Despite over a century of study, the relationship between lunar cycles and earthquakes remains controversial and difficult to quantitatively investigate. Perhaps as a consequence, major earthquakes around the globe are frequently followed by 'prediction' claims, using lunar cycles, that generate media furore and pressure scientists to provide resolute answers. The 2010-2011 Canterbury earthquakes in New Zealand were no exception; significant media attention was given to lunarderived earthquake predictions by non-scientists, even though the predictions were merely 'opinions' and were not based on any statistically robust temporal or causal relationships. This thesis provides a framework for studying lunisolar earthquake temporal relationships by developing replicable statistical methodology based on peer reviewed literature. Notable in the methodology is a high accuracy ephemeris, called ECLPSE, designed specifically by the author for use on earthquake catalogs, and a model for performing phase angle analysis. The statistical tests were carried out on two 'declustered' seismic catalogs, one containing the aftershocks from the Mw7.1 earthquake in Canterbury, and the other containing Australian seismicity from the past two decades. Australia is an intraplate setting far removed from active plate boundaries and Canterbury is proximal to a plate boundary, thus allowing for comparison based on tectonic regime and corresponding tectonic loading rate. No strong, conclusive, statistical correlations were found at any level of the earthquake catalogs, looking at large events, onshore events, offshore events, and the fault type of some events. This was concluded using Schuster's test of significance with α=5% and analysis of standard deviations. A few weak correlations, with p-5-10% of rejecting the null hypothesis, and anomalous standard deviations were found, but these are difficult to interpret. The results invalidate the statistical robustness of 'earthquake predictions' using lunisolar parameters in this instance. An ambitious researcher could improve on the quality of the results and on the range of parameters analyzed. The conclusions of the thesis raise more questions than answers, but the thesis provides an adaptable methodology that can be used to further investigation the problem.