Is there a statistical or philosophical argument for choosing between ellipses or convex hulls to highlight differences between groups on an NMDS plot?
My guess is that, visually, hulls can de-emphasize differences between groups, since more of the plot area will be covered by a given hull compared to an ellipse scaled according to some confidence interval. But does that mean it is more "honest" to use hulls, or might outliers have undue influence on the interpretation?
Sadly (!) I think my confusion is partly due to the fact that I don't really understand the meaning of a "confidence interval" in NMDS ordination space. I'm worried that I've managed to produce ellipses that don't mean what I think they mean.
For example, if you generate an NMDS using species abundance data, and you have 95% confidence interval ellipses are non-overlapping, is the interpretation that you can be 95% confident that the groups of interest are different from one another with respect to species composition? Or what?
Great question! I was just wondering this myself. I think convex hull tend to overstate the information content of the data, whereas the ellipses handle this more honestly. For a small number of data points you get a large ellipse, which implies that the locus is uncertain, whereas the convex hull could be small (which implies greater certainty).
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