Example: Suppose a researcher is using a 3 3 contingency table and is testing the null hypothesis of independence at the .01 level of significance. Using the formula above, degrees of freedom for a 3 3 table equal 4. Turn to page 620 and locate 4 in the df column. Move 5 columns to the right of 4 df and the critical value is 13.277. Therefore, if the researcher’s chi-square statistic were equal to or greater than the critical value of 13.277, the null hypothesis of independence would be rejected at the .01 level of significance, and the alternative hypothesis would be supported.