For rapid comparison of two sequences, k-word counts are sometimes employed. One popular statistic is D_2 which is the dot product of the k-word count vectors.  We assume the sequences are generated iid. In an earlier paper it was shown that there is a distinct distributional regime for the case of uniformly distributed letters and non uniformly distributed letters, and moreover the distribution in the non uniform cases is dominated by contributions from the individual sequences. In this talk we consider the power of D_2 and related statistics to detect sequences with different k-word distributions. The work is  joint with David Chew, Gesine Reinert and Fengzhu Sun.