Invalid Permutation Tests
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 failin...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/769780 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832557011449937920 |
|---|---|
| author | Mikel Aickin |
| author_facet | Mikel Aickin |
| author_sort | Mikel Aickin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-39f193a99846494e907b69dfc0b731b9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-39f193a99846494e907b69dfc0b731b92025-02-03T05:43:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/769780769780Invalid Permutation TestsMikel Aickin0Department of Family & Community Medicine, University of Arizona, Tucson, AZ 85724, USAPermutation 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.http://dx.doi.org/10.1155/2010/769780 |
| spellingShingle | Mikel Aickin Invalid Permutation Tests International Journal of Mathematics and Mathematical Sciences |
| title | Invalid Permutation Tests |
| title_full | Invalid Permutation Tests |
| title_fullStr | Invalid Permutation Tests |
| title_full_unstemmed | Invalid Permutation Tests |
| title_short | Invalid Permutation Tests |
| title_sort | invalid permutation tests |
| url | http://dx.doi.org/10.1155/2010/769780 |
| work_keys_str_mv | AT mikelaickin invalidpermutationtests |