EPSEM Sample

Sampling involves the selection of a portion of the population being studied. In probability sampling, each element in the population has a known, nonzero chance of being selected through the use of a random selection procedure. EPSEM refers to an equal probability of selection method. It is not a specific sampling method such as systematic sampling, stratified sampling, or multi-stage sampling. Rather it refers to the application of a sampling technique that results in the population elements having equal probabilities of being included in the sample. EPSEM samples are self-weigh ting; that is, the reciprocal of the probability of selection of each element in the selected sample is the same. Thus the base sampling weighting for each selected element in the sample is a constant equal to or greater than one (1.00).

The most common examples of equal probability of selection methods are (a) simple random sampling, (b) unrestricted random sampling, (c) systematic random sampling, (d) stratified sampling, and (e) proportionate stratified sampling. Simple random sampling refers to equal probability of selection element sample without replacement. Unrestricted random sampling refers to equal probability of selection element sample with replacement. Systematic random sampling refers to the selection of elements using a sampling interval and a random start. Stratified sampling refers to the formation of mutually exclusive and exhaustive groupings of elements. Proportionate stratified sampling then entails selecting a sample from the strata so that the proportion of the total sample allocated to each stratum equals the proportion of the total elements in the population in each stratum. So for example, if a stratum contains 25% of the population elements, 25% of the sample would be selected from that stratum.

A multi-stage sample can also be an EPSEM sample. The simplest example is a multi-stage design based on equal probabilities of selection at each stage of sampling. A more common practical example is a multi-stage design that results in an overall equal probability of selection of each element in the population, but at each stage the probabilities of selection are not equal. In two-stage sampling the clusters are usually of unequal size (i.e. the number of elements in the clusters vary from cluster to cluster, with some small clusters and some large clusters). If a probability proportional to size (PPS) sample of clusters is drawn, the larger the cluster the greater its probability for selection. So, at the first stage, the probabilities of selection are unequal. At the second stage of sampling, an equal number of elements are selected using simple random sampling from the sample clusters. So, at the second stage, the within-cluster probability of selection of an element is higher if the cluster is smaller. However, the product of the first-stage selection probability of the cluster and the second-stage probability of selection of the element within the cluster is a constant for all elements in the population. Thus, an EPSEM sample is achieved.