A cautionary note on the use of non-parametric tests in the Analysis of Environmental Data

Observations made on many environmental variables do not often follow a normal distribution. Even the widely used logarithmic transformation does not guarantee normality of the transformed data. Because of this, resort is often made, when comparing groups of observations, to non-parametric test procedures. Although the null hypothesis of interest in such analyses is often that the means of two groups are the same, this is not the null hypothesis tested in these procedures. This implies that use of these tests as procedures for means may be invalid, in that even when the group means are equal, the test does not have the Type I error chosen. Further problems arise with non-independent data. We report the results of a Monte Carlo study where: (a) the means of the two groups are the same, but other characteristics differ; (b) the differences of pairs in a paired-comparison model are dependent; and (c) the marginal distributions of pairs are dependent, but not identical. We note that frequently used non-parametric procedures when the assumptions are violated are not valid. The results demonstrate the importance of understanding the assumptions required for the validity of non-parametric test procedures.