FA-74403 / Experiment statistics / Member archive

Welch unequal-variance t statistic: The t denominator mixes variances before dividing · case 03

Unequal arm sizes give a standard error that is neither pooled nor Welch.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

a is control, b treatment. With sample variances (divisor n - 1), t = (mean_b - mean_a) / sqrt(va/na + vb/nb) and Welch-Satterthwaite df = (va/na + vb/nb)^2 / ((va/na)^2/(na-1) + (vb/nb)^2/(nb-1)). Fewer than two values in an arm or zero total variance -> None. Return [round(t, 6), round(df, 6)].

Why this case matters

Online experiment readouts drive launch decisions; a silent formula slip flips conclusions.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
unequal sizes and variances	`[3.59521, 6.594671]`	`[2.713602, 6.594671]`	Failed

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