Solving some statistical problems in analyses of experiments on choices of food and on associations with habitat

Abstract

Statistical tests for non-random associations with components of habitat or different kinds of prey require information about the availability of sub-habitats or types of prey. The data are obtained from sampling (Stage 1 samples). Tests are then constructed using this information to predict what will be the occupancy of habitats or composition of diet under the null hypothesis of random association. Estimates of actual occupancy of habitats or composition of diet are then obtained from Stage 2 sampling and tests are done to compare the observed data from Stage 2 with what was predicted from Stage 1. Estimates from each stage of sampling are subject to sampling error, particularly where small samples are involved. The errors involved in Stage 1 sampling are often ignored, resulting in biases in tests and excessive rejection of null hypotheses (i.e. non-random patterns are claimed when they are not present). Here, accurate tests are developed which take into account both types of error. For animals in patchy habitats, with two or more types of patch, the data from Stages 1 and 2 are used to derive maximal likelihood estimators for the proportions of area occupied by the sub-habitats and the proportions of animals in each sub-habitat. These are then used in χ 2 tests. For composition of diets, data are more complex, because the consumption of food of each type (on its own) must be estimated in separate experiments or sampling. So, Stage 1 sampling is more difficult and the maximal likelihood estimators described here are more complex. The accurate tests described here give much more realistic answers in that they properly control rates of Type I error, particularly with small samples. The effects of errors in Stage 1 sampling are, however, shown to be important, even for quite large samples. The tests can and should be used in any analyses of non-random association or preference among sub-habitats or types of prey.