- A significance level (common choices are 0.01, 0.05, and 0.10)
- Degrees of freedom
The Chi-square distribution table is commonly used in the following statistical tests:
- Chi-Square Test for Goodness of Fit
- Chi-Square Test for Homogeneity
- Chi-Square Test for Independence
When you conduct each of these tests, you’ll end up with a test statistic X2. To find out if this test statistic is statistically significant at some alpha level, you have two options:
- Compare the test statistic X2 to a critical value from the Chi-square distribution table.
- Compare the p-value of the test statistic X2 to a chosen alpha level.
Let’s walk through an example of how to use each of these approaches.
Suppose we conduct some type of Chi-Square test and end up with a test statistic X2 of 27.42 and our degrees of freedom is 14. We would like to know if these results are statistically significant.
Compare the test statistic X2 to a critical value from the Chi-square distribution table
The first approach we can use to determine if our results are statistically significant is to compare the test statistic X2 of 27.42 to the critical value in the Chi-square distribution table. The critical value is the value in the table that aligns with a significance value of 0.05 and a degrees of freedom of 14. This number turns out to be 23.685:
Since out test statistic X2 (27.42) is larger than the critical value (23.685), we reject the null hypothesis of our test. We have sufficient evidence to say that our results are statistically significant at alpha level 0.05.
Compare the p-value of the test statistic X2 to a chosen alpha level
The second approach we can use to determine if our results are statistically significant is to find the p-value for the test statistic X2 of 27.42. In order to find this p-value, we can’t use the Chi-square distribution table because it only provides us with critical values, not p-values.
So, in order to find this p-value we need to use a Chi-Square Distribution Calculator with the following inputs:
Note: Fill in the values for “Degrees of Freedom” and “Chi-square critical value”, but leave “cumulative probability” blank and click the “Calculate P-value” button.
The calculator returns the cumulative probability, so to find the p-value we can simply use 1 – 0.98303 = 0.01697.
Since the p-value (0.01697) is less than our alpha level of 0.05, we reject the null hypothesis of our test. We have sufficient evidence to say that our results are statistically significant at alpha level 0.05.
When to Use the Chi-square Distribution Table
If you are interested in finding the Chi-square critical value for a given significance level and degrees of freedom, then you should use the Chi-square Distribution Table.
Instead, if you have a given test statistic X2 and you simply want to know the p-value of that test statistic, then you would need to use a Chi-Square Distribution Calculator to do so.