The degree of starshape of a genealogy is readily detectable using summary statistics and can be taken as a surrogate for the effect of past demography and other non-neutral forces. Summary statistics such as Tajima's D and related measures are commonly used for this. However, it Is well known that because of their neglect of the genealogy underlying a sample Such neutrality tests are far from ideal. Here, we investigate the properties of two types Of Summary statistics that are derived by considering the genealogy: (i) genealogical ratios based on the number Of Mutations Oil the rootward branches, which can be inferred from Sequence data using simple algorithm and (ii) summary statistics that use properties of a perfectly star-shaped genealogy. The power of these measures to detect a history of exponential growth is compared with that of standard summary statistics and a likelihood method for the single and multi-locus case. Statistics that depend oil pairwise measures such as Tajima's D have comparatively low power, being sensitive to the random topology Of the underlying genealogy. When analysing multi-locus data. we find that the genealogical measures are most powerful. Provided reliable outgroup information is available they may constitute a useful alternative to full likelihood estimation and standard tests of neutrality.