A comparison of the power of categorical and correlational tests applied to community ecology data from gradient studies

Summary Where gradients exist it is possible for a global test of community change to fail to achieve significance even though pairwise tests between groups of samples from opposite ends of gradients reveal significant differences. This study examines the power of alternative tests in situations where spatial (or temporal) gradients exist. Data from an oilfield survey in the Norwegian sector of the North Sea are used to examine the power of two types of test. There is no theoretical statistical framework with which to examine the formal power of the non‐parametric multivariate tests. A univariate analogue is used to demonstrate the behaviour and relative power of linear regression and anova to detect different strengths of gradients. Two multivariate tests are then contrasted using simulations. anosim (Analysis of Similarities) is a categorical analysis and, for an ecological matrix of pairwise dissimilarities among all samples, tests null hypotheses of the anova type: H 0 : There are no differences between groups of samples. This test is compared with relate , a non‐parametric Mantel test which is used here to test the null hypothesis: H 0 : The dissimilarities among samples in the ecological matrix are not (monotonically) correlated with corresponding ‘model’ distances between samples along the gradient. It is demonstrated that, where a gradient is present in the data, an appropriate univariate test based on linear regression always has greater power than anova to detect it. This is especially true where the gradient is weak and/or replication is low. It is shown that the multivariate tests behave in a similar way to their univariate analogues. Where there is a detectable gradient in the data the correlative test ( relate ) has greater potential to detect it than does the categorical test anosim . The differences in power are especially apparent at low to intermediate strengths of gradient. Distributing replicates among more groups decreases the power of both tests, but especially anosim , to detect a constant gradient effect. Although demonstrated using a practical application, the findings presented here are general in nature and applicable to any ecological investigation in which a gradient in response may be hypothesized.