What is the probability that direct detection experiments have observed
  Dark Matter?
  In Dark Matter direct detection we are facing the situation of some
experiments reporting positive signals which are in conflict with limits from
other experiments. Such conclusions are subject to large uncertainties
introduced by the poorly known local Dark Matter distribution. We present a
method to calculate an upper bound on the joint probability of obtaining the
outcome of two potentially conflicting experiments under the assumption that
the Dark Matter hypothesis is correct, but completely independent of
assumptions about the Dark Matter distribution. In this way we can quantify the
compatibility of two experiments in an astrophysics independent way. We
illustrate our method by testing the compatibility of the hints reported by
DAMA and CDMS-Si with the limits from the LUX and SuperCDMS experiments. The
method does not require Monte Carlo simulations but is mostly based on using
Poisson statistics. In order to deal with signals of few events we introduce
the so-called "signal length" to take into account energy information. The
signal length method provides a simple way to calculate the probability to
obtain a given experimental outcome under a specified Dark Matter and
background hypothesis.
