When testing for clustering in inhomogeneous populations with distance based methods we can either choose tests where the uneven density is taken into account. Examples of this approach are found in Whittemore et al (1987), Cuzick an Edwards (1990) and Diggle and Chetwynd (1991).
An alternative approach is to define a new distance such that the uneven density is compensated for when the distances are computed, and once this is done, more traditional distance-based spatial methods can be used to formulate an appropriate test. This is the method chosen for this study, in which the performance of tests applied with a Density Adjusted Distance (DAD) are compared to the performance of tests according to Whittemore, Cuzick & Edwards and Diggle & Chetwynd by simulation.
The tests are compared in different types of data sets and for various kinds of clustering. It is shown that no test is the optimal choice for all alternative hypotheses, and that the tests are unequally sensitive to the structure of the underlying data. Testing with DAD is often a good alternative, and this distance measure has also got potential for further use in analysis of spatial data.