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The Conditional error principle permits adaptation of a testing design if, conditional on the observed interim information, the modified future rule's Type I error does not exceed the original rule's conditional future rejection probability. Averaging then preserves the original unconditional error bound. For a completed single-look test that has not rejected, there is no future conditional error budget under that original design.

A group sequential design evaluates accumulating data at several planned interim analyses instead of committing to one final test. At each analysis, a prespecified rule can stop for efficacy, stop for futility, or continue collecting observations. The design specifies both the timing of analyses and the sequential stopping boundaries.

Repeated inspection changes the probability of rejecting a Null hypothesis. Even two independent tests, each at significance level $0.05$, reject at least once with probability $1-0.95^2=0.0975$ under their common Null hypothesis. Tests on accumulating observations are dependent, so their rejection boundaries require their actual joint distribution rather than that independence calculation. An Alpha-spending function distributes the permitted type I error over information fractions; it does not make unchanged fixed-sample critical values valid at every analysis.

For a simple valid construction with $K$ planned analyses, choose separate rejection events whose null probabilities are each at most $\alpha /K$. The union bound makes the probability of any rejection at most $\alpha$, whatever their dependence. More efficient boundaries exploit the dependence between successive test statistics. A Futility boundary removes rejection paths, and a Conditional error principle can justify a later design adaptation while preserving the original error guarantee. The possibility of early stopping also affects point estimation and confidence intervals; fixed-sample formulas do not automatically retain their usual interpretation after selection.

A second opportunity to reject raises the trial's overall Type I error above the nominal 10% in general. If $A$ and $B$ denote rejection at the first and second analyses, the overall error isThe cumulative-data test statistics are correlated, so neither 20% nor $1-0.9^2=19\%$ is the general answer. The latter requires independent tests, which is not the situation here.

The rejection thresholds and the stopping/continuation rule must be calibrated jointly. A prespecified group sequential design or alpha-spending function can allocate a total error budget of 10% across the analyses, using their joint null distribution. A conservative alternative planned in advance is two tests each at 5%, controlled by the Bonferroni inequality. An unplanned change to a design with a remaining error budget can be justified by the conditional error principle. Here, however, an original single-look test at 10% has no remaining conditional rejection probability after its final nonrejection. Keeping its entire original rejection region and adding a new positive-probability rejection opportunity cannot in general retain a 10% overall error rate. The two-look rule therefore needs prospective joint calibration; an already observed result cannot retrospectively create an unused error budget.