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. The method of sequential analysis is first attributed to 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. Its value to the war effort was immediately recognised, and led to its receiving a "restricted" classification. At the same time, George Barnard led a group working on optimal stopping in Great Britain. 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 from first principles at about 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. Peter Armitage introduced the use of sequential analysis in medical research, especially in the area of clinical trials. Sequential methods became increasingly popular in medicine following Stuart Pocock's work that provided clear recommendations on how to control Type 1 error rates in sequential designs. When researchers repeatedly analyze data as more observations are added, the probability of a Type 1 error increases. Therefore, it is important to adjust the alpha level at each interim analysis, such that the overall Type 1 error rate remains at the desired level.