2.Spatial Autocorrelation

Question 1

spatial autocorrelation

Answer 1

• spatial autocorrelation has the effect of making insignificant relationships appear
significant
• this false significance arises not because the independent variable is related to the
dependent variable, but because the observations in the independent variable are
related to each other
• we can assess the effect of spatial autocorrelation by understanding and detecting
spatial patterns
• while spatial pattern analysis is necessary to understand the effects of dependence, it
can also be used to study data clustering

Question 2

• spatial data can be classified in 2 primary categories:

Answer 2

• dispersed: the data is spread out, with the
individual points separated by a relatively
constant distance
• the mean centre is representative of the
dataset as a whole
• clustered: the data is grouped with small
distances between the points and large
distances between the groups
• the mean centre is not representative of
the dataset as a whole

Question 3

• the study of spatial patterns is known as

Answer 3

point pattern analysis,

Question 4

variance mean ration

Answer 4

we can describe the pattern by determining the
variance-mean ratio (VMR)
• if 𝑉𝑀𝑅 =
𝑠
2
𝑥ҧ
= 1, then the pattern is random
• if 𝑉𝑀𝑅 =
𝑠
2
𝑥ҧ
< 1, then the pattern is
regular/uniform
• if 𝑉𝑀𝑅 =
𝑠
2
𝑥ҧ
> 1, then the pattern is clustered

Question 5

How to try and figure out whether our VMR value is significantly different then a random pattern:

Answer 5

X2=(m-1)s2/mean

-m is number of grid cells used

Question 6

.IF TEST STATISTIC IS LESS THEN THE CRITICAL STATISTIC THEN WE _______ THE NULL HYPOTHESIS-

Answer 6

accept

-it is not significant enough to be different then random

Question 7

One problem with quadrat analysis?

Answer 7

• although the quadrat method is used extensively, mainly because it is easy to use, it
suffers 1 major problem: the size (and hence number) of cells strongly affects the
results
• if the cells are too small, there will be a large number of cells with 0 points and
large scale clustering may be missed
• if the cells are too large, they will miss any small scale patterns
• determining the size of the cells should be use-specific – ie, it should depend on the
specific dataset you are using
• some researchers have suggested that to optimize the quadrat method, the mean
number of points per cell should be between 1.6 and 2.0
• using this guideline, you can test different cell sizes until you get the optimal size,
then proceed with the computation

Question 8

Nearest Neighbour analysis

Answer 8

• nearest neighbour analysis determines the average distance between each point and it’s
nearest neighbouring point(s) and compares that distance with an expected distance if
the pattern was completely random

Question 9

Problems when measuring nearest neighbour

Answer 9

1. Shape of study area effects results, an elongated area will force points to be close to each other, lowering the value of R(observed) and increasing clustering
2. Boundary Effects can influence results, nearest neighbour could be just outside the boundary
3. Nearest neighbour in basic terms only deals with paurs of points, but you can fix this by using high order distances.

Question 10

lag

Answer 10

spatial distance between 2 observations in the dataset

Question 11

semivariogram

Answer 11

the semivariogram is a commonly used graphical device for describing spatial
autocorrelation – again, the mathematics are complicated enough that you’ll want to
use software to compute it