N

The total population size is traditionally labeled N, as opposed to the sample size, which is termed n. The population size N refers to the total number of elements in the population, target population, or universe.

N also refers to the number of elements on the sampling frame from which the sample is to be drawn. Since in many cases, the list of population elements contains foreign elements, the accurate number of eligible population elements is less than the number of elements on the list. In other cases, the population list not only contains foreign elements but also contains omissions and inaccuracies. These further put into question the validity of the value of N, which should be assessed carefully both before and after sample selection and survey implementation.

In some situations N is unknown, and in fact one of the objectives of the survey is to estimate N and its distributional characteristics. In other situations N is known only approximately, and its estimate is refined based on the information obtained from the survey.

It is almost always true that N is larger than n and usually by orders of magnitude. In fact, the ratio (n/N) is often referred to as the sampling fraction. Often the population size N is so large relative to n that we can safely assume that with replacement sampling holds even if without replacement sampling is implemented in practice. The relative sizes of n and N also play a role in determining whether the finite population correction factor [1 − (n/N)] is sufficiently different from 1 to play a role in the calculation of sampling variance.