Systematic Sampling

Systematic sampling involves selecting units at a fixed interval. There are two common applications. The first is where there exists a list of units in the population of interest that can be used as a sampling frame. Then, the procedure is to select every Ath on the list. The second is where no list exists, but sampling of a flow is to be carried out in the field. (Examples of flows include visitors to a museum, passengers arriving at a station, and vehicles crossing a border.) Then, the procedure is to select every Ath unit passing a specified point. This is conceptually equivalent to creating a list of units in the order that they pass the point and then sampling systematically from the list, so the principles of systematic sampling can be illustrated by considering only list sampling.

The first step in systematic sampling is to calculate the sampling interval, A = N/n. For example, to select a sample of n = 100 from a list of N = 1,512 units, then A = 15.12. The second step is to generate a random start. This will determine which is the first unit on the list to be sampled. In fact, it will determine the entire sample, because the remaining selections are obtained by repeatedly adding the fixed interval; no further random mechanism is involved. The random start should be a number between 1 and 1 + A. Step 3 is to successively add A to the random start. Thus, if the random start is 4.86, the following numbers will be obtained: 4.86, 19.98, 35.10, 50.22,…, 1501.74. The final step is to ignore the decimal places—the sampled units are the 4th, 19th, 35th, 50th,… 1501st on the list. This procedure will result in the selection of exactly n units. In the case of flow sampling, N is unknown, so A is usually chosen on practical grounds.

A common motivation for using systematic sampling is practical simplicity. The case of flow sampling is a good example. In many situations, there is no other way to select a random sample from a flow, because no lists exist and it is not possible to create such a list in order to sample subsequently from the list in some other way. Practical considerations also apply in other situations. For example, consider sampling from a set of card files arranged in a series of filing cabinets. Systematic sampling avoids the need to remove the cards from the cabinets and re-sort them, or to number all the cards. It is necessary only to count through them.

If the units are ordered in a meaningful way, systematic sampling has the (typically beneficial) effect of achieving implicit stratification (see stratified sample). This is often perceived as an advantage of systematic sampling over simple random sampling.

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Many surveys employ systematic sampling within explicit strata. Again, the same argument applies to systematic flow sampling. If a survey is sampling visitors to a museum and there is a tendency for visitors with different characteristics to be represented in different proportions at different times of day, then systematic sampling over the course of a whole day should result in improved precision of estimation compared with a simple random sample of the same size of that day's visitors.

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