Correlation and Autocorrelation. Defined. Correlation – the relation (similarity) between two entities Autocorrelation – the relation of entity to itself as the function of distance (time, length, adjacency). Correlation Coefficient. For Interval and Ratio Data.
Values range from -1 to 1 with zero indicating no correlation.
Rough estimates: 0-0.3 Weak, 0.3-0.7 Moderate, 0.7-1.0 Strong
Ho is that the true correlation is zero, with n-2 degrees of freedom.
Assumes that one or both variables are normally distributed.
Most statistics books also provide a table for testing correlation coefficients at different levels of significance developed by R.A. Fisher and others.
Compare values on a profile (variables x,y).
Can also be done using rasters.
n* = number of pairs
Range is -1 to 1
Values range from -1 to 1 with zero indicating no autocorrelation.
Graph of autocorrelation and lag (l) is the opposite of the semivariogram.
Where N is the number of casesXi is the variable value at a particular locationXj is the variable value at another locationXbar is the mean of the variableWij is a weight applied to the comparison between location i and location j
Similar to correlation coefficient, it varies between –1.0 and + 1.0
How to decide the weight wij ?
The weight indicates the spatial interaction between entities.
wij = 1 if two geographic entities are adjacent; otherwise, wij = 0.
2) The distance between geographic entities.
wij = f(dist(i,j)), dist(i,j) is the distance between i and j.
3) The length of common boundary for area entities.
wij = f(leng(i,j)), leng(i,j) is the length of common boundary between i and j.
Morans I: 0.66
P: < 0.001
Moran’s I: 0.012p: = 0.515
Interpreting the CountyC values
0 < C < 2
C=0: maximal positive spatial autocorrelation
C=1: a random spatial pattern
C=2: maximal negative spatial autocorrelation.
This figure suggests a linear relation between Moran's I and Geary's C, and either statistic will essentially capture the same aspects of spatial autocorrelation.