Sequential analysis

In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost.

History

Sequential analysis was first developed by Abraham Wald with Jacob Wolfowitz, W. Allen Wallis, and Milton Friedman while at Columbia University's Statistical Research Group as a tool for more efficient industrial quality control during World War II. Another early contribution to the method was made by K.J. Arrow with D. Blackwell and M.A. Girshick.

A similar approach was independently developed at the same time by Alan Turing, as part of the Banburismus technique used at Bletchley Park, to test hypotheses about whether different messages coded by German Enigma machines should be connected and analysed together. This work remained secret until the early 1980s.

Applications of sequential analysis

Clinical trials

In a randomized trial with two treatment groups, classical group sequential testing is used in the following manner: If n subjects in each group are...
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