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The purpose of this paper is to analyze the spatial patterns of different phenomena in the same geographical space. Andresen’s spatial point pattern test computes a global index (the S-index) that informs on the similarity or dissimilarity of spatial patterns. This paper suggests a generalized S-index that allows perfect similarity and dissimilarity in all situations.

The relevance of the generalized S-index is illustrated with police data from the San Francisco Police Department. In all cases, the original S-index, its robust version – which excludes zero-crime areas – and the generalized alternative were computed.

In the first example, the number of crimes greatly exceeds the number of areas and there are no zero-value areas. A key feature of the second example is that most street segments were free of any criminal activity in both patterns. Finally, in the third case, one type of event is considerably rarer than the other. The original S-index is equal to the generalized index (Case 1) or theoretically irrelevant (Cases 2 and 3). Furthermore, the robust index is unnecessary and potentially biased when the number of at least one phenomenon being compared is lower than the number of areas under study. Thus, this study suggests to replace the S-index with its generalized version.

The generalized S-index is relevant for situations when events are relatively rare –as is the case with crime – and the unit of analysis is small but plentiful – such as addresses or street segments.