The muon ionization cooling experiment (MICE) will demonstrate a new technique for reducing the transverse emittance of a beam of muon particles, which are a species of lepton heavier than the electron species, essential for the realization of a future Neutrino Factory research facility. The first use of the Grid within MICE was to run thousands of Monte Carlo simulations to determine the alignment and statistical errors associated with measurements in MICE, which are made at two points in space on a similar sample of particles. The results of this study quantified the effect of correlations between emittance measurements. As a consequence, it has been determined that an order of magnitude less muons are required to achieve the required statistical accuracy than assuming uncorrelated measurements. This first application of the Grid within the MICE experimental domain has yielded results that could significantly impact upon the necessary running time of the experiment.