A Revisit To Contingency Table And Tests Of Independence: Bootstrap Is Preferred To Chi-Square Approximations As Well As Fisher's Exact Test

doi:10.1080/10543406.2014.920851

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Title:	A Revisit To Contingency Table And Tests Of Independence: Bootstrap Is Preferred To Chi-Square Approximations As Well As Fisher's Exact Test
Authors:	Lin, Jyh-Jiuan;Chang, Ching-Hui;Pal, Nabendu
Contributors:	淡江大學統計學系
Keywords:	Hypothesis testing;level of a test;size;power of a test;62G10;62D99;62Q05
Date:	2014
Issue Date:	2014-09-03 15:34:52 (UTC+8)
Publisher:	Philadelphia: Taylor & Francis Inc.
Abstract:	To test the mutual independence of two qualitative variables (or attributes) it is a common practice to follow the Chi-Square tests (Pearson's as well as likelihood ratio test) based on data in the form of a contingency table. However, it should be noted that these popular Chi-Square tests are asymptotic in nature, and are useful when the cell frequencies are 'not too small'. In this paper we explore the accuracy of the Chi-Square tests through an extensive simulation study, and then propose their bootstrap versions which appear to work better than the asymptotic Chi-Square tests. The bootstrap tests are useful even for small cell frequencies as they maintain the nominal level quite accurately. Also, the proposed bootstrap tests are more convenient than the Fisher's exact test which is often criticized for being too conservative. Finally, all test methods are applied to a few real-life datasets for demonstration purposes.
Relation:	Journal of Biopharmaceutical Statistics
DOI:	10.1080/10543406.2014.920851
Appears in Collections:	[Graduate Institute & Department of Statistics] Journal Article

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