  Competitive limits on the weakly interacting massive particle (WIMP)
spin-independent scattering cross section are currently being produced by 76Ge
detectors originally designed to search for neutrinoless double beta decay,
such as the Heidelberg-Moscow and IGEX experiments. In the absence of
background subtraction, limits on the WIMP interaction cross section are set by
calculating the upper confidence limit on the theoretical event rate, given the
observed event rate. The standard analysis technique involves calculating the
90% upper confidence limit on the number of events in each bin, and excluding
any set of parameters (WIMP mass and cross-section) which produces a
theoretical event rate for any bin which exceeds the 90% upper confidence limit
on the event rate for that bin. We show that, if there is more than one energy
bin, this produces exclusion limits that are actually at a lower degree of
confidence than 90%, and are hence erroneously tight. We formulate criteria
which produce true 90% confidence exclusion limits in these circumstances,
including calculating the individual bin confidence limit for which the overall
probability that no bins exceeds this confidence limit is 90% and calculating
the 90% minimum confidence limit on the number of bins which exceed their
individual bin 90% confidence limits. We then compare the limits on the WIMP
cross-section produced by these criteria with those found using the standard
technique, using data from the Heidelberg-Moscow and IGEX experiments.
