Lecture outline

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Lecture outline

• Point Pattern Descriptions
• Mean center
• Standard distance
• Point Pattern Detectors
• Quadrat analysis
• Nearest Neighbor analysis

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Why examine point patterns?

• The goal is to describe the pattern and hopefully
  better understand the underlying geographic
  process that is controlling the pattern
• Identify the factors that control the spatial and
  possibly the temporal patterns

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Mean center

• Gives the average location for a set of points
• Location is defined in geographic units (lat/lon,
  UTM) or in an arbitrary coordinate system
• Arbitrary coordinate system
• Has origin and orientation
• Known measurement units

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Mean center definition
where
are the coordinates of the mean center
xi, yi are coordinates of point i, and n is the
number of points in the data set
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mc
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Standard distance

• Conceptually similar to standard deviation in
  classical statistics
• Indicates how points in a distribution deviate
  from the mean center
• Expressed in distance units

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Standard distance circle

• SD is usually used as the radius of a circle with
  the mean center as the center of the circle

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What can we learn from it?

• Different standard circles can be drawn for
  different events such as different types of
  crimes or different seasons for lightning strikes
• Visual comparison of the spatial spread of events

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Quadrat Analysis

• Evaluates point distributions by examining how
  its density changes over space
• This density is compared with a theoretically
  constructed random pattern to see if the point
  distribution in question is more clustered or
  more dispersed than a random pattern

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Procedure

• Overlay a square grid over the points
• Count the number of points per grid
• Create a frequency distribution of the number of
  squares with a number of points

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Expectations

• Clustered most of the points in one or a few
  squares
• Uniform all the squares would have a similar
  number of points
• Random some have quite a few, some have only a
  few, some have none

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Frequency distribution table
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Potential problems with quadrat analysis

• Configuration with the placement of the grid
  orientation and placement
• Size of the quadrat

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Nearest Neighbor Analysis

• Quadrat Analysis density concept (points per
  area)
• Nearest Neighbor Analysis spacing concept (area
  per point)
• Test compares the observed average distance with
  those of a known pattern

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The R statistic

• Test to see if there is an irregular distribution
• Ratio of the observed average distance between
  nearest neighbors and an expected

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Measure the observed

• Calculate the distance between each point and all
  other points
• For each point, select the nearest
• Calculate the average of all the nearest distances

This is robs
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Calculate the expected average distance
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Compare

• R ranges from 0 (completely clustered) to R1
  (random) to R2.149 (dispersed)
• But, how do we know to what degree the pattern is
  more clustered than a random pattern?

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Example
1.0
2.149
0.67
2.0
0.33
1.67
0.00
1.33
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Potential problems with NNA

• Results highly sensitive to scale in particular
  the delineation of the study area
• Study area should be justified by meaningful
  criteria depending on the process being observed
• May need to use rivers or mountain ranges rather
  than political boundaries

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