Comparing Two Means Using Partially Paired and Unpaired Data

A new test statistic is proposed to test the equality of two normal means when the data is partially paired and partially unpaired. The test statistic is based on a linear combination of the differences of both paired and unpaired sample means. Using t-distribution as the approximate null distribution, the proposed method is evaluated against some other standard methods known in the literature. For samples from normal and logistic distributions with equal variances, the proposed method appears to perform better than other methods with respect to power while keeping the type I error rates very competitive.