# spatial statistics and geoda

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### #1 larry83 Posted 26 October 2009 - 01:38 AM

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I'm looking for some advice on how to solve a problem with the paper I'm working on. I have two point layers and basically I just want to determine if the spatial distribution of one set is statistically different from the other. I only care about distance here and do not need to consider any attributes of the points besides that.

There may be a way to accomplish this in both Geoda and perhaps the spatial statistics tools in arcgis. Originally I thought that I could simply use the average nearest neighbor tool in arcgis on each point set individually which would give me a z score for each set and then I could compare those two z scores to see if they are significantly different. I do not think this is correct though and I'm looking for a better way to accomplish this.

I could merge the two point layers to create one point layer and simply create an attribute that would identify the two original sets, but I'm not sure how that would really help me in this situation. Any suggestions?

### #2 frax Posted 26 October 2009 - 03:02 AM

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Do you want to get a spatial dimension to the comparison too? Just one value for how well the match, or the spatial distribution of matchiness? (could it match better in one area of the map and worse in another? Is this relevant?)

What if you would grid the points, and calculate a density grid, that you could then compare?
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### #3 gregsd Posted 26 October 2009 - 03:42 AM

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I'm looking for some advice on how to solve a problem with the paper I'm working on. I have two point layers and basically I just want to determine if the spatial distribution of one set is statistically different from the other. I only care about distance here and do not need to consider any attributes of the points besides that.

There may be a way to accomplish this in both Geoda and perhaps the spatial statistics tools in arcgis. Originally I thought that I could simply use the average nearest neighbor tool in arcgis on each point set individually which would give me a z score for each set and then I could compare those two z scores to see if they are significantly different. I do not think this is correct though and I'm looking for a better way to accomplish this.

I could merge the two point layers to create one point layer and simply create an attribute that would identify the two original sets, but I'm not sure how that would really help me in this situation. Any suggestions?

have a look at CRIMESTAT.

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### #4 MapMedia Posted 26 October 2009 - 08:28 AM

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You could create Thiessen polygons for each set then calculate the overlap as a % of either.
If you want a robust statistical test, the Geospatial Analyst extension for ArcGIS can help - but I am hopeful you can find an Arcscript for this.

### #5 larry83 Posted 26 October 2009 - 01:41 PM

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thanks a lot guys.

frax, I really only need to get one value for how well the two point sets match. Yet, it would be helpful to get information as to if the two point sets match better in certain areas.

gregsd, thanks a lot. I'll look into crimestat today to see if it has any functions that arcgis and geoda do not.

mapmedia, thanks. I think the problem with the thieseen polygon creation is that I am trying to determine if the overall spatial distribution is significantly different. I think the creation of the thiessen polygons would force me to look at each pair of points individually but I am not sure on this. I have the spatial analyst and geostatistical analyst extensions available, but i have not been able to figure out a way to accomplish this with either of them. Although, I admit to not using these extension much so i may be missing something.

I assumed that nearest neighbor analysis would accomplish my goal, but now I'm not sure as it simply gives me a z score for each point set. The z score is a significance test in itself, so two different z score can't be compared for significant difference?

Anway, I'll take a look at the crimestat manuals to see what functions it has and try to think of other ideas.

thanks for the help

### #6 dsl Posted 26 October 2009 - 11:59 PM

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What do you mean " spatial distribution of one set is statistically different from the other?" Do you mean one is random the other is not, one is clustered the other is not, etc..? I'll state first that I'm not a statistics expert or spatial statistics expert.

As I understand it the way these point pattern statistics work is to test your point distribution against a"truely" random distribution of points. This is excerpted from a great book - The ESRI Guide to GIS Analysis Volume 2.

"The nearest neighbor index measures how similar the mean distance is to the expected mean distance for a hypothetical random distribution." Pg 89

And

"The null hypothesis is that the features are randomly distributed....To help you decide whether or not to reject the null hypothesis - and conclude that there is a pattern other than random -- the GIS calculates a Z-Score..." pg 90

So in a sense by calculating these statistics for two point distributions you can say that one is random/not random and the other is random/not random. Or more statistically you "fail to reject the null hypotheses" or "reject the null hypotheses."

There are also a number of other methods to do this (K-Function for example).

Hope that helps,
David

### #7 larry83 Posted 11 November 2009 - 12:42 AM

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thanks for all the help guys. I tried all week, but couldn't really find a good way to accomplish this. I think I will take mapmedia's advice and create thiessen polygons and calculate the overlap as a percentage. Is there an easy way to do this? I tried using the intersect tool but that didn't seem to work.

### #8 Nick H Posted 11 November 2009 - 05:08 AM

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Just to mention that it is (said to be) possible to load 'R-project' layers into Quantum GIS. Not tested here, I'm afraid.

Regards, N.

### #9 Ed Gage Posted 12 November 2009 - 01:41 AM

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It sounds to me like a bivariate Moran's I test (bi-Moran's I) for spatial cross-correlation would be appropriate. Can do this in R easily with the Spatial package; don't know about other options such as GeoDa.
Good luck.

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