Advanced Higher Geography: Inferential Statistics
Nearest Neighbour Index
Nearest Neighbour Index
The nearest neighbour index summarises, in one number, how clustered, uniform or random the distribution
of a series of points are.
Method
1. Plot all of the points onto a map
2. Draw a table and find the distance from each point to its nearest neighbour (the point closest to it)
 It is quite possible that one point may be the nearest neighbour to several other points. That’s
fine.
3. Add all of the nearest-neighbour distances and divide the result by the number of points (n)
 This gives the mean observed distance of all of the points to their nearest neighbour (D)
4. Calculate the nearest neighbour index using this formula:
 NNI = nearest neighbour index
NNI = 2D
n
 D = mean observed nearest neighbour distance
A
 √ = square root of
 n = total number of points
 A = area of map
√
The results can be interpreted from the following scale:
0
Completely
Clustered
1.0
Completely
random
2.15
Completely
uniform
If the index value were 0.7, then we would express this as being more nearly random than clustered. If it
were 1.9, it would be more nearly uniform than random.
Nearest neighbour does not
have a critical values table to
determine a significant level of
clustering or uniformity.
Instead, we use the diagram
below. If the index value lies
out-with the shaded area, we are
95% certain of the points being
regularly spaced or clustered.
Nearest Neighbour Index
Advanced Higher Geography: Inferential Statistics
Example
∑D = 24
n = 10
point
1
2
3
4
5
6
7
8
9
10
D = 24 = 2.4km
10
A = 256km2
NNI = 2D
√
n
A
Nearest
neighbour
2
1
2
5
6
5
8
7
10
9
Distance
apart (km)
2.5
2.5
5
4
3
3
1
1
1
1
24
NNI = (2 x 2.4) x (√(10 x 256)
= (2x2.4) x 0.2
= 0.96 (an almost random distribution)
Possible Problems
There are a number of problems with the nearest neighbour index:
 It cannot distinguish between a single and a multi-clustered pattern. Both the distributions in the
picture below, although different, have a NNI of approximately o.
Single and multi-clustered point patterns


An index of 1.0 does not always mean that the
distribution is totally random. Two sub-patterns on
the map, when combined in one index, may give a
false impression of randomness. The picture below
has a NNI of approximately 1.0 although it is clearly
not random.
A distribution with an index of 1.0 should not be interpreted as being caused by random or
chance factors. A pattern of settlements might have an NNI of 1.0, but every settlement is
located at the site of a spring: the settlement cannot be said to be caused by chance.