Distribution‐Free and Robust Statistical Methods: Viable Alternatives to Parametric Statistics

Abstract

After making a case for the prevalence of nonnormality, this paper attempts to introduce some distribution—free and robust techniques to ecologists and to offer a critical appraisal of the potential advantages and drawbacks of these methods. The techniques presented fall into two distinct categories, methods based on ranks and "computer—intensive" techniques. Distribution—free rank tests have features that can be recommended. They free the practitioner from concern about the underlying distribution and are very robust to outliers. If the distribution underlying the observations is other than normal, rank tests tend to be more efficient than their parametric counterparts. The absence, in computing packages, or rank procedures for complex designs may, however, severely limit their use for ecological data. An entire body of novel distribution—free methods has been developed in parallel with the increasing capacities of today's computers to process large quantities of data. These techniques either reshuffle or resample a data set (i.e., sample with replacement) in order to perform their analyses. The former we shall refer to as "permutation" or "randomization" methods and the latter as "bootstrap" techniques. These computer—intensive methods provide new alternatives for the problem of a small and/or unbalanced data set, and they may be the solution for parameter estimation when the sampling distribution cannot be derived analytically. Caution must be exercised in the interpretation of these estimates because confidence limits may be too small.