Pulsar Timing Arrays (PTA) present a unique opportunity to characterize the low frequency regime of gravitational waves in our Universe. Currently there are several different PTA collaborations around the world, and by combining their respective datasets we can improve our sensitivity to the signals of a nanohertz-frequency stochastic gravitational wave background. In our work we analyzed the International Pulsar Timing Array Data Release 2 (IPTADR2), as well as its constituent datasets, in order to better characterize how the data combination process improves our ability to detect gravitational waves. IPTADR2 (Perera et al. 2019) combines the NANOGrav 9 year dataset (Arzoumanian et al. 2015), the Parkes Pulsar Timing Array Data Release 1 extended (Manchester et al. 2013), and the European Pulsar Timing Array Data Release 1 (Desvignes et al. 2016) into a single dataset, creating unique opportunities to analyze for evidence of a stochastic gravitational wave background. Additionally, we implement a new method for incoherent data combination, involving creating a Pulsar Timing Array consisting of the various dataset versions of the same pulsar. These analyses will provide a better understanding of the data combination effects as well as new ways to synthesize future datasets before they are made.