  Many types of new physics can lead to contact interaction-like modifications
in e^+ e^- processes below direct production threshold. We examine the
possibility of uniquely identifying the effects of graviton exchange, which are
anticipated in many extra dimensional theories, from amongst this large set of
models by using the moments of the angular distribution of the final state
particles. In the case of the e^+ e^- --> f bar{f} process we demonstrate that
this technique allows for the unique identification of the graviton exchange
signature at the 5 sigma level for mass scales as high as 6 sqrt(s). The
extension of this method to the e^+ e^- --> W^+ W^- process is also discussed.
