Systematic Sampling

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Abstract
Systematic sampling is a simple and flexible way of selecting a probability sample from a finite population. It was introduced in the early days of probability sampling in survey research and it remains in widespread use today. A systematic sample is obtained by selecting a random start between 1 andkfrom a list of the population and then taking everykth element thereafter. The ordering of the list determines the precision of the survey estimates; a random order produces a sample that has the same precision as a simple random sample, whereas an order that is monotonically associated with the variables under study gives greater precision than a simple random sample. A single‐stage systematic sample is equivalent to the selection of a single cluster and, hence, variance estimation is not possible without a model assumption. Systematic sampling is widely used to select units with unequal probabilities without replacement, as, for instance, with probability proportional to size sampling in multistage surveys. In such cases, the collapsed stratum technique is frequently used for variance estimation. Systematic sampling is often applied in two dimensions in spatial surveys of geographical areas.

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