When testing a single hypothesis it is well known that increasing the sample size after a non-significant result and repeating the hypothesis test several times at unadjusted critical levels, the overall Type I error rate will be severely inflated. In contrast, if a large number of hypotheses are tested controlling the False Discovery Rate, such "Hunting for Significance" has (under suitable assumptions on the stopping rule) asymptotically no impact on the error rate.

An important field of application are micro array studies, where thousands of hypotheses are tested simultaneously and sample size calculations depend on many unknown parameters. Instead of relying on preliminary assumptions, a sequential design allows to estimate the power of the experiment at every interim analysis and to increase the sample size until the estimated power is large enough.