Normality test for Directional Distribution tool?

Question

I am anticipating a question in class this week about the Directional Distribution (Standard Deviational Ellipse) tool.

I will be pointing out that when you use a standard deviational ellipse and make a statement that 68% of the population is inside the one-stdev ellipse, you are assuming a bivariate normal distribution.  I haven’t seen a KS or Shapiro Wilks test in the software to test for normality in the point pattern. Would this be possible or even appropriate?

curtvprice · Answer

Seems to me this should be doable from the tool's output, as you get the parameters required (ellipse coordinates) to calculate a z-score for every point in your dataset. Though it would be a bit of coding.  Thanks for your thoughts.

Great point about R - ArcGIS, Steve Kopp‌ reminded me to get on the upcoming Aug 31 Esri Training webinar Go Deeper with Data Analytics w ArcPro & R. They have been doing some really interesting things recently with R integration, which is great, why re-invent for GIS what are becoming very standard technologies and methods!

That MVN package uses Henze-Zirkler, cool beans! From Wikipedia article Normality Test

More recent tests of normality include the energy test[9] (Székely and Rizzo) and the tests based on the empirical characteristic function (ECF) (e.g. Epps and Pulley,[10] Henze–Zirkler,[11] BHEP test[12]). The energy and the ECF tests are powerful tests that apply for testing univariate or multivariate normality and are statistically consistent against general alternatives.

I think I'm going to like grad school better than last time around because internet.

DanPatterson_Retired · Answer

Curtis... move is provided in the how-directional-distribution-standard-deviation works

I tried to see if I could get the download for

Fisher, N. I., T. Lewis, and B. J. J. Embleton. Statistical Analysis of Spherical Data. 1st ed. Cambridge: Cambridge University Press, 1987. Cambridge Books Online. Web. 26 April 2016.

I remember the solid copy as being good... but I don't have my Open Athens account info here.

In short... as with any statistical tool... you can use it... you won't be stopped, but should you?  There is no associated testing of what is returned as you note.

You could make some data and calculate the normal pdf and associated info from before-i-forget-8-bivariate-distribution then throw in a couple of straggler points along the 'b' axis to show what affect outliers have upon the returned values.

ADDENDUM

Of course this gives rise to introducing the R-Bridge and using multivariate tests ... there are other links using 'normalcy' and 'multivariate' as keyword searches

https://cran.r-project.org/web/packages/MVN/vignettes/MVN.pdf

https://cran.r-project.org/web/packages/MVN/MVN.pdf