Introduction

Consider the following sampling problem, taken from a real consulting session we encountered. A biologist was studying the density of a large mammal in different habitats in a large study area. He had defined eight habitat types. The species was always close to water bodies, so the biologist viewed water bodies as the sampling unit. He had delineated the habitats along each water body in the study area. During each of three field seasons, aerial surveys of most or all of the study area were flown two to four times per year. Individual animals were plotted on maps and the habitat each was in, at the time it was sighted, was subsequently determined. The biologist wished to determine which habitats were used disproportionately. More specifically, he wished to estimate density in each habitat and then test the null hypothesis that actual density was the same in each habitat. Ideally, this step would be carried out using a comprehensive test. If the null hypothesis was rejected, then pairwise comparisons would be made as explained in Section 3.7.

This example presents us with a host of problems from an analytical standpoint. Habitat patches varied in size and care must be taken in defining the population units if density is the characteristic of interest. It is problematic whether we have a random sample of habitats since the entire study area was covered in at least some of the surveys. The variable, number of individuals, was recorded at specific times so the population unit is an areatime, but we do not have a simple random sample of area-times within each year because there were only two to four surveys per year.