How to compare the means of two samples that include paired observations and independent observations: A companion to Derrick, Russ, Toher and White (2017) - Derrick, Ben; Toher, Deirdre; White, Paul (Tutorials in Quantitative Methods for Psychology, 2017)
Standard approaches for comparing the means of two samples, comprising both paired observations and independent observations, involve the discarding of valuable information. An alternative test which uses all of the available data, is the partially overlapping samples t-test. Two variations of the test are available, one assuming equal variances, and one assuming separate variances. Issues with standard procedures, and considerations for choosing appropriate tests in the partially overlapping scenario are discussed. An example with details of how to apply the partially overlapping samples t-test is given along with an R package that implement these new tests.