Review of the partially overlapping samples framework: Paired observations and independent observations in two samples

A frequently asked question in quantitative research is how to compare two samples that include some combination of paired observations and unpaired observations. In our publications and R package, we refer to the scenario as "partially overlapping samples". Most frequently the desired comparison is that of central location. Depending on the context, the research question could be a comparison of means, distributions, proportions or variances. In the 20th century, traditional approaches that discard either the paired observations or the independent observations were customary. In the 21st century approaches that make use of all available data are becoming more prominent. Traditional and modern approaches for the analyses for each of these research questions are reviewed. We conclude that tests that report a directly measurable difference between the two groups provide the best solutions.