Come r: The R Project for Statistical Computing

R: rank vs. order. If you’re learning R you’ve come across… | by Rebecca Peltz

If you’re learning R you’ve come across the sort, rank and order functions. Because there is similarity and even overlap in the semantics, questions come up: what exactly does each do and what are the use cases for each?

All three functions require that the values they operate on are comparable. Comparisons in R can apply to string, numeric, complex and logical date types.

Rank vs Order Confusion

Sort, Rank, and Order are functions in R. They can be applied to a vector or a factor. If you are used to thinking of data in terms of rows and columns, a vector represents a column of data. A factor is created from a vector and represents discrete labeled values. In the R code below, X is loaded with data and then sorted, ranked, and ordered. R reports the results as vectors.

X = c(3,2,1) 
X 
3 2 1 
sort(X)
[1] 1 2 3
rank(X)
[1] 1 2 3
order(X)
[1] 1 2 3

It seems clear enough:

• you load data into a vector using the “c”ombine function
• when you view X it appears arranged as it was loaded
• when you sort X, you see a vector containing values from X arranged in ascending order
• when you rank X, you see a vector containing values from X arranged in ascending order (like sort)
• when you order X, you see a vector containing values from X arranged in ascending order (like sort)

Now, let’s apply a simple permutation when creating the X vector and run these functions.

X = c(2,3,1) 
X 
2 3 1
sort(X)
[1] 1 2 3
rank(X)
[1] 2 3 1
order(X)
[1] 3 1 2

In the output above the sort function affirms what we stated above, but the rank and order are more difficult to explain. Now, look at a different vector with a similar permutation on a different range of integers.

X = c(5,6,4) 
X 
5 6 4
sort(X)
[1] 4 5 6
rank(X)
[1] 2 3 1
order(X)
[1] 3 1 2

In the code above we see the same rank and order for “5, 6, 4” as we did for “2, 3, 1”. The reason that these two sequences have the same rank and order is that rank and order are reporting on relative locations as opposed to relative values. Rank and order are based on the results of an ascending sort of data in the vector. Specifically, the range of values returned by rank and order is the range of indexes of values in the original sequence.

• Rank references the position of the value in the sorted vector and is in the same order as the original sequence
• Order returns the position of the original value and is in the order of sorted sequence, that is smallest value to largest value

The graphic below helps tie together the values reported by rank and order with the positions from which they come.

Involutive Cycles

The “1,2,3” sequence first presented that returned the vector “1,2,3” for both Rank and Order is actually a special sequence because these values and several other permutations of “1,2,3” cause rank and order to behave as involutory functions. An involuntary function is a function that is its own inverse.

X = c(1,2,3)
RANK(X) == ORDER(X) == X
RANK(ORDER(X)) == X
ORDER(RANK(X)) == 1:length(X)

In the code below, you can see all six of the permutations of “1,2,3” tested to see if they are involutive (a function that when applied twice will give you the starting value). The two permutations that do not result in involutive functionality can be identified by the cycles which they break down into. See the article rank vs order in R below for more information on involutive cycles.

X = c(1,2,3)
all(order(rank(X)) == X)
[1] TRUEX = c(2,3,1)
all(order(rank(X)) == X)
[1] FALSEX = c(3,1,2)
all(order(rank(X)) == X)
[1] FALSEX = c(1,3,2)
all(order(rank(X)) == X)
[1] TRUEX = c(2,1,3)
all(order(rank(X)) == X)
[1] TRUEX = c(3,2,1)
all(order(rank(X)) == X)
[1] TRUEall(order(X)[rank(X)] == rank(x)[order(X)]) == 1:length(X)
TRUE

While it’s tempting when learning to look at simple data sets to help understand the behavior of functions, it can lead to confusing conclusions when the arrangement of the data affects the output of the functions.

Sorted Sequences

For any vector sequence in ascending order, the code below demonstrates the relationship between Order and Rank as they interact with each other. The Order of the Rank will always equal the Rank of the Order.

X = c(100,200,300)
all(order(X)[rank(X)] == rank(X)[order(X)])
TRUE

In addition, the code below verifies that for any sequence in ascending order both the Order of the Rank and the Rank of the Order will always equal a vector made up of the positions of the ordered elements.

x = c(100,200,300)
all(order(X)[rank(X)] == 1:length(X))
TRUE
all(rank(X)[order(X)] == 1:length(X))
TRUE
1:length(X)
[1] 1 2 3

Use Case for the Order Function

You can use the order function to sort a dataframe.

The sort command can be used to create a new vector from any vector of comparable values into a vector arrange in an ascending sequence. The default sort order is ascending, but there are options to make it descending, as well as options for dealing with undefined values and specifying a sorting method.

When you read data from a file system into a data frame or construct the data frame in code, you have a structure that contains rows and columns of data that may be of different types. In order to “sort” the row of a data frame by column values, whether it’s a single column or multiple columns, you must use the order command as the sort command only sorts vectors.

To see how this works, the example below builds up a data frame from raw data loaded into vectors. This data could easily have been read in from a CSV or other formatted text file as well. Note: enclosing the last instruction in parentheses causes the data frame to be referenced by the test.data variable and displays what’s in the test.data variable. The first integer in the display is a counter identifier assigned by R to the rows in the data frame.

size = 5
sex=sample(c("male","female"),size,replace=T)
age = sample(21:100, size, replace=T)
degree = sample(c("BA","BS","MS","MBA"), size, replace=T)
(test.data = data.frame(sex=sex, age=age, degree=degree))sex age  degree
1 female  30     BA
2   male  49     BA
3   male  39    MBA
4   male  27     MS
5   male  61     MS

We can sort the data by age using the order command. The order function is passed the name of the column to order by and the order is ascending. The result of the order command is a vector where each value references the value of the position of the item in the original data frame and it, itself, is located in the sorted data’s position. For example, the 1st age in the original data frame is 30 and in the sorted data frame 30 will be in the 2nd position. Therefore, the value 1 is located in the 2nd position of the order vector.

Once the order vector is obtained it is used to extract data from the original test. data. You can see the original counter id in the result and how it matches the order vector used to do the sort. R extracts data from a data frame (or matrix) using the square brackets with a Row, Column designation.

order(test.data$age)
[1] 4 1 3 2 5test.data[order(test.data$age),]
sex age degree
4   male  27     MS
1 female  30     BA
3   male  39    MBA
2   male  49     BA
5   male  61     MS

The data frame can be sorted in descending order by using the negative sign in front of the column name specified by the order command.

order(-test.data$age)
[1] 5 2 3 1 4test.data[order(-test.data$age),]5   male  61     MS
2   male  49     BA
3   male  39    MBA
1 female  30     BA
4   male  27     MS

We can also provide multi-column sorts by adding multiple columns to the order command.

order(test.data$degree,-test.data$age)
[1] 2 1 3 5 4
test.data[order(test.data$degree,-test.data$age),]sex age degree
2   male  49     BA
1 female  30     BA
3   male  39    MBA
5   male  61     MS
4   male  27     MS

Use Case for the Rank Function

You can use the rank function to create a value that represents the relative standing of a value within its sequence.

The IEEE provided a list of the top 10 programming languages for 2017. They are stored in a file, in my local file system, sorted in alphabetical order by language name. The code below will read them into a variable which references them by the name language.ieee and displays the contents.

(language.ieee =read.csv(file="language-scores.csv"))
X   language score
1   2          C  99.7
2   5         C#  87.7
3   4        C++  97.1
4   9         Go  75.1
5   3       Java  99.5
6   7 JavaScript  85.6
7   8        PHP  81.2
8   1     Python 100.0
9   6          R  87.7
10 10      Swift  73.1

We can get a vector of the ranked data. The data in the rank vector appears as float because there is a tie: C# is tied with R for 5th and 6th place. There are options for dealing with ties in the rank function, but the default is to use the “average” method and assign each the average value. The values themselves represent the descending order of the corresponding value by the position of the value in the original data set. A higher rank value represents a larger data value.

rank(language.ieee$score)
9.0  5.5  7.0  2.0  8.0  4.0  3.0 10.0  5.5  1.0

I can use the rank vector to order the data by rank, that is, the descending order of scores, by supplying the negative rank to the order command.

language.ieee[order(-rank(language.ieee$score)),]
X   language score
8   1     Python 100.0
1   2          C  99.7
5   3       Java  99.5
3   4        C++  97.1
2   5         C#  87.7
9   6          R  87.7
6   7 JavaScript  85.6
7   8        PHP  81.2
4   9         Go  75.1
10 10      Swift  73.1

Calculating rank is not only used for ordering data. Correlation of rankings can be used to test the null hypothesis of the relationship between two variables. Since variables may differ in type and scale, rank provides a sort of normalization. For example see studies on the use of Spearman’s Rank Correlation: https://geographyfieldwork.com/SpearmansRank.htm.

Conclusion

R is a statistical programming language with many functions that help with formatting and processing data. Its services are made available through function calls. In addition to reading the documentation, it helps to run data sets through these functions to help figure out what exactly they do. Sort, Order, and Rank are semantically the same, but in practice, they have very different uses and sometimes work with each other to achieve the desired result.

Comer Definition & Meaning – Merriam-Webster

com·​er

ˈkə-mər 

1

: one that comes or arrives

welcomed all comers

2

: one making rapid progress or showing promise

Example Sentences

We’re giving free T-shirts away to the first comers.

She’s regarded as a comer in political circles.

Recent Examples on the Web

Between up-and-comer Notre Dame (Hingham), longtime powerhouse Bridgewater-Raynham/West Bridgewater, and new co-op Falmouth/Mashpee/Barnstable, the league has at least three teams jockeying for sectional spots.

—Kat Cornetta, BostonGlobe.com, 14 Jan. 2023

Well, next Sunday night’s game between the Kansas City Chiefs and Tampa Bay Buccaneers looks to be the last matchup between up-and-comer Patrick Mahomes and all-time great Tom Brady (barring another Super Bowl).

—Vulture, 27 Sep. 2022

Franklin — Foxborough, an up-and-comer in Division 2, will try to upset perennial Division 1 contender Franklin.

—Trevor Hass, BostonGlobe.com, 15 Dec. 2022

This game pits a future Hall of Fame quarterback in Ben Roethlisberger against an up-and-comer in Joe Burrow, who will still be starting his return from last year’s ACL injury.

—Jeremy Cluff, The Arizona Republic, 20 Sep. 2021

At this show, Mark will help NPR Music celebrate its 15th anniversary alongside indie mainstay Hurray for the Riff Raff, up-and-comer Yendry and DJ Cuzzin B. 7 p.m. $45.

—Chris Kelly, Washington Post, 25 Nov. 2022

Until Pac-12 play, the toughest potential challenges on the schedule for the Cardinal are up-and-comer Gonzaga, quickly-faltering Tennessee and Creighton.

—Marisa Ingemi, San Francisco Chronicle, 23 Nov. 2022

An up-and-comer, sturdy, fortified by its own domestic league, backed by a rowdy crowd traveling from their home country right next door.

—Jason Gay, WSJ, 22 Nov. 2022

Novavax has been a late comer on the vaccine scene in the US, though it has been widely used in many other countries, including as a booster dose in Europe, Japan, Australia, New Zealand, Switzerland and Israel.

—Jacqueline Howard, CNN, 19 Oct. 2022

See More

These example sentences are selected automatically from various online news sources to reflect current usage of the word ‘comer. ‘ Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

Word History

First Known Use

14th century, in the meaning defined at sense 1

Time Traveler

The first known use of comer was
in the 14th century

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Dictionary Entries Near

comer

come prima

comer

come round

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“Comer.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www. merriam-webster.com/dictionary/comer. Accessed 30 Jan. 2023.

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