2 – Relationships between variables

This chapter monitors the quality of drinking water in a region. To do this one needs to fill bottles with samples of water and analyses the contents. Some of the items measured are acidity, chemical content, including traces of lead or other metals, coloration, and number of microbes. The point illustrated, and of principal interest in this chapter, is that one is interested in more than one variate for each bottle analyzed. However, complications arise when one starts to define the details of an appropriate random sampling scheme. One could begin by identifying all the kitchen mains supply taps in the region. The simplest procedure would be to number all the taps and use computer generated random numbers to select those from which the bottles would be filled on each occasion. Such a procedure is an example of a simple random sampling scheme.