Ellipse outsizing convex hull when plotting 95% of the data - are ellipse estimates at the .95 p interval are frequently bigger than the convex hulls?

[addielynne]

Hi all,

I'm having a strange thing happen with some of my data at the .95 p interval. The ellipse when 95% of the data is plotted suddenly gets huge and is way bigger than the convex hull, which is not what I am used to seeing. I am wondering if ellipse estimates at the .95 p interval are frequently bigger than the convex hulls? Things look pretty normal at the 50-85% range, but then the problem emerges at 95%. Photos of the 0.75, 0.85, and 0.95 p interval attached. Any information much appreciated!

[AndrewLJackson]

There is a vignette "Points inside or Outside Ellipse" included in the package that attempts to test for this and has some additional explanation. That code might give you a starting point if you want to develop further tests. But you can see that, for smaller sample sizes, there is a tendency for the ellipse to contain more than 95% of the data.