Point_Pattern_Overview - Point Pattern Analysis using...

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Point Pattern Analysis using Spatial Inferential Statistics 1
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From Centrographic Statistics (previously): Centrographic Statistics calculates single, summary measures PPA analyses the complete set of points From Spatial Autocorrelation (discussed later): with PPA , the points have location only; there is no “magnitude” value With Spatial Autocorrelation points have different magnitudes; there is an attribute variable. How Point Pattern Analysis (PPA) Briggs Henan University 2010 2
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Two primary approaches: Point Density using Quadrat Analysis Based on polygons Analyze points using polygons! Uses the frequency distribution or density of points within a set of grid squares. Point Association using Nearest Neighbor Analysis Based on points Uses distances between the points Although the above would suggest that the first approach examines first order effects and the second approach examines second order effects, in practice the two cannot be separated. Briggs Henan University 2010 3 Approaches to Point Pattern Analysis
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Quadrat Analysis: The problem of selecting quadrat size Briggs Henan University 2010 4 Too small: many quadrats with zero points Too big: many quadrats have similar number of points O.K. Length of Quadrat edge = A=study area N= number of points Modifiable Areal Unit Problem
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Briggs Henan University 2010 5 Quadrats don’t have to be square --and their size has a big influence Uniform grid --used for secondary data Multiple ways to create quadrats --and results can differ accordingly! Random sampling --useful in field work Frequency counts by Quadrat would be: Number of points in Quadrat Count Proportion Count Proportion 0 51 0.797 29 0.763 1 11 0.172 8 0.211 2 2 0.031 1 0.026 3 0 0.000 0 0.000 64 Q = # of quadarts P = # of points = 15 Census Q = 64 Sampling Q = 38 Types of Quadrats
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Briggs Henan University 2010 6 Quadrat Analysis: Variance/Mean Ratio (VMR ) Apply uniform or random grid over area (A) with width of square given by: Treat each cell as an observation and count the number of points within it, to create the variable X Calculate variance and mean of X, and create the variance to mean ratio: variance / mean For an uniform distribution, the variance is zero. Therefore, we expect a variance-mean ratio close to 0 For a random distribution, the variance and mean are the same. Therefore, we expect a variance-mean ratio around 1 For a clustered distribution, the variance is relatively large Therefore, we expect a variance-mean ratio above 1 Where: A = area of region n = # of points See following slide for example. See O&U p 98-100 for another example
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Briggs Henan University 2010 Note: N = number of Quadrats = 10 Ratio = Variance/mean RANDOM UNIFORM/ DISPERSED CLUSTERED Formulae for variance 1 ) ( 1 2 - = - N X X n i i 1 ] / ) [( 1 2 - = = - N N X X n i i 2 3 1 5 0 2 1 1 3 3 1 Quadrat # Number of Points Per Quadrat x^2 1 3 9 2 1 1 3 5 25 4 0 0 5 2 4 6 1 1 7 1 1 8 3 9 9 3 9 10 1 1 20 60 Variance 2.222 Mean 2.000 Var/Mean 1.111 random x 0 0 0 0 10 10 0 0 0 0 Quadrat # Number of Points Per Quadrat x^2 1 0 0 2 0 0 3 0 0 4 0 0 5 10 100 6 10 100 7 0 0 8 0 0 9 0 0 10 0 0 20 200 Variance 17.778 Mean 2.000 Var/Mean 8.889 Clustered x 2 2 2 2
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