FA-74798 / Experiment statistics / Member archive

Always-valid sequential p-value: The prefactor ignores accumulated sample size · case 03

Likelihood ratios are too large for long streams, overstating significance.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

diffs is a stream of paired differences with known variance sigma2; the normal-mixture likelihood ratio after n observations with running mean m is sqrt(sigma2 / (sigma2 + n tau2)) exp(n^2 tau2 m^2 / (2 sigma2 (sigma2 + n tau2))). The always-valid p-value starts at 1 and is the running minimum of 1 / ratio. Return the p-value after each observation rounded to 6.

Why this case matters

Always-valid p-values let teams monitor continuously without inflating false positives.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
p-value never increases after a reversal	`[0.52026, 0.098264, 0.098264, 0.098264]`	`[0.52026, 0.120349, 0.120349, 0.120349]`	Failed

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