16. Non-parametric Tests

# 16.3 Paired Sample Sign Test

Here we have two measurements from each subject, typically before and after. If the difference between measurements is , assign a , if , assign a , if 0 assign a 0. (Be sure to keep the direction of subtraction consistent with the hypothesis.) We again have 2 cases, for small () and large () samples, as with the median sign test. The critical and test statistics are the same as the median sign test. We’ll work through an example with a small sample.

**Example 16.5** : We have the following data on number of ear infections on swimmers before and after taking a medication that is hypothesized to prevent infections :

Swimmer | Infections before, | Infections after, | Difference () |

A | 3 | 2 | + |

B | 0 | 1 | – |

C | 5 | 4 | + |

D | 4 | 0 | + |

E | 2 | 1 | + |

F | 4 | 3 | + |

G | 3 | 1 | + |

H | 5 | 3 | + |

I | 2 | 2 | 0 |

J | 1 | 3 | – |

In the last column, we have assigned when , when and when . We are interested in reduced infections so is “good” for this situation. Test if the reduction in infections is significant.

1. Hypothesis.

: MD difference 0

: MD difference 0

2. Critical statistic.

Use the Sign Test Critical Values Table with = (no. of ) + (no. of ) = 7 + 2 = 9 and with a one-tailed test to find

3. Test statistic.

4. Decide.

so do not reject .

5. Interpretation.

There is not enough evidence to say that there is a reduction in the number of infections.

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