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