Finding critical value $X^{2*}$ given significance level $\alpha$, using the table with critical $X^2$ values

Assuming a table with a row per degrees of freedom and a column per upper tail probability

Reject the null hypothesis if the observed $X^2$ falls in the highest $\alpha$ area of the $\chi^2$ distribution. In order to find the critical value $X^{2*}$ that corresponds to this upper tail area:

  1. Find the row with the appropriate degrees of freedom (df)
  2. Find the column for the upper tail probability equal to $\alpha$
  3. At the intersection point of this row and column, you find the critical value $X^{2*}$. Observed $X^2$ values that are equal to or larger than $X^{2*}$, lead to rejection of the null hypothesis
Critical chi squared value given alpha