GEOGRAPHICAL STATISTICS
GE 2110
Zakaria A. Khamis
Spatial Association
• While the spatial pattern analysis is based on measuring the
abundance and arrangement of single set of features, SPATIAL
ASSOCIATION is concerned on comparing two or more sets of
features found in the same area, so as to determine their degree of
spatial association
• If one can determine where and how environmental features
change together across the landscape, s/he may be able to better
explain why this spatial association occurs; and s/he may be able to
predict similar association in other areas
• The spatial association may be direct (corals and fish), or indirect
(Big fishes at the coral)  due to the third party
Spatial Association
• It is difficult to imagine that direct or indirect spatial associations
among features will ever be totally predictable  the ability to
predict implies a deep and complete knowledge of the
environment that goes beyond what you can see on maps and
images
• The quantitative analysis of the degree of spatial association
support or spatial association analysis, thus increase the
ability/capacity of describing the existing association among
features across the spatial space
Types of Spatial Association
• There are two basic forms of spatial association  Between
discrete feature and Between continuous phenomena
• Looking at the sets of point, line or area features in same
geographic area  the closer they are to each other, the greater
their spatial association
• Also the spatial association may be detected between numerical
values computed for features in the same data collection units 
when two sets of values increase or decrease similarly within the
units they have a strong positive spatial association vice versa is
true for negative spatial association
Types of Spatial Association
• When there is no systematic spatial relationship between feature
values, the assumption is that  no spatial association between
values of the features
• On the other hand, continuous features spatial association can be
analyzed and the relationship between the values can be generated
 the spatial association between elevation and temperature
which change in magnitude at the same time
• The highest positive spatial association is when the phenomena
reach their peaks and valleys at the same locations, the vice versa is
true for negative spatial association
Judging Spatial Association Visually
• For centuries geographers have used subjective visual judgment to
define the spatial association between two sets of features on maps
• Visual judgments of spatial association are easier to make when
the features being compared are superimposed; however, it is not
always possible to superimpose the features in one map, thus the
comparison between maps can be done by arranging the maps
side-by-side
• Map comparison is simplified if the maps to be compared are on
the same map projection, same scale and orientation
Spatial Association Measure
• Observation is the first important step in describing spatial
association, but visual observation lack with quantitative rigor
(firmness)
• The problem is that visual analysis is subjective, people make
different interpretation when viewing the maps
• Without quantitative measures of spatial association, there is no
way to tell how similar people’s observation are better than other.
Visual observation also often lack repeatability
• Many quantitative measures of spatial association have been
devised  Spatial Cross-Correlation, Spearman’s Rank
Correlation Coefficient etc
Spatial Cross-Correlation
• It is a measure of the similarity between two different datasets for
the same data collection units
• The algorithm employs the use of covariance in the data for each
unit, and finally compute the correlation coefficient (r) which is
standardized to range between 1 and -1
n
r
 ( x  x )( y
i 1
i
n x y
i
 y)
Regression
• What is Regression?
• statistical process for estimating the relationships among
variables
• Types of Regressions?
• Linear Regression, Ordinary Least Square – OLS, Polynomial
Regression, Logistic Regression, Geographically Weighted
Regression
Geographically Weighted Regression
• In fact, the idea of calculating Local Indicators can be applied to any
standard statistic (O&U p. 205)
• You simply calculate the statistic for every polygon and its
neighbors, then map the result
• Mathematically, this can be achieved by applying the weights matrix
to the standard formulae for the statistic of interest
• The recent idea of geographically weighted regression, simply calculates a
separate regression for each polygon and its neighbors, then maps
the parameters from the model, such as the regression coefficient
(b) or its significance value
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