Spatial cluster test based on triplets of districts

In analysing geographical data, one is often interested in finding clusters with suspiciously large or small values of the variable under consideratio n. Moran's I tests for general deviations from the null hypothesis of indep endent observations. A new test is proposed based on triplets, essentially three districts of the region with a common corner. Subregions composed of triplets are tested for significant deviation from the general mean. Using triplet clusters serves to reduce the number of potential suspicious subreg ions and to enforce a certain compactness. The rest needs approximations fo r the total number of triplet clusters and for a combinatorial expression. Despite these approximations, the actual error probability is close enough to the nominal one to make the test useful in situations like data mining. The power of the test is compared with that of Moran's I: the latter one is better for homogeneous counter-hypotheses (as was to be expected and is de sired) whereas the triplet test is better for small local deviations from t he independence assumption. (C) 2001 Elsevier Science Ltd. All rights reser ved.