Sampling a Site or Region with Spatial Units
Sometimes the sampling elements available for selection are not the same as the elements we wish to study. This happens most frequently in archaeology in spatially based sampling, as in the excavation of a sample of grid squares in a site or the survey of a sample of grid squares or transects in a region. For instance, suppose we have a random sample of 500 sherds from a site. We may want to estimate, say, the mean thickness of sherds at the site or the percentage of a particular pottery type in the sherds at the site. The elements studied are sherds. Suppose the sample had been obtained by excavating a random sample of ten grid squares. The sampling element here is not the sherd but the grid square. It was ten grid squares that were randomly selected from all the squares in the site grid, not 500 sherds from all the sherds in the site. We thus have a sample, not of 500 independently selected elements, but of ten independently selected elements, and these elements do not correspond to the elements we need to study. Each sampling element is, in this case, a group or cluster of a varying number of the elements of study (sherds). This fact must be allowed for in making estimates of means or proportions. Estimating population means and proportions from samples, and attaching error ranges to those estimates was the subject of Chapters 9 and 11. This chapter extends that discussion to the special case where the sampling elements are different from the elements of study. This chapter on cluster sampling, then, can be considered a special case of the general topics dealt with in Chapters 9 and 11, which can be referred to as simple random sampling to distinguish them from more complex kinds of sampling. Cluster sampling is particularly important in archaeology because so much of the sampling we do is based on spatial units.