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Lecture #10 - Spatial Data Analysis and Spatial Statistics

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Marilyne Jollineau

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Lecture #11 Nov.18, 2011 Spatial Data Analysis - Spatial Statistics  Spatial Statistics  Point Pattern Analysis  Area Pattern Analysis Exam **rulers and coloured pens – pencil AND pens! Spatial Pattern and Relationships  geographers study settlement patterns, land-use patterns, drainage patters, etc.  ‘pattern’ implies some form of spatial regularity which is taken as a sign of a regular ‘process’ at work  we may also be interested in the attributes (e.g., tree species type) that are attached to points  spatial arrangement or distribution of objects/events/cases (represented by points or areas) is of interest yet are often difficult to describe (qualitatively)  today we are talking about how we use them quantitatively *** - patterns and relationships  so, how we can distinguish these patterns statistically so we can conclude that one is “significantly more clustered” and the other is “significantly more dispersed” without knowing anything else about these patterns? (We can test each pattern against a random point pattern  too clustered to have occurred by chance  too dispersed to have occurred by changed – so they are significantly random Point Patterns (Point Data)  Ideal World: Spatially Continuous Phenomena  these data can also be represented by point locations  a continuous measurement (e.g. soil nutrient concentration) attached to each point and this measurement could, in principle, be taken at any other location  the problem is not whether there is a pattern in locations; they are simply the points at which sample measurements were taken 1  our interest is in understanding the pattern in the values at these locations  can perhaps use this understanding to predict values of that variable at other locations Types of Distortion  Three general patterns: > RANDOM: any point is equally likely to occur at any location and position of any point is not affected by the position of any other point. There is no apparent ordering of the distribution > UNIFORM, REGULAR, or DISPERSED: every point is as far from all of its neighbours as possible > CLUSTERED: many points are concentrated close together, and large areas that contain very few, if any, points Two Primary Approaches  POINT DENSITY approach using QUADRAT ANALYSIS based on observing the frequency distribution or density of points with a set of grid squares (density) 1. Variance to mean ratio approach 2. Frequency distribution comparison approach  POINT INTERACTION approach using NEAREST NEIGHBOUR ANAYLSIS based on distances of points one from another (interactions)  *** what is not just happening in one place, but its relationship with what is happening in another place > we know that things closer together often share commonalities then things farther apart Quadrat Analysis (QA): VMR  QA examines the frequency of points occurring in various parts of the study area  a uniform grid is laid over the study area and the number of points per quadrat are determined  treat each quadrat as an observation and count the number of points within it, to create the variable, x  the frequency count (the number of points occurring within each quadrat) is recorded  geographers always select portion of studies, but this can have a negative impact as this area can disclude an important factor and throw off statistics Quadrat Anaysis (QA)  Variance of dataset is subsequently calculated  the variance-mean ratio index (VMR) is then used to standardize the degree of variability in cell frequencies relative to the average cell frequency 2  a random distribution would indicate that the variance and mean are the same  therefore, we would expect a variance mean ration around 1  values other than 1 would indicate a non-random distribution Diagram: Variance is 0 in dispersed, 2 in random, and 17 in clustered and mean always 2 Limitations of QA  results often depend on quadrat size and orientation  if the quadrats are too small, they may contain only a couple of points  if they are too large, they may contain too many points  an alternative is to test different sizes (or orientations) to determine the effects of each test on the results  it is a measure of dispersion, and not really pattern, because it is based primarily on the density of points, and not their arrangement in relation to one another
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