Space-Time randomization

"Randomization" is a broad term, used differently in different contexts. Within ClusterSeer, randomization techniques vary among methods.

For the Knox, K-NN, and Mantel tests, ClusterSeer randomizes the space-time relationships by shuffling the time distances between cases or events while holding the spatial distances constant. The statistics are then recalculated on the randomized datasets. The null hypothesis for each of these tests is that there is no significant relationship between the spatial and temporal distances, so that breaking them should be no problem. If there is significant space-time association in the dataset, the random shuffling of the times will tend to produce datasets with less space-time association, and the observed value will be significant when compared to the randomizations.

For the Direction method, the significance of the average direction is evaluated through a randomization procedure which holds the sine and cosine matrices constant and randomly assigns connections between pairs of cases. This is equivalent to holding the locations of the cases fixed while randomizing their times of occurrence. This randomization procedure is repeated to generate a distribution of the angular concentration under the null hypothesis. A P-value is determined by comparing the angular concentration from the original (not randomized) data to this null distribution.