Nearest Neighbour Analysis

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Nearest Neighbour Analysis
Page 402 in Integrated Approach
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Nearest Neighbour Settlement
Settlements often appear on maps as dots. Dot
distributions are commonly used in geography yet
their patterns are often difficult to describe.
Sometimes patterns are obvious, such as when
settlements are extremely nucleated (grouped
together) or dispersed (far apart). In reality,
the pattern is likely to between these 2 extremes
and any description will be subjective. One way
that a pattern can be measured objectively is
through the use of nearest neighbour analysis.
However, it is important to note that it is only
a technique and does not offer any explanation of
patterns.
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Nearest Neighbour Analysis produces a figure
(expressed as Rn) which measures the extent to
which a particular pattern is clustered
(nucleated), random or regular (uniform).
Clustering occurs when all the dots are very
close to the same point. Eg coalfields where
villages coalesce. Rn 0
Random distributions occur where there is no
pattern at all. Rn equals 1.0. The usual
pattern for settlement is random with a tendency
for clustering or regularity
Regular patterns are perfectly uniform. They
have a Rn value of 2.15 which means that each
place is equidistant.
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Clustered Random
Regular (nucleated) tendency towards
tendency towards (uniform)
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Using nearest neighbour analysis

• Figure 14.27 in the book shows a map of 30
  settlements in parts of the East Midlands where
  it might be expected that there would be evidence
  of regularity in the distribution.

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Using nearest neighbour analysis

1. The settlements in the study area were located
   (the minimum number recommended for nna is 30).
   Each settlement was given a number.
2. The nearest neighbour formula was applied. This
   formula is

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Sometimes you will see this formula!
Where Rn nearest neighbour value D Obs mean
observed nn distance A area under study N
total number of points
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But we will use this formula!
Where Rn description of distribution Ð the
mean distance between the nearest neighbors (km)
A area under study (km2) N total number of
points
Rn 2dvn/a
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Using nearest neighbour analysis

1. To find d, measure the straight line distance
   between each settlement and its nearest
   neighbour, eg settlement 1 to 2, settlement 2 to
   1, settlement 3 to 4 etc One point may have more
   than one nearest neighbour. In this case the
   mean distance between all the pairs of nearest
   neighbours was 1.72km ie the total distance
   netween each pair (51.7km) divided by the number
   of points (30).

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Using nearest neighbour analysis

1. Find the total area of the map ie 15km x 12km
   180km2
2. Calculate the nn statistic, Rn by using the
   formula.

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Rn 2dvn/a
Rn 2 x 1.72 v 30/ 180 Rn 3.44 v 0.17 Rn
3.44 x 0.41 Rn 1.41
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Using nearest neighbour analysis

• 6. Using this Rn value, determine how clustered
  or regular is the pattern. A value of 1.41 shows
  that there is a fairly strong tendency towards a
  regular pattern of settlement.

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Using nearest neighbour analysis

• 7. However, there is a possibility that this
  pattern has occurred by chance. Using the graph
  on the next slide, it is apparent that the values
  of Rn must lie outside the shaded area before a
  distribution of clustering or regularity can be
  accepted as significant. Values lying in the
  shaded area at the 95 probability level show
  random distribution. The graph confirms that our
  Rn value of 1.41 has a significant element of
  regularity.

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Limitations and problems

• The size of the area chosen is critical.
  Comparisons will be valid only if the selected
  areas are a similar size
• The area chosen should not be too large as this
  lowers the Rn value or too small.

• Distortion will occur in valleys, where nearest
  neighbours may be separated by a river
• Which settlements are to be included? Are
  hamlets acceptable?
• There may be difficulty in working out the centre
  of the settlement for measurement purposes

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Limitations and problems

• The boundary of an area is important. It the
  area is small or is an island there is little
  problem but if the area is part of a larger
  region the boundaries must have been chosen
  arbitrarily.

• In a case like this it is likely that the nearest
  neighbour of some points will be off the map.

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Some Practice activities
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Dispersion map for Activity 1
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Settlement number NearestNeighbour Distancekm 1
2 13.0 2 3 9.0 3 2 9.0 4 2
9.5 5 8 9.0 6 7 12.5 7 6
12.5 8 5 9.5 9 8 12.5 10 11
4.0 11 10 4.0 12 11 8.5
Nearest Neighbour Measurements for Activity 1