Spatial correlation between layers

Question

Really basic question...  We have multiple layers of point data (representing locations of different species).  We have identified one "key" species.

We've mapped the data, and made density layers and directional ellipses for each species.  We can visually see that some species are spatially correlated with the "key" species and some are not.

We want to be able to express simply and quantitatively (with pairwise correlation coefficients or similar) which other species tend to occur near to the "key" species and which species are not particularly spatially correlated with the "key" species.

This seems like a really rudimentary task in ArcGIS, but we can't figure out how to do it.  Any help is most appreciated!

Eric6346 · Answer

I wouldn't go so far as to say that they "can't" be tested.  However, using a correlation coefficient that assumes independent samples is not a valid way of testing it.  You should just acknowledge that you are ignoring spatial correlation and calculating the correlations for exploratory purposes.

The reason I wouldn't say that they "can't" be tested is that I've read a few papers about testing correlations between two spatially-correlated rasters (such as this one), but we don't have pre-built tools to do it in ArcGIS.

MargaretYacobucci · Answer

You can input all of your density rasters into Band Collection Statistics to get a correlation matrix between all pairs of rasters.  However, keep in mind that Pearson correlation coefficients assume independent samples, and your density maps will have spatial autocorrelation.  Be careful before using these correlations to calculate p-values.

Thanks Eric!  So, is it correct to say that, no, there isn't a way to express *with statistical significance* which species' localities tend to spatially correlate?  The approach you describe gives correlation values for pairs of density rasters, but one can't do statistical tests on them due to autocorrelation.

Eric6346 · Answer

You can input all of your density rasters into Band Collection Statistics to get a correlation matrix between all pairs of rasters.  However, keep in mind that Pearson correlation coefficients assume independent samples, and your density maps will have spatial autocorrelation.  Be careful before using these correlations to calculate p-values.