Exact tests for one sample correlated binary data

In this paper we developed exact tests for one sample correlated binary data whose cluster sizes are at most two. Although significant progress has been made in the development and implementation of the exact tests for uncorrelated data, exact tests for correlated data are rare. Lack of a tractable likelihood function has made it difficult to develop exact tests for correlated binary data. However, when cluster sizes of binary data are at most two, only three parameters are needed to characterize the problem. One parameter is fixed under the null hypothesis, while the other two parameters can be removed by both conditional and unconditional approaches, respectively, to construct exact tests. We compared the exact and asymptotic p-values in several cases. The proposed method is applied to real-life data.