>>>>> Gustavo Zapata Wainberg
>>>>> on Mon, 3 May 2021 20:48:49 +0200 writes:
> Hi!
> I'm wrinting this post because there is an inconsistency
> when median() is calculated for even or odd vectors. For
> odd vectors, attributes (such as labels added with Hmisc)
> are kept after running median(), but this is not the case
> if the vector is even, in this last case attributes are
> lost.
> I know that this is due to median() using mean() to obtain
> the result when the vector is even, and mean() always
> takes attributes off vectors.
Yes, and this has been the design of median() for ever :
If n := length(x) is odd, the median is "the middle" observation,
and should equal to x[j] for j = (n+1)/2
and hence e.g., is well defined for an ordered factor.
When n is even
however, median() must be the mean of "the two middle"
observations,
which is e.g., not even *defined* for an ordered factor.
We *could* talk of the so called lo-median or hi-median
(terms probably coined by John W. Tukey) because (IIRC), these
are equal to each other and to the median for odd n, but
are equal to x[j] and x[j+1] j=n/2 for even n *and* are
still "of the same kind" as x[] itself.
Interestingly, for the mad() { = the median absolute deviation from the median}
we *do* allow to specify logical 'low' and 'high',
but that for the "outer" median in MAD's definition, not the
inner one.
## From <Rsrc>/src/library/stats/R/mad.R :
mad <- function(x, center = median(x), constant = 1.4826,
na.rm = FALSE, low = FALSE, high = FALSE)
{
if(na.rm)
x <- x[!is.na(x)]
n <- length(x)
constant *
if((low || high) && n%%2 == 0) {
if(low && high) stop("'low' and 'high'
cannot be both TRUE")
n2 <- n %/% 2 + as.integer(high)
sort(abs(x - center), partial = n2)[n2]
}
else median(abs(x - center))
}
> Don't you think that attributes should be kept in both
> cases?
well, not all attributes can be kept.
Note that for *named* vectors x, x[j] can (and does) keep the name,
but there's definitely no sensible name to give to (x[j] + x[j+1])/2
I'm willing to collaborate with some, considering
to extend median.default() making hi-median and lo-median
available to the user.
Both of these will always return x[j] for some j and hence keep
all (sensible!) attributes (well, if the `[`-method for the
corresponding class has been defined correctly; I've encountered
quite a few cases where people created vector-like classes but
did not provide a "correct" subsetting method (typically you
should make sure both a `[[` and `[` method works!).
Best regards,
Martin
Martin Maechler
ETH Zurich and R Core team
> And, going further, shouldn't mean() keep
> attributes as well? I have looked in R's Bugzilla and I
> didn't find an entry related to this issue.
> Please, let me know if you consider that this issue should
> be posted in R's bugzilla.
> Here is an example with code.
> rndvar <- rnorm(n = 100)
> Hmisc::label(rndvar) <- "A label for RNDVAR"
> str(median(rndvar[-c(1,2)]))
> Returns: "num 0.0368"
> str(median(rndvar[-1]))
> Returns: 'labelled' num 0.0322 - attr(*, "label")=
chr "A
> label for RNDVAR"
> Thanks in advance!
> Gustavo Zapata-Wainberg
> [[alternative HTML version deleted]]
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