Systematic random sample

Selecting

Systematic or interval sampling, as it is sometimes called, is based on random sampling, but often is easier to complete than simple random sampling. As with all random sampling, the investigator must define the target population, find or create a suitable sampling frame, and number each element in the frame. Instead of drawing each element at random, the investigator calculates a sampling interval and uses this interval in selecting elements to be included in the sample.

We can use our faculty illustration to show how a systemic sample, is selected. Calculation of the interval is based on the ratio of the sample size to the size of the target population. Using the faculty illustration, we want a sample of 100 faculty members from a target population of 500. The ratio then becomes 100/500 or 1 in 5. To get a sample of 100, we will need to establish an interval of 5. Then, selecting 1 name out of every 5 names in the sample frame will give us a sample of 100 names. Using a faculty list as the sampling frame, we select every fifth name. But, we have to do this in a random way. To create a random systemic sample, we:

1. Number each element (name) on the sampling frame.    In our example, the names, as before, would be numbered from 1 to 500.

2. Establish the sampling interval that is needed.   As already explained, we will use an interval of 5.

3. Using the box method or a table of random numbers, select a random start point. In this case, we are looking for a number between 1 and 5. Using the procedures defined previously, we would select a starting point. Let's say the number chosen was 4.   Sample element 4 would therefore become the first member of the sample.

4. Select elements from the sampling frame that occur at the stated interval. Starting with the fourth name on the list, we would select every fifth name. Thus, the sample would consist of names represented by numbers 4, 9, 14, 19, etc., up to 499 on the list of faculty members. The resulting 100 numbers and corresponding names is a systematic random sample.

Caution in using systematic samples

Systematic sampling can introduce a special kind of bias.   To illustrate how this could happen, suppose you were studying the levels of job satisfaction among staff of a government ministry. Since the ministry has a complete list of all staff, you decide to use systematic sampling. Also, you decide to use a sampling interval of 20. Now, suppose that the first name you selected was a supervisor and that a supervisor's name appeared as every 20th name thereafter. If this were the case, you would have selected a supervisor for the first sample member. Then, by using the interval of 20 you would have selected only supervisors for the rest of the sample.    Thus, the entire sample would be made up of supervisors.   The problem with this is that a sample based on supervisors only would not be representative of the population of all staff of the ministry.   With their higher positions, supervisors have greater responsibilities, are better paid, and have more privileges. Consequently, their job satisfaction levels certainly would be different from the rest of the other staff.   Obviously, any results based on responses of only supervisors would be biased and could not be used to describe the morale of the staff in the ministry.

This kind of problem can occur in using an interval sample in any formal organization, such as a government ministry, university, or military unit. When you plan to use a systematic sample, check to see if the names on the sampling frame are arranged in any systematic order.   If some kind of order exists, then a simple random sample should be used or another method, called a stratified sample, which we describe next, should be used.