A comparison of Bayesian and classical testing procedures for the association parameter in a 2x2 contingency table

Mathematics and Statistics

Keywords

Bayes factor, contingency tables, empirical and Hierarchical Bayes , noninformative prior , mid P-value

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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A comparison of Bayesian and classical testing procedures for the association parameter in a 2x2 contingency table. / Saberi, Z.; Ganjali, Mojtaba; Berridge, Damon et al.
In: Journal of Applied Probability and Statistics, Vol. 5, No. 1, 05.2010, p. 53-67.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Bibtex

@article{66a6a981f42c4d33b053f7f38c36e902,

title = "A comparison of Bayesian and classical testing procedures for the association parameter in a 2x2 contingency table",

abstract = "Bayesian alternatives to classical tests for Fisher{\textquoteright}s exact test in 2£2 contingency tablesare considered. Point null test versus one-sided hypothesis is tested using the log oddsratio in 2£2 contingency tables. Hierarchical Bayes, empirical Bayes and noninformative Bayes procedures are compared with the appropriate classical procedures, eitherthe p-value in Fisher{\textquoteright}s exact test or a randomized test. A conjugate prior at the ﬁrststage and a noninformative prior at the second stage are used for the hyperparameter(s)in the hierarchical approach. For different testing procedures, the likelihood of makinga type I error is chosen to be approximately the same. Then the power of different testsis compared: the larger the power, the better the test. In small samples, the randomized test performs well in comparison with the other methods. For moderate samples,empirical Bayes and randomized test procedures perform better than other approaches",

keywords = " Bayes factor, contingency tables, empirical and Hierarchical Bayes , noninformative prior , mid P-value",

author = "Z. Saberi and Mojtaba Ganjali and Damon Berridge and P. Ofoghi",

year = "2010",

month = may,

language = "English",

volume = "5",

pages = "53--67",

journal = "Journal of Applied Probability and Statistics",

publisher = "Islamic Countries Society of Statistical Sciences",

number = "1",

}

RIS

TY - JOUR

T1 - A comparison of Bayesian and classical testing procedures for the association parameter in a 2x2 contingency table

AU - Saberi, Z.

AU - Ganjali, Mojtaba

AU - Berridge, Damon

AU - Ofoghi, P.

PY - 2010/5

Y1 - 2010/5

N2 - Bayesian alternatives to classical tests for Fisher’s exact test in 2£2 contingency tablesare considered. Point null test versus one-sided hypothesis is tested using the log oddsratio in 2£2 contingency tables. Hierarchical Bayes, empirical Bayes and noninformative Bayes procedures are compared with the appropriate classical procedures, eitherthe p-value in Fisher’s exact test or a randomized test. A conjugate prior at the ﬁrststage and a noninformative prior at the second stage are used for the hyperparameter(s)in the hierarchical approach. For different testing procedures, the likelihood of makinga type I error is chosen to be approximately the same. Then the power of different testsis compared: the larger the power, the better the test. In small samples, the randomized test performs well in comparison with the other methods. For moderate samples,empirical Bayes and randomized test procedures perform better than other approaches

AB - Bayesian alternatives to classical tests for Fisher’s exact test in 2£2 contingency tablesare considered. Point null test versus one-sided hypothesis is tested using the log oddsratio in 2£2 contingency tables. Hierarchical Bayes, empirical Bayes and noninformative Bayes procedures are compared with the appropriate classical procedures, eitherthe p-value in Fisher’s exact test or a randomized test. A conjugate prior at the ﬁrststage and a noninformative prior at the second stage are used for the hyperparameter(s)in the hierarchical approach. For different testing procedures, the likelihood of makinga type I error is chosen to be approximately the same. Then the power of different testsis compared: the larger the power, the better the test. In small samples, the randomized test performs well in comparison with the other methods. For moderate samples,empirical Bayes and randomized test procedures perform better than other approaches

KW - Bayes factor

KW - contingency tables

KW - empirical and Hierarchical Bayes

KW - noninformative prior

KW - mid P-value

M3 - Journal article

VL - 5

SP - 53

EP - 67

JO - Journal of Applied Probability and Statistics

JF - Journal of Applied Probability and Statistics

IS - 1

ER -

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