[R] about the 95%CI around the median...

Frank E Harrell Jr f.harrell at vanderbilt.edu
Mon Aug 4 15:31:36 CEST 2008

Gavin Simpson wrote:
> On Mon, 2008-08-04 at 17:00 +1000, Simon Blomberg wrote:
>> See ?fivenum in the stats package. If you just type 
>> stats::fivenum
>> you will get the code. The crucial calculations are in the last few
>> lines.
> That will only give the code to calculate the five number summary, but
> Fernando wants to know how the confidence interval is calculated in
> boxplot.stats.
> To see the code just type boxplot.stats followed by return at the
> command line in R.
> The relevant line is:
>     conf <- if (do.conf) 
>         stats[3] + c(-1.58, 1.58) * iqr/sqrt(n)
> Which is working on the median (stats[3]). Details of this computation
> are in ?boxplot.stats which should have been Fernando's first port of
> call. Two works are cited in support of the calculation with full
> references in the References section of that help page.
> G

I wonder why we don't just use the exact nonparametric confidence 
interval for the median, which is just as easy to compute.  Also, it 
will be asymmetric if the data are skewed, as it should be.


>> Simon.
>> On Mon, 2008-08-04 at 16:19 +0930, Fernando Marmolejo Ramos wrote:
>>> Dear people
>>> I've learnt that by using the "boxplot.stats" command in the "grDevices" library
>>> I can get the 5-number summaries of a boxplot, plus other important information,
>>> like the confidence interval around the median.
>>> I'm interested in knowing the actual formula to used in that package to
>>> calculate that confidence interval.
>>> Can someone help me with this?
>>> Cheers,
>>> Fernando

Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University

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