[R] R summary (and quantiles)

[Liaw, Andy]

When all else fails, read the help page...

?fivenum says to look at ?boxplot.stats, and the "Details" section of
?boxplot.stats has, well, details.  Tukey had reasons to call those hinges
rather than quartiles.

Andy

> -----Original Message-----
> From: Knut M. Wittkowski [mailto:kmw at rockefeller.edu]
> Sent: Thursday, May 29, 2003 5:58 PM
> To: Matthias Kirschner
> Cc: R-help at stat.math.ethz.ch
> Subject: Re: [R] R summary (and quantiles)
> 
> 
> Matthias
> 
> The function "fivenum", defines quantiles by assuming that 
> the i-th order 
> statistic is the
> 
>          (i-0.5)/(length(x))
> 
> quantile. Thus, it defines a 25% quantile by finding the 
> cutoff point where 
> 25% are below and 75% above. In this example, this is the "center" of 
> 27.08, counting half of this measurement as "above" and half 
> as "below". 
> This makes a lot of sense, but problem with this definition 
> is that the min 
> is not the 0% quantile, but the 1/2n-quantile.
> 
>  > (order(x)-.5)/(length(x))
>   [1] 0.02272727 0.06818182 0.11363636 0.15909091 0.20454545 
> 0.25000000
>   [7] 0.29545455 0.34090909 0.38636364 0.43181818 0.47727273 
> 0.52272727
> [13] 0.56818182 0.61363636 0.65909091 0.70454545 0.75000000 0.79545455
> [19] 0.84090909 0.88636364 0.93181818 0.97727273
> 
> The function "summary" is based on a definition of quantiles 
> that is biased 
> to equate the min to the 0%-quantile and max to the 
> 100%-quantile. "The 
> algorithm linearly interpolates between order statistics of 
> x, assuming 
> that the ith order statistic is the
> 
>          (i-1)/(length(x)-1)
> 
> quantile."
> 
> The solution is simple: Never use
> 
>          quantile or
>          summary
> 
> if you are interested in quantiles ;-)
> 
> At 00:55 2003-05-30 +0200, you wrote:
> >Dear all
> >i use R only a few days and don't understand the difference between
> >fivenum(x) und summary(x).
> >
> > > x
> >  [1] 20.77 22.56 22.71 22.99 26.39 27.08 27.32 27.33 27.57 
> 27.81 28.69 29.36
> >[13] 30.25 31.89 32.88 33.23 33.28 33.40 33.52 33.83 33.95 34.82
> > > fivenum(x)
> >[1] 20.770 27.080 29.025 33.280 34.820
> > > summary(x)
> >    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
> >   20.77   27.14   29.03   29.17   33.27   34.82
> >
> >And why is the 1st Qu. 27.14 although
> >qL=x(1/4*(n+1))=x(23/4)=x(5 3/4)
> >x(5)=26.39
> >x(6)=27.08
> >why is ql in summary between x(6) und x(7)??
> >
> >I have learned that 1st Qu. = q(0.25)... so i am a little confused.
> >
> >Thanks a lot
> >Matze
> >______________________________________________
> >R-help at stat.math.ethz.ch mailing list
> >https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 
> Knut M. Wittkowski, PhD,DSc
> ------------------------------------------
> The Rockefeller University, GCRC
> 1230 York Ave #121B, Box 322, NY,NY 10021
> +1(212)327-7175, +1(212)327-8450 (Fax)
> kmw at rockefeller.edu
> http://www.rucares.org/statist/
> 
> ______________________________________________
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> 

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