Geography Reference
In-Depth Information
Variable 1
Variable 2
45
40
z 12.917 0.1784y
169
18
37
15
17
174
162
161
35
30
25
150
144
161
160
2
5
2
14
1 20
3
131
127
162
163
5
3
15
10
5
42
18
18
20
0
142
148
158
158
120
130
140
150
160
170
180
Variable 1
80
70
60
630
651
62
48
50
40
30
20
548
641
68
56
10
z 153.71 0.1542y
0
540
560
580
600
620
640
660
Variable 1
Figure 4.12 Two scatter plots and fi tted lines for different aggregations of the same values.
Wong (1997) explores changes in measures of residential segregation (i.e. the degree
to which members of dif erent groups live in dif erent areas). Wong argues that, if the
counts of the population group are negatively spatially autocorrelated (neighbouring
zones are dissimilar), using zones of dif erent sizes will result in dif erent segregation
measure values. Conversely, if the counts are positively spatially autocorrelated (neigh-
bouring zones are similar), then using zones of dif erent sizes will make little dif er-
ence for zones smaller than the area (or scale) over which counts are positively
autocorrelated. In general, the degree of spatial autocorrelation is important when
considering the ef ect of changing the zonal system used.
Figure 4.12 gives an artii cial example of the potential ef ects of altering the aggrega-
tion of values. In this case, two sets of variables are given for two dif erent aggrega-
tions. Regression of one variable on the other is then conducted using the two sets of
aggregations. Note that the sample size is very small and this example is used purely
for illustrative purposes. Recall from Section 3.4 that assessing sample size is impor-
tant when considering regression results. In the example, the slope changes from posi-
tive to negative as the values are aggregated over larger units. Even where the sign
doesn't change, the ef ects of changing the size or form of zones may be highly signii -
cant. Openshaw and Taylor (1979) explore the issue using regression for many dif er-
ent zonal systems and they demonstrate large dif erences where the form of zones
varies but their number is the same (the zoning ef ect) and where the number of zones
varies (the scale ef ect). Note that r 2 tends to increase with increased aggregation, and
this would clearly be the case given the example in Figure 4.12.
In summary, the potential impact of the size and shape of zones on results should be
considered and it should be remembered that any pattern apparent in mapped areal
data may be due as much to the zoning system used as to the underlying distribution
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