degrees of freedom | Χ^{2} crit for α = 0.05 |
---|---|

1 | 3.84 |

2 | 5.99 |

3 | 7.81 |

4 | 9.49 |

5 | 11.07 |

6 | 12.59 |

7 | 14.07 |

8 | 15.51 |

9 | 16.92 |

10 | 18.31 |

11 | 19.68 |

12 | 21.03 |

13 | 22.36 |

14 | 23.68 |

15 | 25.00 |

16 | 26.30 |

17 | 27.59 |

18 | 28.87 |

19 | 30.14 |

20 | 31.41 |

So, so far we have a chi-squared statistic, which has a p-value associated with it. This would be fine IF we actually knew what that p-value was. But we don’t. And in fact, finding out the p-value for any given chi-squared statistic would involve a complicated mathematical formula. Believe it or not, biologists are not actually big on complicated mathematical formulae. So instead we have a chi-squared lookup table (see right). This table consists of a set of critical values that correspond to a particular level of significance (usually α = 0.05) and degrees of freedom.

How do you know that this chi-squared critical value is the one and only chi-squared critical value that fits your dataset? It turns out that **you only need to know one thing about your dataset, which is how many rows are in your original chi-squared table.** For example, our chi-squared table had 2 data rows, one row for M/F and one row for T/W/Th. This means that the degrees of freedom, or “df” (more on those on the next page) equals 1. Therefore you look at the chi-squared critical value under degrees of freedom = 1 on the lookup table.

In general, the formula for degrees of freedom is:

df = number of data rows – 1