We obtain our critical values at our chosen alpha level and relevant degrees of freedom. F ratios require two different degrees of freedom -- one number for our numerator (the effect of interest) and one number for our denominator (our error estimate).

As we can see from our summary table, all effects have "1" as the numerator degrees of freedom and "36" as the denominator degrees of freedom. Using an alpha level of .05, the F tables provide a critical value of F (1, 39) = 4.11 at a = .05. Comparing our sample values of F to the critical value of 4.11, we can see that we would reject the Null Hypothesis for the main effect for Factor A (35.592 > 4.11) and the Null Hypothesis for the main effect for Factor B (81.815 > 4.11). We fail to reject the null for the A x B interaction (0.333 < 4.11).

Our final step is to examine a graph of the cell means in order to determine the direction of our effects.