8: Detour stop #2: What’s a chi-squared table?

degrees of freedom Χ2 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