## Stratified Sampling

Stratified sampling is a samplingmethod useful when the population to be sampled falls into distinctcategories. It is desirable that the sample reflect the population,so that the proportion of each category in the sample reflects theproportion of that category in the population.

Suppose that school pupils are to besurveyed on their opinion of school dinners. The school has 1000pupils, and the sample size is to be 150. The pupils are cateforisedinto sex and year groups as shown in the table below.

Year Group | Male | Female |

7 | 76 | 74 |

8 | 59 | 79 |

9 | 80 | 64 |

10 | 72 | 60 |

11 | 69 | 68 |

12 | 70 | 70 |

13 | 74 | 85 |

The formula for finding the number ineach category to be sampled is

Year Group | Male | Female |

7 | ||

8 | ||

9 | ||

10 | ||

11 | ||

12 | ||

13 |

We must round the numbers in the tableso that each is a whole number.

Year Group | Male | Female |

7 | 11 | 11 |

8 | 9 | 12 |

9 | 12 | 10 |

10 | 11 | 9 |

11 | 10 | 10 |

12 | 11 | 11 |

13 | 11 | 13 |

The numbers in the table add to 151 –1 more than the sample size of 150, but we have rounded both 10.5'sup. If we round one of them down, then the sample size is 150. Thenumber in each category to be sampled is given in the table below.

Year Group | Male | Female |

7 | 11 | 11 |

8 | 9 | 12 |

9 | 12 | 10 |

10 | 11 | 9 |

11 | 10 | 10 |

12 | 11 | 11 |

13 | 11 | 13 |

Within each category, simple randomsampling is used to select the pupiils.

Advantages

1. it can give more more representativepicture – or more accurate estimates - than simple random samplingwhen there the population is divided into distinct categories

2. It reflects the population structure

Disadvantages

1. within the categories or strata theproblems occur as for simple random sampling

2. if the strata are not clearlydefined they may overlap