Standard deviations in the directional distribution tool

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09-30-2015 11:40 AM
JoseeRousseau
New Contributor

Hi,

I am using the Directional Distribution (Standard Deviational Ellipse) tool under the Spatial Statistics toolbox and Measuring Geographic Distribution toolset for an analysis I wish to publish. The results of running the tool looks great but I want to make sure I understand how they were created.

The ArcGIS help website mentions “When the underlying spatial pattern of features is concentrated in the center with fewer features toward the periphery (a spatial normal distribution) a one standard deviation ellipse polygon will cover approximately 68 percent of the features; two standard deviations will contain approximately 95 percent of the features”. The key word in that sentence is “When […]”. 

  1. How do I know whether each ellipse follows a spatial normal distribution?
  2. If my spatial distribution is not normal, how are the ellipses created?  Does the tool ignores the two standard deviations requested option?
  3. I have less than a handful of ellipses that were created using less than 5 points. Regardless of the low sample size, those ellipse seem to have a buffer between the location of the points and the boundary of the ellipse with the ellipse being larger. How was the size of the ellipse determined? I can provide a figure if needed.

Thank you for all your help,

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2 Replies
DanPatterson_Retired
MVP Esteemed Contributor

A figure would help...but a few comments

  • you could do a quick count by eye to see if your point counts generally meet the requirement
  • you could do statistical tests to see if the distribution is indeed normal (not needed unless you are making some claims about statistical importance)
  • the ellipses are created in the same fashion regardless if they are normal or not.  The angle of the ellipse and the a and b axes of the ellipse are controlled by the variances and correlation (see texts as far back as Ebdon, D. 1975 ISBN 0-631-1388-6)

For mechanics, I am sure you have seen the first, but may have missed the second

http://desktop.arcgis.com/en/desktop/latest/tools/spatial-statistics-toolbox/directional-distributio... and

http://desktop.arcgis.com/en/desktop/latest/tools/spatial-statistics-toolbox/h-how-directional-distr...

PS  5 points?....don't get too excited about those ellipses, they hardly meet conditions for any sort of testing or representation.

EDIT

I you are interested in the bivariate normal distribution, there is a starting point here

https://community.esri.com/blogs/dan_patterson/2015/06/16/before-i-forget-8-bivariate-distribution

JoseeRousseau
New Contributor

Thank Dan!

Indeed I had not found some the links you suggested. I'll do some more reading and see if all my questions are answered ;-).

And you are right about the low sample size for some of my ellipses. Thankfully, most have hundreds if not thousand of points.

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