22.9 Correlation

The connection functions perason and spearman rank correlation as well as covariance can be calculated for different files. The calculation returns a covariance and correlation coefficient matrix. Optionally a t-test can be performed and partial correlation can be calculated. Different options for treating NODATA values are available.

Correlations are special types of Connection functions since they do not result in the creation of new raster layer. Instead the correlation information is stored within a seperate file.The correlation output can be viewed through drag and drop of the connection within the file tree into the right window.

[Picture]

Figure 74: Correlation Matrix

Find mor specific information under perason correlation and spearman rank correlation.

22.9.1 The Correlation Settings Dialog

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Figure 75: Correlation Dialog

If all files contain a NODATA value for the same pixels they are excluded from calculation. If only one file has a NODATA value, the treatment can be specified. There are three options

  • NODATA SKIP: The selection of this option results in a pairwise deletion of nodata values.
  • MEAN INITIATION: The selection of this option results in a substitution of all NODATA values with the mean value of the file.
  • ZERO INITIATION: The selection of this option results in a substitution of all NODATA values with zero values.

Both, Pearson and Spearman Rank Correlation offer the poosibility to calculate partial correlation coefficients and p-values calculated from a student-t-distribution.

22.9.2 Pearson Correlation

The connection function pearson product moment correlation coefficient is a measure for the linear correlation between two variables x and y with a value between +1 and -1. While + 1 indicates a perfect positive correlation -1 indicates a perfect negative correlation. In both cases all data points are on exactly on one line in a xy diagram. The pearson correlation coefficient is calculated according to the formula

cov(x,y)- E-((x-−-¯x)(y-−-¯y)) ρx,y = σx ⋅σy = σx ⋅σy
(11)

22.9.3 Spearman Rank Correlation

The connection function spearman rank correlation coefficient is a measure of the correlation (not necessarily linear) between two variables x and y with a value between +1 and -1. While + 1 indicates a perfect positive correlation -1 indicates a perfect negative correlation. It is the pearson correlation coefficient between the variables x and y after they have been converted to ranks. NODATA values are pairwise deleted from calculations.

The formula for the calculation of the correlation coefficient is

cov(xrank,yrank) E-((xrank −-¯xrank)(yrank −-¯yrank)) ρxrank,yrank = σxrank ⋅σyrank = σxrank ⋅σyrank
(12)