The Nearest Neighbor Index (NNI) is a complicated tool to measure
precisely the spatial distribution of a patter and see if it is regularly dispersed
(=probably planned), randomly dispersed, or clustered. It is used for spatial
geography (study of landscapes, human settlements, CBDs, etc). Use the
formula given above using D(Obs) (=mean observed nearest neighbour
distance), area under study (a) and number of points (n).
Note that the sample MUST be greater than 30 to obtain a meaningful NNI.
Possible problem: if you have one single cluster, or various small clusters, the NNI will still be approximately 1 and therefore cannot reveal that both distributions are very different.
The NNI measures the spatial distribution from 0 (clustered pattern) to 1 (randomly dispersed pattern) to 2.15 (regularly dispersed /uniform pattern):
Possible problem: if you have one single cluster, or various small clusters, the NNI will still be approximately 1 and therefore cannot reveal that both distributions are very different.
The NNI measures the spatial distribution from 0 (clustered pattern) to 1 (randomly dispersed pattern) to 2.15 (regularly dispersed /uniform pattern):
Example:
study of the distribution of pine trees as part of sand dune vegetation
Let’s take a sample in a sand dune area near the Ocean. If the forest is natural, the tree distribution should be random, rather than the regular pattern expected if trees have been planted by humans as part of a sand stabilization scheme.
Hypothesis: the trees have grown at an average even distance from each other to form a stable ecosystem over the decades, but are distributed randomly instead of in a regular way because the woodland is natural and not planted by humans.
The nearest neighbor formula will produce a result between 0 and 2.15, where the following distribution patterns form a continuum. You must first select an area of woodland using random numbers, and mark out a 20x20 m (400m2): in this quadrant we count 18 trees, which is not enough to make the calculation reliable. We need at least 30 points (trees) so we will have to pick a larger quadrant. Let’s choose a quadrant of 30x30m = 900 m2. A survey shows that our random 30x30m quadrant contains 36 trees. You must then measure the distance between each tree and its nearest neighbor:
Let’s take a sample in a sand dune area near the Ocean. If the forest is natural, the tree distribution should be random, rather than the regular pattern expected if trees have been planted by humans as part of a sand stabilization scheme.
Hypothesis: the trees have grown at an average even distance from each other to form a stable ecosystem over the decades, but are distributed randomly instead of in a regular way because the woodland is natural and not planted by humans.
The nearest neighbor formula will produce a result between 0 and 2.15, where the following distribution patterns form a continuum. You must first select an area of woodland using random numbers, and mark out a 20x20 m (400m2): in this quadrant we count 18 trees, which is not enough to make the calculation reliable. We need at least 30 points (trees) so we will have to pick a larger quadrant. Let’s choose a quadrant of 30x30m = 900 m2. A survey shows that our random 30x30m quadrant contains 36 trees. You must then measure the distance between each tree and its nearest neighbor:

D(Obs) = 120.30 / 36 = 2.80 m
(average nearest distance between 2 trees)
a = 900 m2 (size of the area) n = 36 (number of trees in the quadrant) The NNI formula leads to Rn = 1.12, which indicates that the distribution of trees might random: 
You can use the critical table below to determine the certainty level of the result: according to this critical table, with Rn = 1.12 and 36 trees in the
sample, our sample falls in the yellow shaded area below, which means that we can say with 95% certainty that the trees are distributed
randomly.