Spatial Autocorrelation

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Spatial Autocorrelation

• Join Count Analysis

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Join Count

• Nominal variables mapped in two colors (B W).
  Therefore, the join, or border can be classified
  as WW, BB, BW
• Different Join Patterns
• Rooks Case
• Queens Case
• Bishops Case

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Join Counts
BB
WW
BW
Tot.
Map
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Computing the Joins

• When using a computer to compute joins, we will
  have twice as many joins (ex. WB, BW). Just
  divide by two
• If we have nb Black cells and nw n nb white
  cells the probability p of a black cell is
• pb nb /n
• pw nw /n

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Computing the probabilities

• Start with first cell. The probability it is
  black is pb and the probability of white is pw
• The probability of BB in two adjacent cells is
• pb pb or pb2
• Probability of BW is
• pb pw pb pw or 2 pb pw

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• Therefore, if there are L joins on a map, the
  expected number of cells of each type is
• E(BB) m(BB) pb2L
• E(WW) m(ww) pw2L
• E(BW) m(BW) 2pbwL

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Test Statistics for Join-Count
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Example from Election 2000

• A spatial analysis of Election 2000
• Did the blue and red map really say something
  significant about the locations where people
  voted by County?
• ArcView example

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