Systematic Sampling

Systematic sampling is a random method of sampling that applies a constant interval to choosing a sample of elements from the sampling frame. It is in common use in part because little training is needed to select one. Suppose a sample of size n is desired from a population of size N = nk. Systematic sampling uses a random number r between 1 and k to determine the first selection. The remaining selections are obtained by taking every kth listing thereafter from the ordered list to yield the sample of size n. Because it designates the number of records to skip to get to the next selection, k is referred to as the skip interval.

Systematic sampling is particularly desirable when on-site staff, rather than a data collection vendor, select the sample. For example, one-page sampling instructions can be developed for a survey of mine employees that explain how the mine operator is to order the employees and then make the first and subsequent sample selections using a pre-supplied random starting point. Systematic sampling is also useful in sampling on a flow basis, such as sampling clients entering a facility to obtain services such as emergency food assistance or health care. In this situation, the facility manager is approached to determine how many clients might visit in the specified time period. This population estimate

is used to determine the skip interval k based upon the desired sample n of clients from the facility. At the end of specified time period, the actual population N of clients is recorded.

Frequently, the population size N, together with the desired sample size n, results in a skip interval k that is a real number as opposed to an integer value. In this case, the simplest solution is to round k down to create a skip interval that is an integer. This approach results in a variable sample size (n or n + 1), but it is preferable for use by nontechnical staff. Alternately, the list can be regarded as circular, with a random number between 1 and N selected and then a systematic sample of size n selected using the integer value of k obtained by rounding down. An easily programmable option is to select a real number between 1 and k as the random starting point and then continue adding the real number k to the random starting point to get n real numbers, which are rounded down to integers to determine the records selected for the sample.

Systematic sampling can be viewed as a form of implicit stratification. Conceptually, the frame is split into n zones each of size k and one selection made from each zone. When the frame is sorted by key analysis domains prior to selection, this implicit stratification results in a sample that is close to the results of stratification with proportional allocation. Care must be taken in ordering the sample and in using a pre-ordered frame when systematic sampling is planned. A frame sorted by age, for instance, could produce samples that skew young or skew old, depending on the random start. The worst case scenario is a list that has an underlying periodicity to the observations, and this periodicity corresponds to the skip interval.

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