### <<<back to sign test

The **sign test** can be used to test for:

- Differences
- In related data (e.g. repeated measures)
- In the nominal format

To find the correct **critical value** when calculating whether results are statistically significant using the sign test, you need to know:

- Whether your experimental hypothesis is one-tailed or two-tailed
- Your sample size (n) – e.g. the number of participants in your trial
- The level of significance (
*p*)

**Your results are statistically significant if the observed value is equal to or less than the critical value.**

*Note: Tables like the ones below will be provided in the exam – you don’t have to memorise all these critical values!*

## One-tailed

**One-tailed: **The experimental hypothesis predicts a change in only *one* direction (also called a *directional* hypothesis).

The following are critical values for one-tailed experiments with sample sizes (n) between 5-20 and *p* values of 0.1, 0.05, and 0.02.

n |
p = 0.1 |
p = 0.05 |
p = 0.02 |

5 |
0 | 0 | – |

6 |
1 | 0 | 0 |

7 |
1 | 0 | 0 |

8 |
1 | 1 | 0 |

9 |
2 | 1 | 1 |

10 |
2 | 1 | 1 |

11 |
3 | 2 | 1 |

12 |
3 | 2 | 2 |

13 |
3 | 3 | 2 |

14 |
4 | 3 | 2 |

15 |
4 | 3 | 3 |

16 |
5 | 4 | 3 |

17 |
5 | 4 | 4 |

18 |
6 | 5 | 4 |

19 |
6 | 5 | 4 |

20 |
6 | 5 | 5 |

Your results are statistically significant *if the observed value is equal to or less than the critical value.*

## Two-tailed

**Two-tailed: **The experimental hypothesis predicts a change in *either* direction (also called a *non-directional* hypothesis).

The following are critical values for two-tailed experiments with sample sizes (n) between 5-20 and *p* values of 0.1, 0.05 and 0.02.

n |
p = 0.1 |
p = 0.05 |
p = 0.02 |

5 |
0 | – | – |

6 |
0 | 0 | – |

7 |
0 | 0 | 0 |

8 |
1 | 0 | 0 |

9 |
1 | 1 | 0 |

10 |
1 | 1 | 0 |

11 |
2 | 1 | 1 |

12 |
2 | 2 | 1 |

13 |
3 | 2 | 1 |

14 |
3 | 2 | 2 |

15 |
3 | 3 | 2 |

16 |
4 | 3 | 2 |

17 |
4 | 4 | 3 |

18 |
5 | 4 | 3 |

19 |
5 | 4 | 4 |

20 |
5 | 5 | 4 |

Your results are statistically significant *if the observed value is equal to or less than the critical value.*