Finding critical value $F^*$ given significance level $\alpha$, using the table with critical $F$ values

Assuming a table giving five upper tail probabilities (denoted $p$ or $\alpha$) per df numerator / df denominator combination
Reject the null hypothesis if the observed $F$ falls in the highest $\alpha$ area of the $F$ distribution. In order to find the critical value $F^*$ that corresponds to this upper tail area:

  1. Find the column with the correct number of degrees of freedom in the numerator. This is the degrees of freedom corresponding to the numerator in the formula for the $F$ value (e.g., df model, df between, df regression, etc.)
  2. Find the rows with the correct number of degrees of freedom in the denominator. This is the degrees of freedom corresponding to the denominator in the formula for the $F$ value (e.g., df error, df within, df residual, etc.)
  3. You now have five options for a critical value $F^*$, each corresponding to a different upper tail area (which you can find in the column named "$p$" or "$\alpha$"). Pick the critical $F$ value that corresponds to the upper tail area $\alpha$. Observed $F$ values that are equal to or larger than $F^*$, lead to rejection of the null hypothesis


Critical F value given alpha