  Observational studies of star formation reveal spatial distributions of Young
Stellar Objects (YSOs) that are `snapshots' of an ongoing star formation
process. Using methods from spatial statistics it is possible to test the
likelihood that a given distribution process could produce the observed
patterns of YSOs. The aim of this paper is to determine the usefulness of the
spatial statistics tests Diggle's G function (G), the `free-space' function
(F), Ripley's K and O-ring for application to astrophysical data. The spatial
statistics tests were applied to simulated data containing 2D Gaussian clusters
projected on random distributions of stars. The number of stars within the
Gaussian cluster and number of background stars were varied to determine the
tests' ability to reject complete spatial randomness (CSR) with changing
signal-to-noise. The best performing test was O-ring optimised with overlapping
logarithmic bins, closely followed by Ripley's K. The O-ring test is equivalent
to the 2-point correlation function. Both F and G (and the minimum spanning
tree, of which G is a subset) performed significantly less well, requiring a
cluster with a factor of two higher signal-to-noise in order to reject CSR
consistently. We demonstrate the tests on example astrophysical datasets drawn
from the Spitzer catalogue.
