Abstract:

This paper has argued that the sample size necessary in a survey does not primarily depend upon the size of the population from which the sample is to be drawn, but from other factors concerning the basic characteristics of the population and the quality of the information required from the sample. Hence the idea of a constant percentage sample size is a myth; there never has been, or will be, a sampling plan that requires a constant percentage of the population to be sampled, valid for all population sizes. To determine the correct sample size, for defined precision and confidence, some knowledge is required of P for attribute sampling or S for measured variates. This knowledge is not always available and thus, it may sometimes be argued, the procedures outlined earlier are vitiated. But, whilst it is often true that P or S are not precisely known, an approximate value is commonly available and this may well be good enough. Furthermore, a small error in P or S may not vitally affect the value of N obtained. If a big error is found, this would become clear as the sampling progressed and, should circumstances warrant it, a re-calculation of N can made and the remaining balance of the freshly estimated sample size N obtained on a statistical basis. Finally, this paper has only discussed straightforward single sample plans. Whilst the basic thesis of the paper holds whatever the kind of sampling plan envisaged, e.g. double sampling, or stratified sampling, the determination of the necessary sample size becomes more involved and the reader must be referred to the more specialised standard works on sampling, whether for the general background, the mathematical theory, or the survey design and analysis necessary for rigorous sampling.