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STATISTICS

STATISTICS. Advanced Higher. Nearest Neighbour Index. Advanced Higher. STATISTICS. Nearest Neighbour index The nearest neighbour index summarises how clustered, uniform or random the distribution of a series of points are. . Advanced Higher. STATISTICS. Method

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STATISTICS

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  1. STATISTICS Advanced Higher Nearest Neighbour Index

  2. Advanced Higher STATISTICS Nearest Neighbour index The nearest neighbour index summarises how clustered, uniform or random the distribution of a series of points are.

  3. Advanced Higher STATISTICS • Method • Plot all of the points onto a map • 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. • 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) • Calculate the nearest neighbour index using this formula: • NNI = nearest neighbour index D = mean observed nearest neighbour distance • √ = square root of • n = total number of points • A = area of map

  4. Advanced Higher STATISTICS The results can be interpreted from the following scale: 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.

  5. Advanced Higher STATISTICS 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.

  6. Advanced Higher STATISTICS • 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 0. • 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.

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