Abstract: The empirical cumulative distribution function (ecdf) naturally arises in nonparametric statistics, e.g. when testing for the equality of two distribution functions. Three such tests will be given along with a quick power study to highlight some of their differences. A more computationally efficient method for calculating the ecdf, as compared to what the definition suggests, is provided. The computational complexity of both ecdf algorithms is then discussed. Lastly, a few notes about some of R's methods will be mentioned.