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Systematic Sampling

Systematic sampling (also called interval sampling) is a probability sampling technique that selects population elements at fixed intervals. This sampling method can be used when there is an available list of all elements of the population of interest or when a convenience sample is selected using fixed intervals (also called a flow sample, e.g., selecting every 10th student entering a school building). Systematic sampling is also practical when the sampling frame covers a well-defined spatial area (e.g., selecting every fifth room from a college dormitory). In education research, systematic sampling could be used to sample students from rosters within schools or to select parents for a survey using an administrative list of e-mail addresses, among other situations. This entry reviews principles of systematic sampling, the relationship between systematic sampling and select other sampling methods, and practical considerations for implementation.

Basic Principles and Estimation Procedures

When an ordered list of population elements is available to serve as a sampling frame (e.g., a list of all students in a school), systematic sampling is straightforward. In this case, every kth element from the sampling frame is selected, starting at an element chosen at random from the first k. First, determine a sampling interval, k = N/n, where n is the desired sample size and N is the number of elements in the population. For example, to select a sample of n = 100 students from N = 1,315 students, k = 13.15. Second, generate a random start between zero and k to determine the first element of the population to be sampled (can be done using Microsoft Excel, dedicated statistical software, or online tools; often these generate numbers between zero and one, in this case multiply by k such that the result is between zero and k). Third, add k to the random start repeatedly. For example, if 5.16 is the random start, numbers generated will be: 5.16, 18.31, 31.46, 44.61, …, 1307.01. Finally, round the numbers to integers, which are the list positions of the sampled elements: 5, 18, 31, 45, …, 1307. This procedure will result in selecting exactly 100 individuals at an approximately equal interval (exactly equal intervals if k is an integer). Note that if the random start is less than 0.50, rounding to an integer will yield zero, and the first list position will be selected after the first time k is added. In the case of a flow sample where a sampling frame is unavailable, establish a sampling interval based on the desired proportion of the population to be sampled.

The sample mean, y=i=1nyin, where yi is the value of the outcome of interest for the ith sampled element, is an unbiased estimate of the population mean. With a randomly ordered population list, the population variance can be estimated by i=1nyi−y2n−1. However, nonrandom list orders (discussed later in this entry) require more complex variance estimates.

Relationship to Other Sampling Methods

If the population list order is random, systematic sampling has similarities to simple random sampling. However, using simple random sampling, any set of n population elements has the same chance of being selected. Many simple random samples will never be selected by systematic sampling (e.g., any sample including two adjacent population elements). The systematic sampling random start determines the rest of the sample, rather than each selection being made independently of all other selections as in simple random sampling. That being said, the probability of selection for each population element is equal for simple random and systematic sampling, 1k.

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