An Inverse Normal Transformation Solution for the comparison of two samples that contain both paired observations and independent observations

Inverse normal transformations applied to the partially overlapping samples t-tests by Derrick et.al. (2017) are considered for their Type I error robustness and power. The inverse normal transformation solutions proposed in this paper are shown to maintain Type I error robustness. For increasing degrees of skewness they also offer improved power relative to the parametric partially overlapping samples t-tests. The power when using inverse normal transformation solutions are comparable to rank based non-parametric solutions.