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Invalid Permutation Tests
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-05-25
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Permutation tests are often presented in a rather casual manner, in both introductory and advanced statistics textbooks.
The appeal of the cleverness of the procedure seems to replace the need for a rigorous argument that it produces valid hypothesis tests.
The consequence of this educational failing has been a widespread belief in a “permutation principle”, which is supposed invariably to give tests that are valid by construction, under an absolute minimum of statistical assumptions.
Several lines of argument are presented here to show that the permutation principle itself can be invalid, concentrating on the Fisher-Pitman permutation test for two means.
A simple counterfactual example illustrates the general problem, and a slightly more elaborate counterfactual argument is used to explain why the main mathematical proof of the validity of permutation tests is mistaken.
Two modifications of the permutation test are suggested to be valid in a very modest simulation.
In instances where simulation software is readily available, investigating the validity of a specific permutation test can be done easily, requiring only a minimum understanding of statistical technicalities.
American Psychological Association (APA)
Aickin, Mikel. 2010. Invalid Permutation Tests. International Journal of Mathematics and Mathematical Sciences،Vol. 2010, no. 2010, pp.1-10.
https://search.emarefa.net/detail/BIM-497371
Modern Language Association (MLA)
Aickin, Mikel. Invalid Permutation Tests. International Journal of Mathematics and Mathematical Sciences No. 2010 (2010), pp.1-10.
https://search.emarefa.net/detail/BIM-497371
American Medical Association (AMA)
Aickin, Mikel. Invalid Permutation Tests. International Journal of Mathematics and Mathematical Sciences. 2010. Vol. 2010, no. 2010, pp.1-10.
https://search.emarefa.net/detail/BIM-497371
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-497371