# Systematic sampling

This, the most widely used form of cluster sampling, will be illustrated by its application to a frequently occurring problem situation that is, a researcher has a complete list from which probability sample is to be selected.

Example: Assume one wishes to study dentists’ attitudes toward dental insurance and decides to sample 20 dentists from a list of 100 dentists. One way of doing this is as follows:

1. Draw a random number between 1 and 5. Assume the number chosen is 2.
2. Include in the sample the dentists numbered 2, 7, 12, 17, 22, —-97. That is, starting with number 2, take every fifth number.

The above is an illustration of systematic sampling. That this is a particular kind of cluster sampling is readily seen if all possible samples produced by this procedure are considered.

Selecting a Systematic Sample:

A systematic sample can be selected from a list of universe items using a four step procedure.

1. The first step is to determine the total number of items in the universe. Divide this figure by the desired sample size. The result is called the sampling interval.

Sampling interval = number of universe items / desired sample size

2. Select a random number between 1 and the sampling interval figure. This identifies the first element on the universe list to be included in the sample.
3. Add the sampling interval to the random number selected in step 2. The total represents the second element on the universe list to be included in the sample.
4. Continue adding the sampling interval to each total to create a new total. Each new total represents another element on the universe list to be included in the sample.

Example: To illustrate, reconsider the problem of choosing a sample of n = 216 from the hotel chain’s list of N= 21,476 prospects. Simple random sampling is a perfectly valid way to do this. However, it is much simpler to use systematic sampling. The sampling interval is 21,476/ 216, or about 99. Draw a random number between 01 and 99. Assume the random number is 14, then the sample will consist of the universe list items numbered 14, 113, 212, 311 and so on.

Advantages of Systematic sampling:

In one form or another, wide use is made of systematic sampling. The principal advantage of this technique is its simplicity. When sampling from a list, it is easier to choose a random sample start and select every kth item thereafter than to make a simple random selection. The technique is faster and less subject to error than simple random selection. Hence, systematic sampling is often used in place of simple random sampling. For example, it might be used instead of simple random sampling for selecting items within strata in a stratified design.

In common with simple random sampling, the mean of a systematic sample is an essentially unbiased estimate of the universe mean. As each of the five possible samples shown has the same chance of being chosen and the average of the five sample means is equal to the universe mean, the sample mean provides an unbiased estimate.

It is often found that systematic sampling is somewhat more efficient statistically than is simple random sampling. This will be the case when adjacent universe items on the listing are similar and items widely removed from one another are dissimilar. For example, if a list were made up by listing grocery stores in order according to dollar sales volume and the variable being sampled was correlated with sales, then it would be expected that systematic sampling would be more precise than simple random sampling. The ordering of stores by dollar volume in this case would set up an implicit stratification, and the systematic sampling would operate much like a stratified random sampling, with a single store chosen out of each stratum.

• Johntumaku

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