A collaborative study including Dr. Hani Samawi, director of the Karl E. Peace Center for Biostatistics and Dr. Robert Vogel, interim department chair of biostatistics at Georgia Southern University Jiann-Ping Hsu College of Public Health, provide several methods to compare two Gaussian distributed means in the two sample location problems under the assumption of partially dependent observations. Simulation studies indicate that the test procedure is frequently more powerful than other methods depending on the ratio of the unpaired data and the strength and direction of the correlation between the two variables. The tests used in this comparative study are illustrated with an example based on data from a small gynecological study.