# Interpreting the chi-square test

For Dilbert's test, with 1 df , the chi-square-crit is 3.84, whereas his chi-square-calc was 0.167. What does critical value mean? Basically, On the other hand, |

### Why do you think the chi-square-crit increases as the degrees of freedom increases?

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

- I need a hint ... : If you have, say, 15 degrees of freedom,

how many rows are in your table?

- ...another hint ... : For every row in the table you need to calculate another deviation.

#### 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-square.

So it makes sense that the critical value also increases.

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

Even finer print: or, you may be asked to find the p-value corresponding to the chi-square-calc. In that case you have to find the right df first, then find the two chi-square-crits that your chi-square-calc falls between, then note the p-value.

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