Apparatus and methods for quantifying a difference between a first population distribution data set and a second population distribution data set. The apparatus and methods may use randomly generated population distribution differences to generate a mapping of a population stability index to a population distribution difference function. The population distribution difference function may be more responsive to some differences between the first and second population distribution data sets than is the population stability index. The population distribution difference function thus may be used to identify differences between population distribution data sets. The differences may then be mapped to a corresponding population stability index. The population stability index may then be used to quantify a difference between the first and second data sets.