This chapter focuses on sampling as it should be in order that
- the sample is representative of its population within calculable margins of error;
- groups can validly be compared; and
- the size of differences or correlations between them in the population can be assessed.
The next chapter looks at how we actually draw samples in circumstances where, for one reason or another, these pure theoretical guidelines cannot be applied or it is not efficient to apply them in full, trying nonetheless to apply the same principles in unpromising circumstances.
Because the theory of sampling is based on a branch of mathematics (the theory of probability), we have to start with a short discussion of the mathematical description of samples. However, the mathematics will be kept to a minimum; you need to understand the principles and be able to apply them, but you will seldom or never be required to do the calculations yourself. (If you have some facility with formulae, you will find some in boxes throughout the chapter.) I have provided some simple exercises; I presume you will probably do these on a computer or calculator, if at all.
Having established how samples are described statistically, we can go on to look at how the margin of error in estimating population figures from what is observed in the sample can be calculated. At this point we will also look at different ways in which random samples can be drawn and their advantages and pitfalls. We then move on to look at comparing groups. The importance of comparing like with like is discussed, along with how we obtain groups which can validly be compared when random sampling is not the appropriate method.