Sequential Testing and the Peeking Problem

A fixed-horizon hypothesis test is designed for a planned sample size or observation window. Its nominal significance level controls the probability of rejecting a true null under the specified procedure. If analysts repeatedly inspect ordinary p-values and stop when a result looks significant, they create multiple opportunities to cross the threshold. The chance of at least one false positive can exceed the nominal level, even if each individual look appears conventional. Sequential testing allows data to accumulate over time while adjusting inference for repeated monitoring. Group-sequential designs schedule interim analyses and use boundaries that control overall error. Alpha-spending methods distribute the type-I error budget across those looks. Always-valid p-values or confidence sequences are designed to remain interpretable under continuous monitoring when their assumptions hold. These methods differ in assumptions, efficiency and stopping behavior; they are not interchangeable with ad hoc repeated checks. For a hypothetical test planned to stop at 10,000 users, a team may schedule looks at 25%, 50%, 75% and 100% of the target sample. The rule determines how strong evidence must be at each look and whether futility or safety stopping is allowed. The team should choose the design before examining outcomes and simulate its operating characteristics where appropriate. Sequential validity does not solve every experiment problem. Metric definitions, randomization, sample-ratio checks, multiple outcomes, delayed labels, seasonality and practical effect size still matter. Early stopping can also affect estimates, often making extreme early effects less stable. Record the stopping rule, number and timing of looks, analysis population and final interval. If an experiment was repeatedly peeked at under a fixed-horizon test, do not present the nominal p-value as though the plan were fixed. Use an appropriate sequential analysis or report the limitation transparently. Valid early stopping is possible, but only when the inference method matches the monitoring process.