Sequential analysis

Sequential analysis

In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data is evaluated as it is 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 [Cite journal
authorlink = Abraham Wald
first = Abraham
last = Wald
title = Sequential Tests of Statistical Hypotheses
journal = The Annals of Mathematical Statistics
volume = 16
issue = 2
month = June
year = 1945
pages = 117–186
url = http://links.jstor.org/sici?sici=0003-4851(194506)16%3A2%3C117%3ASTOSH%3E2.0.CO%3B2-7
doi = 10.1214/aoms/1177731118] with Jacob Wolfowitz as a tool for more efficient industrial quality control during World War II.

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.

Sequential analysis has also connection to the problem of "gambler's ruin" studied by among others Huyghens already in 1657 [Cite book
author = B. K. Gosh and P. K. Sen
title = Handbook of Sequential Analysis
publisher = Marcel Dekker
location = New York
year = 1991
isbn = 0-8247-8404-1] .

See also

* Wald test
* Sequential estimation
* Sequential probability ratio test
* Quick detection

Notes & References

* [http://www.tandf.co.uk/journals/titles/07474946.asp Sequential Analysis: Design Methods & Applications] Journal
* Cite book
author = Abraham Wald
title = Sequential Analysis
year = 1947
publisher = John Wiley and Sons
location = New York
* Cite book
author = David Siegmund
title = Sequential Analysis
publisher = Springer-Verlag
location = New York
series = Springer Series in Statistics
year = 1985
isbn = 0-387-96134-8

External links

* [http://www.biostat.harvard.edu/~betensky/bio276.html Course given by Rebecca Betensky at Harvard University] , lecture note slides
* [http://garnet.fsu.edu/~ajeong/DAT/index.htm Software for conducting sequential analysis] and [http://garnet.fsu.edu/~ajeong/index.htm applications of sequential analysis] in the study of group interaction in computer-mediated communication by Dr. Allan Jeong at Florida State University


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