Tests for positive selection have mostly been developed to look for diversifying selection where change away from the current amino acid is often favorable. However, in many cases we are interested in directional selection where there is a shift toward specific amino acids, resulting in increased fitness in the species. Recently, a few methods have been developed to detect and characterize directional selection on a molecular level. Using the results of evolutionary simulations as well as HIV drug resistance data as models of directional selection, we compare two such methods with each other, as well as against a standard method for detecting diversifying selection. We find that the method to detect diversifying selection also detects directional selection under certain conditions. One method developed for detecting directional selection is powerful and accurate for a wide range of conditions, while the other can generate an excessive number of false positives.