Randomization tests : Example using morphological differences in Aphis gossypii (Homoptera: Aphididae)

Morphometric data of Aphis gossypii Glover are used as a case study to illustrate the use of randomization tests. The application of randomization tests in morphological evaluation and identification of species is a powerful tool for characterizing populations and species. It offers the advantage of reducing our reliance on the robustness of more classical approaches to overcome problems of small sample size, unequal sample size, and departures from normality. We review randomization test methodology. We address a few errors that have appeared in the literature. One question is how many randomizations. As a generic starting point, the number of randomizations should be 2 orders of magnitude larger than the inverse of the significant P value, but in critical cases an exact figure can be determined. A new methodology is introduced for using randomization tests to determine if the average of several observations is different from a constant. An extension of the method is used when the null hypothesis states that there are differences. This is important where there is reason to suspect that one is dealing with different populations (e.g., morphological measurements were taken from several distinct populations of an insect) and one needs to identify which populations are the same. This test should not be confused with the typical case where it is simply impossible to identify differences between different sets of observation. We present a SAS program to perform 2-tailed tests for differences between means.