Exploring Spatial Patterns Iap2013

8/12/2019 Exploring Spatial Patterns Iap2013

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EXPLORINGSPATIALPATTERNSIN

YOURDATA


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OBJECTIVES

Learn how to examine your data using the

Geostatistical Analysis tools in ArcMap.

Learn how to use descriptive statistics in ArcMap

and Geoda to analyze data.

Be able to identify Geostatistical Analysis tools that

can be used for further analysis.


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WHYEXPLOREYOURDATA?

It allows you to better select an appropriate tool to

analyze your data.

If you skip exploring your data, you may miss keyinformation about it that may lead to incorrect

conclusions and decisions.


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GEODAVS. ARCMAP

Geodafree, open-source, simple, software

specifically for statistical analysis

ArcMapproprietary, GIS software that canperform statistical analysis along with hundreds of

other analyses


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GEODAVS. ARCMAP

With ArcMap you

can view several

data layers at once.

In Geoda, you view

only one data layer.

Some tools are

found in both

programs, while

some are found inonly one.


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EXPLORETHELOCATIONOFYOURDATA


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EXPLORETHELOCATIONOFYOURDATA

Explore:

size of the study area

mean

median

direction data are oriented

You will see where data are clustered relative to the

rest of the data.


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MEANCENTER

The geographic center for a set of features.

Constructed from the average x and y values for

the input feature centroids (middle points, if input

features are polygons).


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MEDIANCENTER

Median Center is robust to outliers.

Uses an algorithm to find the point that minimizes

travel from it to all other features in the dataset.

At each step (t) in the algorithm, a candidateMedian Center is found (Xt, Yt) and refined until it

represents the location that minimizes Euclidian

Distance dto all features (i) in the dataset.


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DIRECTIONDISTRIBUTION(STANDARD

DEVIATIONALELLIPSE)

Standard deviational ellipses summarize the spatialcharacteristics of geographic features: central tendency,dispersion, and directional trends.

The ellipse allows you to see if the distribution of

features is elongated and hence has a particularorientation.

When the underlying spatial pattern of features isconcentrated in the center with fewer features towardthe periphery (a spatial normal distribution), a one standard deviation ellipse polygon will cover

approximately 68 percent of the features

two standard deviations will contain approximately 95 percentof the features

three standard deviations will cover approximately 99 percentof the features


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EXPLORETHEVALUESOFYOURDATA


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NORMALDISTRIBUTION

Some analysis tools assume a normal distribution:

Mean and median are similar

Data are symmetrical


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DATAFREQUENCYUSINGHISTOGRAMS


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DATADISTRIBUTIONUSINGAQQ PLOT

A normally distributed datasetMany characteristics of a normal datasetNot normal

A normal QQ plot shows the relationship of your data to a normal distribution line.


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BOXPLOT

Displays the median and interquartile range (IQ)(25%-75%)

Hinge = multiple of interquartile range


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MAPS

For examining data values and frequencies:

Quantile Map

Natural breaks

Equal intervals

For finding outliers:

Percentile Map

Box Map

Standard Deviation Map


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QUANTILEMAP

Displays the distribution of values in categories with

an equal number of observations in each category.


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EQUALINTERVALMAP

Sets the value ranges in each category equal in size.

The entire range of data values is divided equally into

however many categories have been chosen.


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NATURALBREAKSMAP

Seeks to reduce the variance within classes and

maximize the variance between classes


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OTHEREXPLORATORYMETHODS

Scatter Plot (2 variables)

Parallel coordinate plot (A pattern of lines is drawn

that connects the coordinates of each observation

across the variables on parallel x-axes.)


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DETECTOUTLIERS


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OUTLIERS

Outliers can reveal mistakes, unusual occurrences,

and shift points in data patterns (a valley in a

mountain range).

You should use more than one method to find

outliers because some techniques will only highlight

data values near the two ends of your range.


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PERCENTILEMAP

Groups ranked data into 6 categories

Lowest and highest 1% are potential outliers


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BOXMAP

Groups data into

4 categories, plus

2 outlier

categories at both

ends

Data are outliers

if they are 1.5 or

3 times the IQ.

Detects outlierswith more

certainty than a

percentile map


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SEMIVARIOGRAMCLOUD

When points closer together have greaterdifferences in their values, this may indicate anoutlier in the data.

The selected points may be outliers.


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VORONOIMAP

Cluster Voronoi maps show spatial outliers in yourdata; simple Voronoi maps can pinpoint data valuesthat are many class breaks removed fromsurrounding polygons.

The gray

polygons may

be outliers.


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HISTOGRAM

Values in the last bars to the left or right, if far

removed from the adjacent values, may indicateoutliers.


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NORMALQQ PLOT

Values at the tails of a normal QQ plot can also beoutliers. This can happen when the tail values do

not fall along the reference line.


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BOXPLOT

Points outside the hinges (represented by the

black, horizontal lines), maybe outliers.


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EXPLORESPATIALRELATIONSHIPSIN

YOURDATA


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SPATIALAUTOCORRELATION

Everything is related, but objects closertogether are more related than objectsfarther apart.

Explore using a semivariogram graph orcloud

Can also be explored using Morans I andGetis-Ord G statistics


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Height (sill) = variation between

data values.

Range= distance between

points at which thesemivariogram flattens out.

As the range increase, height

should increase, since points

further away from each other are

not as related, so there should

be more variation.

If a semivariogram is a

horizontal line, there is no

spatial autocorrelation.


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VARIATIONINYOURDATA

Many spatial statistics analysis techniques assumeyour data are stationary, meaning the relationshipbetween two points and their values depends onthe distance between them, not their exact location.

Explore variation using a Voronoi map.

A Voronoi map is created by defining Thiessenpolygons around each point in your dataset.

Any location inside a polygon represents the areacloser to that data point than to any other data

point.

This allows you to explore the variation of eachsample point based on its relationship tosurrounding sample points.


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A SIMPLEVORONOIMAP

A simple Voronoi map shows the data value at each

location. The map is symbolized using a geometrical

interval classification. This will show the variation in data

values across your entire dataset.

Green = little localvariation

Orange and Red =

greater local variation


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TYPESOFVORONOIMAPS

Simple:The value assigned to a polygon is the valuerecorded at the sample point within that polygon.

Mean:The value assigned to a polygon is the mean value thatis calculated from the polygon and its neighbors.

Mode:All polygons are categorized using five class intervals.The value assigned to a polygon is the mode (most frequently

occurring class) of the polygon and its neighbors.

Cluster:All polygons are categorized using five classintervals. If the class interval of a polygon is different fromeach of its neighbors, the polygon is colored gray and put intoa sixth class to distinguish it from its neighbors.

Entropy:All polygons are categorized using five classesbased on a natural grouping of data values (smart quantiles).The value assigned to a polygon is the entropy that iscalculated from the polygon and its neighbors.

Entropy = - (pi* Logpi),


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EXPLORETRENDSINYOURDATA


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TRENDANALYSIS

You can use the trend analysis tool in Arcmap to

visually compare the trend lines with any patterns in

your data.

When exploring trends, your data locations are

mapped along the x- and y-axes. The values of

each data location are mapped as height (z-axis).

Trends are analyzed based on direction and on the

order of the line that fits the trend. The trend line is

a mathematical function, or polynomial, that

describes the variation in the data.


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These polynomials show

a clear curve, indicating

a second-order trendin the data.

You can determine whether

the order of the polynomial

fits your data based on the

shape created by the line.

A second-order polynomial

will appear as an upward

or a downward curve

(known as a parabola).


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SELECTINGANANALYSISTECHNIQUE


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Each of the following techniques are types of

interpolation. Interpolation creates surfaces based

on spatially continuous data.

Each surface uses the values and locations of your

points to create (or interpolate) the values for the

remaining points in the surface.


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GEOSTATISTICALINTERPOLATION

Creates surfaces using the relationships betweenyour data locations and their values.

Predicts values based on your existing data.

Assumptions:

Data is not clustered.(Simple kriging technique has a declustering option.)

Data is normally distributed.(Transformation options are available.)

Data is stationary (no local variation). Data is autocorrelated.

Data has no local trends.(You can remove trends from data as part of the interpolationprocess. )


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GLOBALDETERMINISTICINTERPOLATION

Creates surfaces using the existing values at each

location.

Uses your entire dataset to create your surface.

Assumptions: Outliers have been removed from the data.

Global trends exist in the data.


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LOCALDETERMINISTICINTERPOLATION

Uses several subsets, or neighborhoods, within an

entire dataset to create the different components of

the surface.

Assumption:

Data is normally distributed.


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INVERSEDISTANCEWEIGHTED

INTERPOLATION(IDW)

A type of local deterministic interpolation.

Assumptions:

Data is not clustered.

Data is autocorrelated.


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OTHERSPATIALSTATISTICALTESTS

Tests for spatial autocorrelation

Getis-Ord General G and Global Morans I (to determine

overall clustering and dispersion of values)

Hot Spot Analysis (Getis-Ord Gi*) andAnselinsLocal

Morans I (to determine specific clusters of high and lowvalues)

Regression

Used to evaluate relationships between two or more

feature attributes. Are location, crime rates, racial make-

up, and income related to housing values in a census

tract?

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Exploring Spatial Patterns Iap2013