Standard approaches for analyzing the difference in two means, where partially overlapping samples are present, are less than desirable. Here are introduced two test statistics, making reference to the t-distribution. It is shown that these test statistics are Type I error robust, and more powerful than standard tests.
Derrick, B., Russ, B., Toher, D., & White, P. (2017). Test statistics for the comparison of means for two samples that include both paired and independent observations. Journal of Modern Applied Statistical Methods, 16(1), 137-157. doi: 10.22237/jmasm/1493597280