We consider the exact likelihood ratio test of independence of binary responses within clusters developed by George and Kodell (J. Amer. Statist. Assoc., 1996, 91, 1602-1611) conditional on the sufficient statistics for the nuisance parameter under the null hypothesis. Only an exchangeability of responses within clusters is assumed for the distribution of the observed vector. Two formulas for the exact P-values are obtained. An algorithm is proposed to avoid unnecessary enumeration when the cluster size is two. We compare the exact and asymptotic P-values in several cases.
Bibliographical noteFunding Information:
This research was supported in part by an appointment to the Postgraduate Research Program at the National Center for Toxicological Research administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the U.S. Department of Energy and the U.S. Food and Drug Administration.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics