# Ranking by specific percentile

Is there a name for ranking categories by their value in a specific percentile (e.g., 66th percentile)?

A fictitious example:

Goethe published 9 books, Schiller published 7, and Herder published 3.

We now rank these books by the number of times they were cited:

Goethe Schiller Herder
972 766 40 *
718 720 * 27
248 * 512 22
241 461
150 37
83 22
17 4
0
0

I put an asterisk * at each column's 66th percentile value (hope I got that right...). Extracting them leads to this ranking:

Rank Author citation count in 33rd percentile
1 Schiller 720
2 Goethe 248
3 Herder 40

This final table is supposed to serve as a new ranking between Schiller, Goethe and Herder (Schiller is ranked #1, Goethe #2, Herder #3).

I would like to know how this ranking-approach is called (so that I can find discussions about implementations, pros/cons etc.) - - your help is very much appreciated!

• It's unclear what you even mean by "approach:" how do you intend to use the results in your bottom table?
– whuber
Commented Jun 20, 2022 at 16:12
• @whuber, I added a sentence explaining that the final table is supposed to serve as a new ranking (according to which Schiller is #1). Commented Jun 22, 2022 at 19:16
• Just putting objects in some kind of order is trivial. What matters to you is how you will use this ranking for any further decisions or analyses. That will suggest how to evaluate the goodness of rankings and can help justify (or debunk) the 33rd percentile approach.
– whuber
Commented Aug 27, 2022 at 15:50

When you have so few observations in a set of observations (9 for Goethe, 7 for Schiller, and 3 for Herder), there are different methods to determine quantiles. For example, in R you can choose any of 7 methods. ( www.rdocumentation.org/packages/stats/versions/3.6.2/topics/quantile .)

Usually observations are listed from smallest to greatest for identifying quantiles, so I think you are looking for the 66.7 th percentile or the 0.667 quantile.

You can play with the different methods of calculating quantiles in R, with the type option in the quantile() function by running the following code in R or at https://rdrr.io/snippets/.

I've never heard of any name for such a ranking technique, except to say that the groups were ranked by the 66.7 th percentile of their observations.

Goethe   = c(972,718,248,241,150,83,17,0,0)
Schiller = c(766,720,512,461,37,22,4)
Herder   = c(40,27,22)

summary(Goethe)
summary(Schiller)
summary(Herder)

sum(Goethe)
sum(Schiller)
sum(Herder)

quantile(Goethe,   0.667, type = 7)
quantile(Schiller, 0.667, type = 7)
quantile(Herder,   0.667, type = 7)