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Ho |
The times of occurrence of the health events are distributed randomly across the case locations. This is another way of saying the time distances between pairs of cases are independent of the spatial distances between pairs of cases. |
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Ha |
Pairs of cases near in space tend to be near in time. |
The test statistic, X, is the number of pairs of cases that are near to one another in both space and time. Pairs of cases will be near to one another when interaction is present, and the test statistic will be large.
Where
N is the number of cases
sij is the space adjacency value, 1 if the distance between cases i and j is less than the critical space distance and 0 otherwise
tij is the time adjacency value, 1 if the waiting time between cases i and j is less than the critical time distance and 0 otherwise.
To run Knox's method, you need to specify the critical space and time distances (Dcrit and Tcrit respectively), so that sij and tij can be calculated. Pairs of cases separated by less than the critical space distance are considered to be near in space. Pairs of cases separated by less than the critical time distance are said to be near in time. If you do not know what critical distances to use, ClusterSeer will use the mean calculated from the dataset.
ClusterSeer calculates the null distribution of X in two ways: using a Chi-squared test and using Monte Carlo simulations. The Chi-squared test calculates the probability of the classification of events into near in space and near in time; near in space, far in time; far in space, near in time; and far in space and time under the null hypothesis of no clustering. This provides a significance based on a comparison of the observed and expected values of X.
