@article{cam07chi,
  title = {Chi-Squared and {{Fisher}}-{{Irwin}} Tests of Two-by-Two Tables with Small Sample Recommendations},
  volume = {26},
  journal = {Stat Med},
  author = {Campbell, Ian},
  year = {2007},
  keywords = {2x2-table,chi-squared-test,exact-tests,fisher-irwin-test},
  pages = {3661-3675},
  citeulike-article-id = {13265608},
  posted-at = {2014-07-14 14:10:00},
  priority = {0},
  annote = {small sample recommendations;latest edition of Armitage's book recommends that continuity adjustments never be used for contingency table chi-square tests;E. Pearson modification of Pearson chi-square test, differing from the original by a factor of (N-1)/N;Cochran noted that the number 5 in "expected frequency less than 5" was arbitrary;findings of published studies may be summarized as follows, for comparative trials:"1. Yate's chi-squared test has type I error rates less than the nominal, often less than half the nominal; 2. The Fisher-Irwin test has type I error rates less than the nominal; 3. K Pearson's version of the chi-squared test has type I error rates closer to the nominal than Yate's chi-squared test and the Fisher-Irwin test, but in some situations gives type I errors appreciably larger than the nominal value; 4. The 'N-1' chi-squared test, behaves like K. Pearson's 'N' version, but the tendency for higher than nominal values is reduced; 5. The two-sided Fisher-Irwin test using Irwin's rule is less conservative than the method doubling the one-sided probability; 6. The mid-P Fisher-Irwin test by doubling the one-sided probability performs better than standard versions of the Fisher-Irwin test, and the mid-P method by Irwin's rule performs better still in having actual type I errors closer to nominal levels."; strong support for the 'N-1' test provided expected frequencies exceed 1;flaw in Fisher test which was based on Fisher's premise that marginal totals carry no useful information;demonstration of their useful information in very small sample sizes;Yate's continuity adjustment of N/2 is a large over correction and is inappropriate;counter arguments exist to the use of randomization tests in randomized trials;calculations of worst cases;overall recommendation: use the 'N-1' chi-square test when all expected frequencies are at least 1, otherwise use the Fisher-Irwin test using Irwin's rule for two-sided tests, taking tables from either tail as likely, or less, as that observed; see letter to the editor by Antonio Andres and author's reply in 27:1791-1796; 2008.}
}

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Pearson modification of Pearson chi-square test, differing from the original by a factor of (N-1)/N;Cochran noted that the number 5 in \"expected frequency less than 5\" was arbitrary;findings of published studies may be summarized as follows, for comparative trials:\"1. Yate's chi-squared test has type I error rates less than the nominal, often less than half the nominal; 2. The Fisher-Irwin test has type I error rates less than the nominal; 3. K Pearson's version of the chi-squared test has type I error rates closer to the nominal than Yate's chi-squared test and the Fisher-Irwin test, but in some situations gives type I errors appreciably larger than the nominal value; 4. The 'N-1' chi-squared test, behaves like K. Pearson's 'N' version, but the tendency for higher than nominal values is reduced; 5. The two-sided Fisher-Irwin test using Irwin's rule is less conservative than the method doubling the one-sided probability; 6. The mid-P Fisher-Irwin test by doubling the one-sided probability performs better than standard versions of the Fisher-Irwin test, and the mid-P method by Irwin's rule performs better still in having actual type I errors closer to nominal levels.\"; strong support for the 'N-1' test provided expected frequencies exceed 1;flaw in Fisher test which was based on Fisher's premise that marginal totals carry no useful information;demonstration of their useful information in very small sample sizes;Yate's continuity adjustment of N/2 is a large over correction and is inappropriate;counter arguments exist to the use of randomization tests in randomized trials;calculations of worst cases;overall recommendation: use the 'N-1' chi-square test when all expected frequencies are at least 1, otherwise use the Fisher-Irwin test using Irwin's rule for two-sided tests, taking tables from either tail as likely, or less, as that observed; see letter to the editor by Antonio Andres and author's reply in 27:1791-1796; 2008.","bibtex":"@article{cam07chi,\n title = {Chi-Squared and {{Fisher}}-{{Irwin}} Tests of Two-by-Two Tables with Small Sample Recommendations},\n volume = {26},\n journal = {Stat Med},\n author = {Campbell, Ian},\n year = {2007},\n keywords = {2x2-table,chi-squared-test,exact-tests,fisher-irwin-test},\n pages = {3661-3675},\n citeulike-article-id = {13265608},\n posted-at = {2014-07-14 14:10:00},\n priority = {0},\n annote = {small sample recommendations;latest edition of Armitage's book recommends that continuity adjustments never be used for contingency table chi-square tests;E. Pearson modification of Pearson chi-square test, differing from the original by a factor of (N-1)/N;Cochran noted that the number 5 in \"expected frequency less than 5\" was arbitrary;findings of published studies may be summarized as follows, for comparative trials:\"1. Yate's chi-squared test has type I error rates less than the nominal, often less than half the nominal; 2. The Fisher-Irwin test has type I error rates less than the nominal; 3. K Pearson's version of the chi-squared test has type I error rates closer to the nominal than Yate's chi-squared test and the Fisher-Irwin test, but in some situations gives type I errors appreciably larger than the nominal value; 4. The 'N-1' chi-squared test, behaves like K. Pearson's 'N' version, but the tendency for higher than nominal values is reduced; 5. The two-sided Fisher-Irwin test using Irwin's rule is less conservative than the method doubling the one-sided probability; 6. The mid-P Fisher-Irwin test by doubling the one-sided probability performs better than standard versions of the Fisher-Irwin test, and the mid-P method by Irwin's rule performs better still in having actual type I errors closer to nominal levels.\"; strong support for the 'N-1' test provided expected frequencies exceed 1;flaw in Fisher test which was based on Fisher's premise that marginal totals carry no useful information;demonstration of their useful information in very small sample sizes;Yate's continuity adjustment of N/2 is a large over correction and is inappropriate;counter arguments exist to the use of randomization tests in randomized trials;calculations of worst cases;overall recommendation: use the 'N-1' chi-square test when all expected frequencies are at least 1, otherwise use the Fisher-Irwin test using Irwin's rule for two-sided tests, taking tables from either tail as likely, or less, as that observed; see letter to the editor by Antonio Andres and author's reply in 27:1791-1796; 2008.}\n}\n\n","author_short":["Campbell, I."],"key":"cam07chi","id":"cam07chi","bibbaseid":"campbell-chisquaredandfisherirwintestsoftwobytwotableswithsmallsamplerecommendations-2007","role":"author","urls":{},"keyword":["2x2-table","chi-squared-test","exact-tests","fisher-irwin-test"],"downloads":0},"search_terms":["chi","squared","fisher","irwin","tests","two","two","tables","small","sample","recommendations","campbell"],"keywords":["2x2-table","chi-squared-test","exact-tests","fisher-irwin-test","*import"],"authorIDs":[],"dataSources":["mEQakjn8ggpMsnGJi"]}