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

Morphometric data of Aphis gossypii Clover are used as a case study to illu strate the use of randomization tests. The application of randomization tes ts 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 ov ercome problems of small sample size, unequal sample size, and departures f rom normality. We review randomization test methodology. We address a few e rrors that have appeared in the literature. One question is how many random izations. 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 methodolog y is introduced for using randomization tests to determine if the average o f several observations is different from a constant. An extension of the me thod is used when the null hypothesis states that there are differences. Th is is important where there is reason to suspect that one is dealing with d ifferent populations (e.g., morphological measurements were taken from seve ral distinct populations of an insect) and one needs to identify which popu lations are the same. This test should not be confused with the typical cas e where it is simply impossible to identify differences between different s ets of observation. We present a SAS program to perform 2-tailed tests for differences between means.