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I have a number of (point) locations at which two variables are measured. The two variables proves correlated (when using Spearman's r; the direction of the correlation is irrelevant here).

How can we assess (graphically and/or statistically) if the two variables covary in space?

For instance, if the two variables tend to increase as one moves (say) to the north, or something along that line.

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This is a common question in fields like pollution tracking and exploration geochemistry but it is seldom straightforward. The fact you seem to have a positive correlation using (non-directional) correlation analysis is encouraging- so long as it is not just reflecting one or two high points. Check this first on an X-Y scatterplot.

There are fancy ways to do cross-correlation of spatial data - see the widely cited paper by Beale et al 2010: "Regression analysis of spatial data" DOI: 10.1111/j.1461-0248.2009.01422.x.

A quick-and dirty approach that I have used is to multiply the two variables and then plot a colour-coded map of their product. Locations that are mutually high enhance each other; those that are low suppress relative to the norm.

You might see groups of clustered highs. These can be examined more using something like inverse distance squared interpolation and contouring. You might also see broad-scale trends across the data space. These can be examined using trend surface analysis.

You don't say what software you are using so I won't take this further.

  • Thank you. I made some web search on the topic, but I am not familiar with most of the approaches I have found. Your "quick and dirty" solution could prove viable. As the software, if it can prove interesting for you in anticipation of further comments, when it comes to spatial statistics I happened to use SAM and GeoDA. – NewAtGis Sep 3 at 14:35

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