Tests of shift in diversification associated with key innovations or directional environmental change can be performed with sister-clade comparisons. This approach is attractive because it does not require detailed phylogenetic information. I propose a new likelihood ratio test based on fitting two models of diversification. I show how this test differs from a previous likelihood ratio test based on the geometric distribution. With simulations from a wide range of situations, I show that the new test performs much better than this test and the traditional test by Slowinski and Guyer. The proposed test performs at least as well as the species richness contrast test that has been proposed by several authors in four versions. A power analysis with low number of pairs of sister clades showed that the new test could detect a shift in diversification with five or less pairs of sister clades, whereas the diversity contrast test cannot detect any shift in this situation. The former appears as more powerful than the latter, and therefore is recommended when the number of pairs of sister clades is low (less than 10). All other tests should not be used as the present study showed they lack statistical power and robustness.