  Aggregation patterns are often visually detected in sets of location data.
These clusters may be the result of interesting dynamics or the effect of pure
randomness. We build an asymptotically Gaussian test for the hypothesis of
randomness corresponding to a Poisson point process. We first compute the exact
first and second moment of the Ripley K-statistic under the homogeneous Poisson
point process model. Then we prove the asymptotic normality of a vector of such
statistics for different scales and compute its covariance matrix. From these
results, we derive a test statistic that is chi-square distributed. By a
Monte-Carlo study, we check that the test is numerically tractable even for
large data sets and also correct when only a hundred of points are observed.
