One of the primary goals in neutrino physics at the present moment is to make a measurement of the neutrino oscillation parameter B13 . This parameter, in addition to being unknown, could potentially allow for the introduction of CP violation into the lepton sector. The MINOS long-baseline neutrino oscillation experiment has the ability to make a measurement of this parameter, by looking for the oscillation of muon neutrinos to electron neutrinos between a Near and Far Detector over a distance of 735 km. This thesis discusses the development of an analysis framework to search for this oscillation mode. Two major improvements to pre-existing analysis techniques have been implemented by the author. First, a novel particle ID technique based on strip topology, known as the Library Event Matching (LEM) method, is optimized for use in MINOS. Second, a multiple bin likelihood method is developed to fit the data. These two improvements, when combined, increase MINOS' sensitivity to sin2(W13 ) by 27% over previous analyses. This thesis sees a small excess over background in the Far Detector. A Frequentist interpretation of the data rules out B13 = 0 at 91 %. A Bayesian interpretation of the data is also presented, placing the most stringent upper boundary on the oscillation parameter to date, at sin2 (2B13 ) < 0.09(0.015) for the Normal (Inverted) Hierarchy and 6cp = 0.