When testing the effect of a categorical variable with, for instance, 3 categories, one first tests whether any category has an effect. This is typically done using a F-test in an ANOVA. If significant, one is often also interested in which level of the categorical variable has an effect. This can be done fixing a reference level and using a Wald test to compare the other levels of the variable to the reference level. However the F-test and the Wald tests may give contradictory results. This document presents a geometrical illustration of when the F-test and Wald test may disagree.