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Hopkins statistic is used to test a Null Hypothesis of spatial randomness. Under the null distribution of spatial randomness, the value of the statistic should be 0.5.
The important point of this protocol is to raise awareness of potential problems. We leave it to the practitioner to decide what do with the answers to these questions.
We can simulate 1000 points uniformly in a unit square and then calculate Hopkins statistic, which is 0.52.
## [1] 0.5217802
Simulate 1000 points from a bivariate normal distribution (with 0 covariance). The sampling frame for generating new points \(u\) is from the minimum value to maximum value of the events in each axis. Roughly -3 to 3 for Normal data. The points form a circular “cluster” within this bounding box and the value of Hopkins statistic is 0.89.
## [1] 0.8927865
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