  Previous analyses of cosmic rays above 40 EeV observed by the AGASA
experiment have suggested that their arrival directions may be clustered.
However, estimates of the chance probability of this clustering signal vary
from 10^{-2} to 10^{-6} and beyond. It is essential that the strength of this
evidence be well understood in order to compare it with anisotropy studies in
other cosmic ray experiments. We apply two methods for extracting a meaningful
significance from this data set: one can scan for the cuts which optimize the
clustering signal, using simulations to determine the appropriate statistical
penalty for the scan. This analysis finds a chance probability of about 0.3%.
Alternatively, one can optimize the cuts with a first set of data, and then
apply them to the remaining data directly without statistical penalty. One can
extend the statistical power of this test by considering cross-correlation
between the initial data and the remaining data, as long as the initial
clustering signal is not included. While the scan is more useful in general, in
the present case only splitting the data set offers an unbiased test of the
clustering hypothesis. Using this test we find that the AGASA data is
consistent at the 8% level with the null hypothesis of isotropically
distributed arrival directions.
