#### 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.

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

##### 22.9.1 The Correlation Settings 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

| (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

| (12) |