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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 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 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**

The settlements in the study area were located (the minimum number recommended for nna is 30). Each settlement was given a number. 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 Đ = the mean distance between the nearest neighbors (km) A = area under study (km2) N = total number of points Rn = 2đ√n/a

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**Using nearest neighbour analysis**

To find đ, 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**

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

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Rn = 2đ√n/a Rn = 2 x 1.72 √ 30/ 180 Rn = 3.44 √ 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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**Nearest Neighbour Measurements for Activity 1**

Settlement number Nearest Neighbour Distance km

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McGraw-Hill/IrwinCopyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 7 Sampling Distributions.

McGraw-Hill/IrwinCopyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 7 Sampling Distributions.

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