We have derived the two point angular autocorrelation function for the
SUGAR data above three threshold energies and those data are shown in tables
1, 2, and 3. It is evident from the tables that, for the data available
for SUGAR, any evidence for clustering is statistically weak. However,
both of the higher energy datasets (tables 2 and 3)
show positive correlations on the whole out to angular distances of the
order of 
.
If that angle had been chosen a priori
for testing as a possible scattering scale,
we would have regarded even the SUGAR data as significant. Since
that decision had not been taken, the result is strongly suggestive but not
usefully significant. As a pilot study for the future Pierre Auger dataset,
this emphasises that we must make a number of a priori decisions
about the analysis procedures.
Rather than picking a likely spread for any clustering, our choice might
have been to determine optimum angular intervals to be used in deriving the two
point function with the hope that our function will be statistically
significant at each angular spacing. In the case of our SUGAR data, this
involves an appropriate a priori choice of the angular interval, which we
selected as 
for the tables. If clustering exists out to a
certain angle, we can then determine the angular deviation, to this
precision, for propagation from various
sources with different spreads provided that the data are dominated by a
small number of sources.
For instance, in the case of the SUGAR data, we might have chosen 
intervals rather than .
The data for both of the higher energy datasets would then have
been arguably significant at the smaller angular spacings but the
4 x 1019eV
dataset would have spread to 
compared to 
for the
6 x 1019eV data. This might seem to be physically consistent due to the
expectation of reduced scattering at the higher energies and, if a source
could be identified, would yield valuable information on intergalactic
magnetic fields.
© Copyright Astronomical Society of Australia 1997