Inferring positive selection at single amino acid sites is of biological and medical importance. Parsimony-based and likelihood-based methods have been developed for this purpose, but the reliabilities of these methods are not well understood. Because the evolutionary models assumed in these methods are only rough approximations to reality, it is desirable that the methods are not very sensitive to violation of the assumptions made. In this study we show by computer simulation that the likelihood-based method is sensitive to violation of the assumptions and produces many false-positive results under certain conditions, whereas the parsimony-based method tends to be conservative. These observations, together with those from previous studies, suggest that the positively selected sites inferred by the parsimony-based method are more reliable than those inferred by the likelihood-based method.