In this section we look at two further techniques for sampling: *systematic* sampling and *quota* sampling.

A *systematic sample* is taken by sampling at regular intervals.

A *quota sample* is when the different categories that make up the population are represented according to their proportion within the overall population.

A typical use of quota sampling is in opinion poll surveys where there is a need to reflect the way the population breaks down between the two genders, into different age groupings, into cultural and ethnic backgrounds, etc. The choice of people selected from each category is left to the person collecting the information.

We will use the class from Example 1 at the beginning of this unit to demonstrate how to use these sampling techniques. The names are listed again below:

1 Alan | 10 Rachel | 19 Sacha | 28 Salif |

2 Lucy | 11 Ben | 20 Halim | 29 Annie |

3 Tom | 12 Emma | 21 Daniella | 30 Karen |

4 Azar | 13 Hannah | 22 Joseph | |

5 Jayne | 14 Grace | 23 Anna | |

6 Nadima | 15 Miles | 24 Sophie | |

7 Matthew | 16 James | 25 Kathryn | |

8 Sushi | 17 Joshua | 26 Helen | |

9 Mohammed | 18 Lisa | 27 Fatoumata | |

Select a systematic sample of size

(a)

5,

As there are 30 pupils in the class, and we want a sample of 6, we calculate 30 ÷ 6 = 5. We can then obtain our sample of size 6 by selecting every 5th member of the class.

This would give:

5 | Jayne |

10 | Rachel |

15 | Miles |

20 | Halim |

25 | Kathryn |

30 | Karen |

(b)

6 from the class.

For a sample of size 5 we could select every 6th member of the class:

6 | Nadima |

12 | Emma |

18 | Lisa |

24 | Sophie |

30 | Karen |

You can select a systematic sample of size 6 by choosing any of the first 5 items as a starting point and then taking every 5th item thereafter. For example, in part (a) we could have started with pupil number 2 (Lucy) and then selected pupils number 7, 12, 17, 22 and 27. This would have generated the sample

Lucy, Matthew, Emma, Joshua, Joseph, Fatoumata.

Similarly, starting with pupil number 4 (Azar) in part (b) would have generated the sample

Azar, Rachel, James, Joseph, Salif.

Create a quota sample of size 10 from the class.

Note that the class contains 12 boys and 18 girls.

As the ratio of boys to girls is 2 to 3 in the class, they must be in the same ratio in the sample.

So for a sample of 10 we need 4 boys and 6 girls. These do not need to be chosen at random, and so could be:

Alan | Lucy |

Tom | Jayne |

Azar | Nadima |

Matthew | Sushi |

Rachel | |

Emma |

If the teacher is selecting the pupils then it is possible that they may choose their favourite 4 boys and 6 girls, which would introduce some bias to the sample. It is best to avoid this possibility by selecting 4 boys randomly from the group of 12 boys, likewise for the girls. This produces a *stratified random sample*. We will look at stratified random samples in more detail in section 18.3