# [R] OT: compare several graphs

Tue Oct 23 10:21:22 CEST 2001

```This sounds interesting. But this tests if the observed data differs
from a random sample. My question is if the observed data differs from
each other.

By, Sven

Kaspar Pflugshaupt wrote:
>
> On 22.10.2001 15:30 Uhr, Jan_Svatos at eurotel.cz wrote:
>
> >
> > Hi Sven,
> >
> > I am just doing something similar-
> > my graphs are densities of nonnegative r.v's (with all probability mass at
> > fixed bounded interval).
> > Then I compute their "distance" by dist (mva package needed), i.e.
> >
> > my.dist<-dist(t(cbind(dens1\$y, dens2\$y)))
> >
> > (provided that dist1\$x==dist2\$x, of course)
> > The problem of course is, how to decide about statistical and/or
> > "practical" significance of a difference.
> > I cannot remain myself of some correct statistical test of such hypothesis
>
> I'm not sure if this is statistically sound (comments, please!), but what
>
>   repeat some 1000 times:
>      shuffle one column randomly, then compute the distance
>   compare your distance to the empirical distribution of
>   "resampled distances"
>
> In terms of R code:
>
>   Nreps <- 5000
>   dists <- numeric(Nreps)
>   for(i in 1:Nreps)
>   {
>      y2 <- sample(dens2\$y)
>      dists[i] <- dist(t(cbind(dens1\$y, y2)))
>   }
>   hist(dists)
>   quantile(dists, 0.05)
>
> If the original distance is lower than the 5% quantile of the resampled
> dists, your two graphs would be "significantly more similar" than "random
> graphs". For a two-sided test, you could use
>
>   quantile(dists, c(0.025, 0.975)).
>
> If this makes sense, there is still the problem of the correct distance
> measurement. By default, dist() calculates euclidean distances. I'm not sure
> it they are appropriate for this kind of data.
>
> As I said, please comment. It's just an idea I had (along the lines of the
> "Mantel test").
>
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