five percent codebook confound in the flip’s early arms and the smooth-perturbation control that was withdrawn are the program’s cases, each carried in the ledger.

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

Ledger

refutes or corrects. NEG-6 [refuted]. Relative per-channel-demeaned error norm is the quotient-tangential quantity that controls softmax-KL. geometric-observation/claims/LEDGER.md:99.

First stated

Chapter 8 section 8.6 of Data Mining as Observation, with the program’s codebook confound in Volume 14’s honest negatives and the negative controls of the constraint-gap review.

Measurements

none

Failures and corrections

NEG-6, [refuted]. Relative per-channel-demeaned error norm is the quotient-tangential quantity that controls softmax-KL. geometric-observation/claims/LEDGER.md:99.

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Confound.lean, theorems mean_outcome, naive_diff, naive_diff_of_balanced, naive_diff_of_no_effect, bias_unbounded, 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, 14.

harness; null model; Simpson's paradox; preregistration.

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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