Standard tests for comparing two sample proportions of a dichotomous dependent variable where there is a combination of paired and unpaired samples are considered. Four new tests are introduced and compared against standard tests and an alternative proposal by Choi and Stablein (1982). The Type I error robustness is considered for each of the test statistics. The results show that Type I error robust tests that make use of all the available data are more powerful than Type I error robust tests that do not. The Type I error robustness and the power among tests introduced in this paper using the phi correlation coefficient is comparable to that of Choi and Stablein (1982). The use of the test statistics to form confidence intervals is considered. A general recommendation of the best test statistic for practical use is made.
Derrick, B., Dobson-Mckittrick, A., Toher, D., & White, P. (2015). Test statistics for comparing two proportions with partially overlapping samples