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Class Notes
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Canada
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Brock University
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Geography
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GEOG 2P07
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Marilyne Jollineau
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Lecture

Description

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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