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 ^[1] with Jacob Wolfowitz 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.^[2].

Essentially the same 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 available, an interim analysis is conducted on the 2n subjects. The statistical analysis is performed to compare the two groups, and if the alternative hypothesis is accepted, the trial is terminated. Otherwise, the trial continues for another 2n subjects, with n subjects per group. The statistical analysis is performed again on the 4n subjects. If the alternative is accepted, then the trial is terminated. Otherwise, it continues with period evaluation until N of the 2n subjects are available. ^[3]

Other Applications

Sequential analysis also has a connection to the problem of gambler's ruin that has been studied by, among others, Huyghens in 1657^[4].

See also

• Optimal Stopping
• Wald test
• Sequential estimation
• Sequential probability ratio test
• Quick detection

Notes

References

• Sequential Analysis: Design Methods & Applications Journal
• Abraham Wald (1947). Sequential Analysis. New York: John Wiley and Sons. 
• Chernoff, Herman (1972). Sequential Analysis and Optimal Design. SIAM. 
• David Siegmund (1985). Sequential Analysis. Springer Series in Statistics. New York: Springer-Verlag. ISBN 0-387-96134-8. 

External links

• Course given by Rebecca Betensky at Harvard University, lecture note slides
• Software for conducting sequential analysis and applications of sequential analysis in the study of group interaction in computer-mediated communication by Dr. Allan Jeong at Florida State University