Use of variograms to detect critical spatial distances for the Knox's test

We aimed to find critical spatial distances (as an input quantity for the Knox's test) using geostatistical methods. The spatiotemporal data set included all individual-chamois cases of scabies observed in Styrian chamois populations in 137 of 2837 game preserves in Styria (a province in the south of Austria) over the time period between 1952 and 1998. Theoretical variogram models were fitted to empirical variograms, which were calculated for cycles of 5 years. The unit of analysis was the mean quadratic deviation between individual-chamois cases of scabies. The "range" (which represents the transition from the state in which spatial correlation exists to the state in which there is absence of spatial correlation) was used as an indicator for the critical spatial distance for the Knox's test. The critical distances for the 5-year cycles varied between 10.8 and 16.0 km. If the time of observation is not considered, the critical "overall" distance amounted to 13.5 km.