Assessing the Goodness-of-Fit of Statistical Distributions When Data Are Grouped

Modeling statistical distributions of phenomena can be compromised by the choice of goodness-of-fit statistics. The Pearson chi-square test is the most commonly used test in the geosciences, but the lesser known empirical distribution function (EDF) statistics should be preferred in many test situations. Using a data set from geomorphology, the Anderson–Darling test for grouped exponential distributions is employed to illustrate ease of use and statistical advantages of this EDF test. Attention to the issues discussed will result in more informed statistic selection and increased rigor in the identification of distribution functions that describe random variables.