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CUPED covariate adjustment: A constant covariate gets a unit coefficient · case 03

Experiments whose covariate never varies report theta = 1.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

theta = cov(y, x) / var(x) over the pooled data of both arms (theta = 0 when x is constant). Each arm's adjusted mean is mean(y_arm) - theta * (mean(x_arm) - pooled mean(x)). Return [theta, adjusted control, adjusted treatment, difference] rounded to 6 places.

Why this case matters

CUPED uses pre-period data to cut variance; mistakes either waste it or bias the estimate.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
constant covariate leaves means unadjusted	`[1.0, 2.0, 3.0, 1.0]`	`[0.0, 2.0, 3.0, 1.0]`	Failed

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