## Hypothesis Testing

Plotting all of the curves from a fully replicated study can produce complex graphs in which the pattern may be difficult to discern. Figure 3 shows the replicate curves from the sand-flat study. It is clear that all replicates in the 0.5 mm samples are less diverse than all samples collected on smaller meshes, but is there evidence for differences in dominance/diversity between the 250 mm samples and the 63 mm samples? If ¿-dominance curves are calculated for replicates at a number of sites, times, or conditions, a Species rank

Figure 3 k-Dominance curves for samples of invertebrates from a marine intertidal sand-flat. Each curve is based on abundances in a single sample. Four replicate samples were collected using three combinations of sieve mesh and sample areas as in Figure 1.

### Species rank

Figure 3 k-Dominance curves for samples of invertebrates from a marine intertidal sand-flat. Each curve is based on abundances in a single sample. Four replicate samples were collected using three combinations of sieve mesh and sample areas as in Figure 1.

measure of dissimilarity can be constructed between any pair of curves, for example, based on their absolute distance apart, summed across the species ranks. When computed for all pairs of samples in a study, this provides a (ranked) triangular dissimilarity matrix, essentially similar in structure to that from a multivariate analysis; thus, 1-way and 2-way ANOSIM tests that are used in multi-variate analysis can be used in exactly the same way to test hypotheses about differences between a priori specified groups of samples. In this case the test shows unequivocally that there is a significant difference between the 250 mm samples and the 63 mm samples: curves within groups are more similar to each other than they are to curves in different groups. What the test does not reveal is the form of those significant differences. For this we need averaged plots (e.g., Figure 1) or plots based on subsets of replicates.