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Which Statistical Test Should We Use for 2 x 2 Tables?
Version 1
: Received: 22 November 2023 / Approved: 23 November 2023 / Online: 23 November 2023 (09:52:23 CET)
How to cite: Cahusac, P. Which Statistical Test Should We Use for 2 x 2 Tables?. Preprints 2023, 2023111495. https://doi.org/10.20944/preprints202311.1495.v1 Cahusac, P. Which Statistical Test Should We Use for 2 x 2 Tables?. Preprints 2023, 2023111495. https://doi.org/10.20944/preprints202311.1495.v1
Abstract
Categorical data analysis of 2 x 2 contingency tables is extremely common, not least because they provide odds and risk ratio statistics in medical research. The χ2 test is most often used, although some researchers use the likelihood ratio test (LRT). Does it matter which test is used? This paper argues that the LRT rather than the χ2 test should be used when we are interested in testing whether two variables are independent, as is typically the case. In contrast, the χ2 test should be reserved for where the data appear to match too closely a particular hypothesis (e.g. the null hypothesis), as may occur in the investigation of data integrity. Finally, it is argued that the evidential approach provides a consistent and coherent way in which tests can be made for each of these situations.
Keywords
2 x 2 table; χ2 test; likelihood ratio test; G-test; likelihood; odds ratio; data integrity; too good to be true
Subject
Medicine and Pharmacology, Epidemiology and Infectious Diseases
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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