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

This study was performed to investigate space–time patterns of Campylobacter spp. colonization in broiler flocks in Norway. Data on the Campylobacter spp. status at the time of slaughter of 16 054 broiler flocks from 580 farms between 2002 and 2006 was included in the study. Spatial relative risk maps together with maps of space–time clustering were generated, the latter by using spatial scan statistics. These maps identified the same areas almost every year where there was a higher risk for a broiler flock to test positive for Campylobacter spp. during the summer months. A modified K-function analysis showed significant clustering at distances between 2·5 and 4 km within different years. The identification of geographical areas with higher risk for Campylobacter spp. colonization in broilers indicates that there are risk factors associated with Campylobacter spp. colonization in broiler flocks varying with region and time, e.g. climate, landscape or geography. These need to be further explored. The results also showed clustering at shorter distances indicating that there are risk factors for Campylobacter spp. acting in a more narrow scale as well.

The paper compares non-parametric (design-based) and parametric (model-based) approaches to the analysis of data in the form of replicated spatial point patterns in two or more experimental groups. Basic questions for data of this kind concern estimating the properties of the underlying spatial point process within each experimental group, and comparing the properties between groups. A non-parametric approach, building on work by Diggle et. al. (1991), summarizes each pattern by an estimate of the reduced second moment measure or K-function (Ripley (1977)) and compares mean K-functions between experimental groups using a bootstrap testing procedure. A parametric approach fits particular classes of parametric model to the data, uses the model parameter estimates as summaries and tests for differences between groups by comparing fits with and without the assumption of common parameter values across groups. The paper discusses how either approach can be implemented in the specific context of a single-factor replicated experiment and uses simulations to show how the parametric approach can be more efficient when the underlying model assumptions hold, but potentially misleading otherwise.