Aggregation and the Pearson Chi‐Square Statistic for Homogeneous Proportions and Distributions in Ecology

Abstract

The null hypothesis that the proportions or relative abundance among j mutually exclusive categories (e.g., species or sizes) is the same for two or more populations (e.g., locations or sexes, respectively) is often tested with Pearson chi—square goodness—of—fit statistic. The chi—square statistic is derived under the assumption that the objects counted are independently and identically distributed. Count data from samples of cluster of groups of objects, for example, with transects, grabs, trawls, and quadrat usually fail to meet these assumptions. Many articles appear in the ecological literature that fail to realize the implications of violating the assumptions implicit in the use of the chi—square distribution test of homogeneity of proportions. Species aggregation, alone and in combination with increased mean abundance, and a large number of categories are shown to increase Type I error rates. Pooling several samples to get a representative sample does not solve the problem for <14 replicate samples for ecologically plausible levels of aggregation. An easily implemented solution is suggested.