MathBench > Statistical Tests

Chi-squared Tests

Interpreting the chi-squared test

 

So, once you know the degrees of freedom (or df), you can use a chi-squared lookup table like the one on the right to show you the chi-squared critical value corresponding to α = 0.05. That's the whole detour summed up in one sentence. Whew.

For Dilbert's test, with 1 df , the chi-squared critical value is 3.84, whereas his chi-squared statistic was 0.167.

What does critical value mean?

sad faceBasically, if the chi-squared statistic you calculated was bigger than the critical value in the table, then the data did not fit the model, which means you have to reject the null hypothesis.

happy faceOn the other hand, if the chi-squared statistic you calculated was smaller than the critical value, then the data did fit the model, and you do not reject the null hypothesis, and go out and party.* (*Assuming you don't want to reject the null. Which you usually don't.)

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

 

Why do you think the chi-squared critical value increases as the degrees of freedom increase?

 

(To make this problem interactive, turn on javascript!)

I think I have the answer: With a lot of degrees of freedom,
you have a lot of rows in your table. Therefore you're adding
more numbers together to get your final chi-squared statistic.
So it makes sense that the critical value also increases.

Fine print: some chi-squared tables have many columns, one for each α value you might be interested in. In that case, you first need to find the 0.05 α value (or any other α value you're asked for), then the df, and then the chi-squared critical value.