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Lecture

This

**preview**shows pages 1-2. to view the full**6 pages of the document.**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

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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

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