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Sequential Testing and the Peeking Problem
In a fixed-horizon experiment, repeatedly checking ordinary p-values and stopping when one crosses a significance threshold can inflate false-positive risk.
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Sequential methods account for repeated looks through a valid stopping rule, allowing monitoring without treating every interim result as an independent fixed-horizon test.
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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.
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The Future of Sequential Testing and the Peeking Problem
Experiment teams can make interim monitoring safer by choosing sequential methods before launch, simulating expected duration and defining safety or futility stops. Dashboards should display the method's valid boundaries rather than a conventional p-value alone. Analysts should report how many looks occurred and whether stopping rules were followed. As experimentation platforms mature, inference and traffic dashboards can share the same prespecified design. This makes early decisions more responsive while preserving a clear account of uncertainty and error control. Record whether any unscheduled looks occurred.
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A team plans a two-week A/B test but checks a conventional p-value every hour and stops as soon as it falls below 0.05. The repeated opportunity to stop changes the test's error behavior.
A group-sequential design predefines interim analysis times and uses adjusted boundaries so early stopping can be considered while controlling the planned error rate.
An alpha-spending approach allocates the overall type-I error budget across scheduled looks, often spending little early and more later according to a prespecified function.
A product team uses an always-valid confidence sequence and a prespecified stopping rule, then reports the monitoring method rather than interpreting a nominal fixed-time p-value after arbitrary peeking.
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What is Sequential Testing and the Peeking Problem?
In a fixed-horizon experiment, repeatedly checking ordinary p-values and stopping when one crosses a significance threshold can inflate false-positive risk. Sequential methods account for repeated looks through a valid stopping rule, allowing monitoring without treating every interim result as an independent fixed-horizon test.
Why can stopping when an ordinary p-value first falls below 0.05 inflate false positives?
Repeated opportunities to reject change the overall error behavior of a fixed-horizon test.
What does a group-sequential design specify in advance?
Group-sequential procedures predefine looks and boundaries to control error while permitting interim decisions.
What does an alpha-spending function allocate?
Alpha spending distributes the total false-positive budget over the sequential analyses.
How do always-valid methods differ from unadjusted repeated p-values?
Always-valid procedures account for continuous monitoring under their assumptions.
Why define interim looks before seeing experiment results?
Prespecification prevents choosing looks or rules in response to favorable results.
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