quantile(), IQR() and median() for factors

I like the idea of median and friends working on ordered factors. 
Just a couple of thoughts on possible implementations.

Adding extra checks and functionality will slow down the function. 
For a single evaluation on a given dataset this slowdown will not be 
noticeable, but inside of a simulation, bootstrap, or other high 
iteration technique, it could matter.  I would suggest creating a 
core function that does just the calculations (median, quantile, 
iqr) assuming that the data passed in is correct without doing any 
checks or anything fancy.  Then the user callable function (median 
et. al.) would do the checks dispatch to other functions for 
anything fancy, etc. then call the core function with the clean 
data.  The common user would not really notice a difference, but 
someone programming a high iteration technique could clean the data 
themselves, then call the core function directly bypassing the 
checks/branches.

Just out of curiosity (from someone who only learned from English 
(Americanized at that) and not Italian texts), what would the median 
of [Low, Low, Medium, High] be?

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

-----Original Message-----
From: r-devel-bounces at r-project.org [mailto:r-devel-bounces at r-
project.org] On Behalf Of Simone Giannerini
Sent: Thursday, March 05, 2009 4:49 PM
To: R-devel
Subject: [Rd] quantile(), IQR() and median() for factors

Dear all,

from the help page of quantile:

"x ??? numeric vectors whose sample quantiles are wanted. Missing
values are ignored."

from the help page of IQR:

"x ??? a numeric vector."

as a matter of facts it seems that both quantile() and IQR() do not
check for the presence of a numeric input.
See the following:

set.seed(11)
x <- rbinom(n=11,size=2,prob=.5)
x <- factor(x,ordered=TRUE)
x
?[1] 1 0 1 0 0 2 0 1 2 0 0
Levels: 0 < 1 < 2

quantile(x)

? 0%? 25%? 50%? 75% 100%
?? 0 <NA>??? 0 <NA>??? 2
Levels: 0 < 1 < 2
Warning messages:
1: In Ops.ordered((1 - h), qs[i]) :
? '*' is not meaningful for ordered factors
2: In Ops.ordered(h, x[hi[i]]) : '*' is not meaningful for ordered
factors

IQR(x)

[1] 1

whereas median has the check:

median(x)

Error in median.default(x) : need numeric data

I also take the opportunity to ask your comments on the following
related subject:

In my opinion it would be convenient that median() and the like
(quantile(), IQR()) be implemented for ordered factors for which in
fact
they can be well defined. For instance, in this way functions like
apply(x,FUN=median,...) could be used without the need of further
processing for
data frames that contain both numeric variables and ordered factors.
If on the one hand, to my limited knowledge, in English introductory
statistics
textbooks the fact that the median is well defined for ordered
categorical variables is only mentioned marginally,
on the other hand, in the Italian Statistics literature this is often
discussed in detail and this could mislead students and practitioners
that might
expect median() to work for ordered factors.

In this message

https://stat.ethz.ch/pipermail/r-help/2003-November/042684.html

Martin Maechler considers the possibility of doing such a job by
allowing for extra arguments "low" and "high" as it is done for mad().
I am willing to give a contribution if requested, and comments are
welcome.

Thank you for the attention,

kind regards,

Simone

R.version

?????????????? _
platform?????? i386-pc-mingw32
arch?????????? i386
os???????????? mingw32
system???????? i386, mingw32
status
major????????? 2
minor????????? 8.1
year?????????? 2008
month????????? 12
day??????????? 22
svn rev??????? 47281
language?????? R
version.string R version 2.8.1 (2008-12-22)

?LC_COLLATE=Italian_Italy.1252;LC_CTYPE=Italian_Italy.1252;LC_MONETARY=
Italian_Italy.1252;LC_NUMERIC=C;LC_TIME=Italian_Italy.1252

--