Sequential test calculator (mSPRT)

Mixture Sequential Probability Ratio Test, based on Johari, Pekelis and Walsh, "Always Valid Inference: Bringing Sequential Analysis to A/B Testing". Mixture prior N(0, τ²) on the ABSOLUTE effect θ = pB − pA. With z = (pB − pA)/SE and ρ = τ²/SE²: Λ = √(1/(1+ρ)) × exp((z²/2) × ρ/(1+ρ)), and p_av = min(1, 1/Λ).

SE² decreasing in 1/n, ρ increasing with sample size: the penalty linked to repeated looks grows with accumulated information. The resulting p-value is valid at any point in time, regardless of when or how often it is checked.

Default τ = baseline rate × 5% expected relative uplift. τ sets sensitivity, not validity: a poorly calibrated τ costs power, not risk control.

Limitation: more conservative than a fixed-horizon test with the same sample size. This is the explicit price of the freedom to look whenever you want.