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8.6 J-function
8.6.1 C omparing nearest-neighbour and empty-space distanc es
Nearest-neighbour distances and empty-space distances have the same probability distribution if
the pattern is completely random. Under various departures from complete spatial randomness,
the nearest-neighbour and empty-sp ace distances te nd to respond in opposite directions — one
becoming larger while the other becomes smaller. This suggests that a comparison of these two
types of distance could be useful in assessing departure from CSR.
The Hopkins-Skellam test (Section 8. 2.2) is an example of such a techn ique. The test statistic
(8.2) is the ratio of the