I have entered values into Excel, and sorted them. I am assuming you are asking
why the value 3 in x2 is ranked 4.5 versus in x5 it has a rank of 5.
X2 looks like this
Value RankOrder
1 1.5 1
1 1.5 2
2 3 3
3 4.5 4
3 4.5 5
4 6 6
5 8 7
5 8 8
5 8 9
6 10 10
9 11 11
The average of 4 and 5 is 4.5.
For x3 we have:
Value RankOrder
1 1.5 1
1 1.5 2
2 3 3
3 5 4
3 5 5
3 5 6
4 7 7
5 9 8
5 9 9
5 9 10
6 11 11
9 12 12
The ranks of the threes are 4, 5, and 6 and the average is 5.
For any set of values adding one value that is the same as an existing value
will always increase the rank of that value. It has not been rounded up, though
it may look that way in the example. If you add another 3 to the data the rank
will increase to 5.5, and adding another three will give a rank of 6. Each
additional 3 will boost the rank by 0.5.
You can get a different result if you change a value. If there is a mistake in
the data and I discover that the second 1 in x2 should be a 3, then the rank
for 3 is 4 and it looks like I have rounded down. If the mistake happened for a
value greater than 3 then it would again look like I had rounded up. However,
the appearance of "rounding" is an illusion easily seen through if you expand
your example to generalize the outcome.
Tim
-Original Message-
From: R-help On Behalf Of Gerrit Eichner
Sent: Friday, August 11, 2023 4:32 AM
To: r-help@r-project.org
Subject: Re: [R] Puzzled by results from base::rank()
[External Email]
Dear Chris,
the members of the triplet would be ranked 4, 5 and 6 (in your example), so the
*mean of their ranks* is correctly 5.
For any set of k tied values the ranks of its elements are averaged (and
assigned to each of its k members).
Hth -- Gerrit
-
Dr. Gerrit Eichner Mathematical Institute, Room 215
gerrit.eich...@math.uni-giessen.de Justus-Liebig-University Giessen
Tel: +49-(0)641-99-32104 Arndtstr. 2, 35392 Giessen, Germany
http://www.uni-giessen.de/eichner
-
Am 11.08.2023 um 09:54 schrieb Chris Evans via R-help:
> I understand that the default ties.method is "average". Here is what
> I get, expanding a bit on the help page example. Running R 4.3.1 on
> Ubuntu 22.04.2.
>
> > x2 <- c(3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5) > rank(x2)
> [1] 4.5 1.5 6.0 1.5 8.0 11.0 3.0 10.0 8.0 4.5 8.0
>
> OK so the ties, each of with two members, are ranked to their mean.
>
> So now I turn one tie from a twin to a triplet:
>
> > x3 <- c(x2, 3)
> > rank(x3)
> [1] 5.0 1.5 7.0 1.5 9.0 12.0 3.0 11.0 9.0 5.0 9.0 5.0 >
> sprintf("%4.3f", rank(x3))
> [1] "5.000" "1.500" "7.000" "1.500" "9.000" "12.000" "3.000"
> "11.000"
> [9] "9.000" "5.000" "9.000" "5.000"
>
> The doublet is still given the mean of the values but the triplet is
> rounded up. What am I missing here?!
>
> TIA,
>
> Chris
>
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