Tests of Significance for 2 × 2 Contingency Tables

Fisher's exact test, and the approximation to it by the continuity-corrected χ<sup>2</sup> test, have repeatedly been attacked over the past 40 years, recently with the support of extensive computer exercises. The present paper argues, on commonsense grounds, supported by simple exa...

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Veröffentlicht in:Journal of the Royal Statistical Society. Series A (General). - Royal Statistical Society, 1948. - 147(1984), 3, Seite 426-463
1. Verfasser: Yates, F. (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1984
Zugriff auf das übergeordnete Werk:Journal of the Royal Statistical Society. Series A (General)
Schlagworte:Ancillary Statistics Binomial Probabilities Conditioning Conservative Test Contingency Tables Contingency Test Continuity Correction Fisher's Exact Test Goodness of Fit Neyman-Pearson Theory mehr... One-Tail Probabilities Quality Control Significance Tests Two-Sided Tests Yates's Correction Mathematics Health sciences Behavioral sciences Physical sciences
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520 |a Fisher's exact test, and the approximation to it by the continuity-corrected χ<sup>2</sup> test, have repeatedly been attacked over the past 40 years, recently with the support of extensive computer exercises. The present paper argues, on commonsense grounds, supported by simple examples, that these attacks are misconceived, and are mainly due to uncritical acceptance of the Neyman-Pearson approach to tests of significance, the use of nominal levels, and refusal to accept the arguments for conditioning on the margins. Two-sided tests have also added to the confusion; it is argued that the best definition of a two-sided probability is twice the observed one-tail probability. 
540 |a Copyright 1984 Royal Statistical Society 
650 4 |a Ancillary Statistics 
650 4 |a Binomial Probabilities 
650 4 |a Conditioning 
650 4 |a Conservative Test 
650 4 |a Contingency Tables 
650 4 |a Contingency Test 
650 4 |a Continuity Correction 
650 4 |a Fisher's Exact Test 
650 4 |a Goodness of Fit 
650 4 |a Neyman-Pearson Theory 
650 4 |a One-Tail Probabilities 
650 4 |a Quality Control 
650 4 |a Significance Tests 
650 4 |a Two-Sided Tests 
650 4 |a Yates's Correction 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Probabilities 
650 4 |a Health sciences  |x Medical sciences  |x Immunology  |x Immunologic techniques  |x Inoculation 
650 4 |a Mathematics  |x Pure mathematics  |x Algebra  |x Polynomials  |x Binomials 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Cognitive processes  |x Thought processes  |x Reasoning  |x Inference 
650 4 |a Mathematics  |x Mathematical procedures  |x Approximation 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Statistical results  |x Statistical properties  |x Statistical significance  |x Significance level 
650 4 |a Mathematics  |x Applied mathematics  |x Computational mathematics  |x Mathematical tables 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics 
650 4 |a Mathematics  |x Pure mathematics  |x Algebra  |x Polynomials  |x Binomials  |x Binomial distributions 
650 4 |a Physical sciences  |x Physics  |x Mechanics  |x Classical mechanics  |x Kinetics  |x Translational motion  |x Degrees of freedom 
655 4 |a research-article 
773 0 8 |i Enthalten in  |t Journal of the Royal Statistical Society. Series A (General)  |d Royal Statistical Society, 1948  |g 147(1984), 3, Seite 426-463  |w (DE-627)1853780618  |w (DE-600)3163510-6  |x 00359238  |7 nnns 
773 1 8 |g volume:147  |g year:1984  |g number:3  |g pages:426-463 
856 4 0 |u https://www.jstor.org/stable/2981577  |3 Volltext 
856 4 0 |u https://doi.org/10.2307/2981577  |3 Volltext 
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952 |d 147  |j 1984  |e 3  |h 426-463