Systematic and random sampling
Systematic sampling means testing a hypothesis by taking several equally spaced items from a larger list, eg selecting the tenth, 20th and 30th visitor to a theme park. This can be particularly useful for product testing, especially when the item must be destroyed during the test.
Example
Megan’s company manufactures smartphones. In order to ensure that each is of a high quality she wants to take a systematic sample of seven phones from every 1,000 produced.
Megan calculates an interval she could use by dividing 1,000 by seven and rounding down to the nearest whole number.
1000/7 = 142.857143...
Therefore an interval she could use is 142.
Megan’s systematic sample can begin with any number as long as the numbers that come after it are equally spaced. Megan chooses to begin with the number 100.
She selects the following phones for testing:
100, 242, 384, 526, 668, 810, 952
Question
To take a systematic sample of eight from a list of 45 people, what would be a sensible interval to use?
- 3
- 5
- 7
- 9
5
45 ÷ 8 = 5.625, or 5 by rounding down to the nearest whole number.
An interval of seven or nine wouldn’t allow you to select eight items from the list as the numbers would quickly get too large: 1, 8, 15, 22, 29, 36, 43, 50 (There aren’t 50 items on the list).
A sample size of three would work but would mean that more items were selected from the first half of the list. A sample size of five is ideal.
