Figure 3.1
Table 3.2
Correlation and regression of simulated data for different types of aggregation
Aggregation method
Correlation coefficient (r)
Regression coefficient (b)
Standard error (s.e.)
Raw data
0.479
0.991
0.015
Random
0.471
0.944
0.148
Systematic
0.982
0.990
0.016
Spatial
0.776
1.078
0.074
Spatial autocorrelation in Y but not in X
 
 
Raw data
0.711
1.007
0.008
spatial
0.346
0.957
0.218

The data were generated using this formula: Y = 10 + X + €

The X values were generated by, first, generating random numbers for each cell in a 120 X 120 square grid. The value of X was then computed using a moving window (i.e., X was the average of the cell itself and its four neighbours), so that a known pattern of spatial autocorrelation existed in the X's.

The aggregration strategy varied between the three methods: 100 cells were selected randomly, systematically on the basis of their X values (i.e., the first 100 cells along the x-axis were grouped, etc.), and in contiguous blocks of 10 x 10 cells.