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Is there a statistical method to compare these density plots other than ANOVA (MANOVA)? I would like to compare the densities among year within each plot and report which of those distributions are "significantly different". The reason is that I am more interested in the spread and where on the distribution of the dataset rather than solely on the mean and variance. Thanks

Here is the code and plot

ggplot(NMPSCFAM, aes(Length, colour= Year)) + 
  geom_density(aes(y = ..count..), alpha=0.3) + xlim(0, 700) +  
  geom_density(aes(colour = Year)) +
  xlab("") +
  ylab(expression(paste("Mean density ( ", m^2, ")", sep = ""))) +
facet_wrap( ~ Family + Sector2, ncol=3, scales = "free")

enter image description here

Edit: Ok so no answers so far. If I did these density plots in a histogram would there be a way to do a Chi-square test on each of the plots? Could any one help me out on how to do this in R?

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The problem with a chi-square is it ignores the ordering, leading to a loss of power.

One possibility: there is a k-group version of a Kolmogorov-Smirnov test$^{[1]}$.

Another is a k-sample Anderson-Darling test. E.g. see Wikipedia.

A third possibility might be to look at an orthogonal-polynomial decomposition of a chi-square (or rather the first few terms in one), which would then be taking account of the ordering. See, for example chapter 6 of Best (1999)$^{[2]}$.

[1]: Conover, W. J. (1965),
"Several k-Sample Kolmogorov-Smirnov Tests",
The Annals of Mathematical Statistics, 36:3 (Jun.), pp. 1019-1026

[2]: Best, D.J. (1999),
Tests of fit and other nonparametric data analysis,
PhD Thesis, School of Mathematics and Applied Statistics, University of Wollongong
http://ro.uow.edu.au/theses/2061 (direct link)

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  • $\begingroup$ thanks for this. I was discussing an orthogonal-polynomial decomposition of a chi-square and thought this may be beyond me. I'll source those papers and have a read. Now to figure out which one and to complete it in R. Once done I'll get back to this post with the results. Regards George $\endgroup$
    – George
    Commented Aug 27, 2014 at 15:24
  • $\begingroup$ There are some papers that discuss this possibility (some by Rayner and Best) as well. If you can't find any I should be able to dig some up. $\endgroup$
    – Glen_b
    Commented Aug 27, 2014 at 20:27

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