Whiskers on the default boxplot {graphics}

From: Jason Rupert <jasonkrupert at yahoo.com>
To: Dennis Murphy <djmuser at gmail.com>
Cc: R Project Help <R-help at r-project.org>
Sent: Wed, May 12, 2010 3:40:12 AM
Subject: Re: [R] Whiskers on the default boxplot {graphics}

Fantastic! 

include the mysterious bit about the upper and lower bound whisker 
positions:

= max(min(x), Q_1 - 1.5 * IQR)

description of boxplot.stats {grDevices}, but evidently I missed it numerous 
times and also did not pick up on this intent from the original description of 
boxplot {graphics}.  

helpfulness is much appreciated and one of the reasons I continue to endorse the 
R tool over numerous others.  

headed for domination in the market. 

again!

Dennis Murphy <
href="mailto:djmuser at gmail.com">djmuser at gmail.com>

Help <
href="mailto:R-help at r-project.org">R-help at r-project.org>

May 12, 2010 2:50:19 AM

{graphics}

:)

it...

I'm just trying to use the default boxplot {graphics} 

capability in R...

So I call something like the 

following:

boxplot(mpg~cyl,data=mtcars, main="Car Milage Data", 

xlab="Number of Cylinders", ylab="Miles Per Gallon") \

That 

produces something as shown in the 
following:
http://www.statmethods.net/graphs/images/boxplot1.jpg

When 

that default boxplot is called, i.e. boxplot {graphics}, as shown in the line of 
code above, it is actually calling into boxplot.stats {grDevices}.  When 
boxplot.stats {grDevices} is called it has a default value for "coef" of 1.5, 
i.e. coef = 1.5.

If I understand the purpose of "coef" 

correctly, it means that the ?whiskers? should extend out 1.5 times the length 
of the box away from the box.   Is that correct?

'length of the box' you mean the interquartile range (IQR = Q_3 - Q_1 where Q 
refers to quartile), then assuming that

for a boxplot,

whisker = max(min(x), Q_1 - 1.5 * IQR)

the *smaller* of the maximum x value and Q_3 + 1.5 IQR,

whisker is located at the *larger* of the smallest x value and Q_1 - 1.5 
IQR.

times the length of the box

that individual points more extreme in value than Q3 + 1.5 IQR are 
plotted

separately on the low

points are called 'outside values'. On

minimum values of x are closer than 1.5 IQR in distance from

quartile, then that is where the whisker is positioned.

sense?

Now I look back at the plot, and 

I'm not sure how 1.5 times the length of the box corresponds with the whisker 
lengths shown in the image:

href="http://www.statmethods.net/graphs/images/boxplot1.jpg" target=_blank 

http://www.statmethods.net/graphs/images/boxplot1.jpg

Is 

it that the whisker length is a total of 1.5 the length of the box and centered 
about the median (2nd Quartile)?

Just trying to get a handle 

on this, so thanks again for all the help in deciphering 
this.

RJ Cunningham <
href="mailto:robut at iinet.net.au">robut at iinet.net.au>


target="_blank" href="http://ast.net">ast.net>

Cc: R Project 

Help <
href="mailto:R-help at r-project.org">R-help at r-project.org>

Sent: 

Tue, May 11, 2010 9:57:48 PM

Subject: Re: [R] Whiskers on the 
default boxplot {graphics}


I think not. Isn't the 
"secret" here?

Arguments:

x: a 

numeric vector for which the boxplot will be constructed

('NA's and 

'NaN's are allowed and omitted).

coef: this determines how 

far the plot 'whiskers' extend out

from the box.  If 'coef' is 

positive, the whiskers extend

to the most extreme data point which is 

no more than

'coef' times the length of the box away from the box. 

A

value of zero causes the whiskers to extend to the 

data

extremes (and no outliers be 

returned).

do.conf,do.out: logicals; if 'FALSE', the 'conf' 

or 'out'

component respectively will be empty in the 

result.

Details:

The two 'hinges' are 

versions of the first and third quartile,...

On Wed 

May 12 10:35 , Jason Rupert  sent:

Humm....Maybe 

I need to look some place else than boxplot.stats {grDevices} for a definition 
of how the upper/lower whiskers are 
produced.

By any chance are 

they "the lowest datum still within 1.5 IQR of the lower quartile, and the 
highest datum still within 1.5 IQR of the upper 
quartile"?

None of the links 

from boxplot.stats {grDevices} seemed to reveal the secret definition of the R 
whiskers.

Thanks 

again.

----- 

Original Message 
----

To: 

David Winsemius <
href="mailto:dwinsemius at comcast.net">dwinsemius at comcast.net>

Cc: 

R Project Help <
href="mailto:R-help at r-project.org">R-help at r-project.org>

Sent: 

Tue, May 11, 2010 9:26:25 PM

Subject: Re: [R] 

Whiskers on the default boxplot 
{graphics}

Wowzers...

From 

?boxplot.stats:

Details

The 

two ?hinges? are versions of the first and third quartile, i.e., close to 
quantile(x, c(1,3)/4). The hinges equal the quartiles for odd n (where n <- 
length(x)) and differ for even n. Whereas the quartiles only equal observations 
for n %% 4 == 1 (n = 1 mod 4), the hinges do so additionally for n %% 4 == 2 (n 
= 2 mod 4), and are in the middle of two observations 
otherwise.

The notches 

(if requested) extend to +/-1.58 IQR/sqrt(n). This seems to be based on the same 
calculations as the formula with 1.57 in Chambers et al. (1983, p. 62), given in 
McGill et al. (1978, p. 16). They are based on asymptotic normality of the 
median and roughly equal sample sizes for the two medians being compared, and 
are said to be rather insensitive to the underlying distributions of the 
samples. The idea appears to be to give roughly a 95% confidence interval for 
the difference in two 
medians.

Is 

a notch equal to the upper/lower whisker?   Is this just a difference of 
terminology or 
something?

Thanks again for 

all the 
insights.

----- 

Original Message ----

From: David 

Winsemius <
href="mailto:dwinsemius at comcast.net">dwinsemius at comcast.net>

Cc: 

R Project Help <
href="mailto:R-help at r-project.org">R-help at r-project.org>

Sent: 

Tue, May 11, 2010 9:00:15 PM

Subject: Re: [R] 

Whiskers on the default boxplot 
{graphics}

On 

May 11, 2010, at 9:45 PM, Jason Rupert 
wrote:

How are the 

lower/upper whiskers defined in the default version of boxplot 
{graphics}?

I tried help(boxplot) and searching 
href="http://www.rseek.org">www.rseek.org, but I was unable to determine an 
absolute answer.

You need 

to follow the links from the help pages and tin this case it appears that you 
did not follow the one 
to

?boxplot.stats

I checked out the definition of boxplot according to Wikipedia 
(http://en.wikipedia.org/wiki/Box_plot%5C), but it also had several 
approaches

listed for how the 

whiskers could be determined, so I'm just curious how the 
default

boxplot {graphics} does 

it.

Thanks for any 
feedback

Follow links with 

the R help system.

and 

insights.

David 

Winsemius, MD

West Hartford, 

CT

ymailto="mailto:R-help at r-project.org" 
href="mailto:R-help at r-project.org">R-help at r-project.org mailing 
list

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