Basics of spatial statistics

EG1106: GI, a primer12th November 2004

Topics Introduction The study of spatial statistics Some basic definitions Types of spatial data Methods of spatial analysis Practical Today

Introduction Don’t be put off by the word ‘statistics” As geographers (or environmental

scientists) we are inherently interested in the spatial dependency of physical and/or human characteristics

We need to quantify the magnitude of this spatial dependency to understand it

The study of spatial statistics SS is an area of study which has developed

out of real-world problems SS is a set of methods that are applied to

data that are spatially correlated Most SS methods operate on the premise

that “data collected over a region in space found more close together are more highly correlated with each other than points further apart” (Cressie, 1991)

The study of spatial statistics Underlying SS and spatial modelling is

a coordinate space that enables measurements of distances and bearings between points according to formulas and functions

This model of space is known as Euclidean space

A 2-D model utilises a Euclidian plane

Some basic definitions Regionalised variable: any variable

distributed in space is said to be regionalised. Examples are:

Price of gold in NYSE (1 dimension) Monthly rainfall (2 dimensions) Ozone conc. in atm. (3 dimensions)

Some basic definitions Random function: a type of

regionalised variable which has both random and structured spatial characteristics

E.g. movement of people (moving home)

Types of spatial data Geostatistical data: data from a

random process where our variable (e.g. magnesium concentration) can be measured at any point (coordinate) over a fixed area or surface (for example a field)

Methods of spatial analysis Linear interpolation: based on inverse-

distance weighting

Does not account for variability in the data due to errors or assumptions

Known Interpolated Known 20 10 0

Methods of spatial analysis Kriging: method attempts to model the

variability in the data as a function of distance, through a variogram

A variogram is a function which summarises the strength of association between responses as a function of distance, and possibly direction

Methods of spatial analysis Not all variables are suitable for point to

surface interpolation Temperature Rainfall Drainage and hydrology Population Etc…

Methods of spatial analysis We typically assume that the degree of

spatial correlation does not depend on where a pair of observations is located, but rather the distance between the two observations

When estimating a surface from point values, kriging is a better approach than simple linear interpolation

Methods of spatial analysis One powerful means of testing an assumed

degree of pattern existence (clustering or scattering) is to use a quadrat analysis

We can select small sub-regions at random and sample the distribution of points within that test region

We compare the distance between points against a randomly distributed field pattern

Randomly distributed field of points

Randomly distributed field of points - sampled

Sample point distribution

Test distribution 1

Test distribution 2

Regular pattern

Methods of spatial analysis One of the best ways of examining point

patterns is to produce a frequency distribution of counts (of the events or cases) within a particular quadrat area

Distances between points within the area and their frequency distribution can be used to objectively test for randomness, clustering or order

Methods of spatial analysis The science of spatial analysis can be quite

complex Be aware not only of concepts of scale and

distance - but also of geographic patterns SS has MANY practical uses - e.g. How could

you objectively test if incidences of cancer were anomalous around a nuclear power station?

Science Direct References The geographic distribution of Parkinson's disease mortality in the United

States, Journal of the Neurological Sciences, Volume 150, Issue 1, 1 September 1997, Pages 63-70 Douglas J. Lanska

Geostatistical and GIS analyses on soil organic carbon concentrations in grassland of southeastern Ireland from two different periods, Geoderma, In Press, Corrected Proof, Available online 24 September 2003, Chaosheng Zhang and David McGrath

Species diversity and spatial distribution of enchytraeid communities in forest soils: effects of habitat characteristics and heavy metal contamination, Applied Soil Ecology, Volume 23, Issue 3, July 2003, Pages 187-198 Pawe Kapusta, ukasz Sobczyk, Anna Ro en and January Weiner

Practical Today

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