What it shows
Systematic sampling takes a random starting point and then every kth unit. Here the population of 120 is numbered 1 to 120, the interval is 15 and the random start is 11, so the sample runs 11, 26, 41 and on to 116.
The population is drawn 12 to a row rather than 15. With rows of 15 the sample would form a single column; with rows of 12 each step moves down and along, which shows that the pattern follows the list order rather than the layout.
How to read it
The shaded first stretch, units 1 to 15, is the range the random start is drawn from.
From unit 11, count 15 places forward in reading order to reach each next selected unit.
Twice, from 11 to 26 and from 71 to 86, the step runs past the end of a row and lands two rows down.
The numbers behind it
- Population N = 120, numbered 1 to 120 in rows of 12. Sample n = 8.
- Interval k = N / n = 120 / 8 = 15. Random start: 11.
- Selected: 11, 26, 41, 56, 71, 86, 101, 116.
Ways to use it in teaching
Discuss periodicity: if every fifteenth house on a street were a corner lot, this method would sample only corner lots.
Students can compute k and choose a start for a population of their own.
Contrast it with simple random sampling: both are probability methods, but only one makes every possible set of units equally likely.
For when each method suits a study, and how to justify the choice in a methodology chapter, see our guide to sampling methods.
Sources
Cochran, W. G. (1977), Sampling Techniques, 3rd ed., New York: Wiley. The numbers follow the worked example in Wikipedia's Systematic sampling article (8 houses from a street of 120).
