A common approach to overcoming the effect of reverberation in speaker localization is to identify the time-frequency (TF) bins in which the direct path is dominant, and then to use only these bins for estimation. Various direct-path dominance (DPD) tests have been proposed for identifying the direct-path bins. However, for a two-microphone binaural array, tests that do not employ averaging over TF bins seem to fail. In this paper, this anomaly is studied by comparing two DPD tests, in which only one has been designed to employ averaging over TF bins. An analysis of these tests shows that, in the binaural case, a TF bin that is dominated by multiple reflections may be similar to a bin with a single source. This insight can explain the high false alarm rate encountered with tests that do not employ averaging. Also, it is shown that incorporating averaging over TF bins can reduce the false alarm rate. A simulation study is presented that verifies the importance of TF averaging for a reliable selection of direct-path bins in the binaural case.