Indexing

Indexing in R

Author

Joseph Mhango

Published

2024-09-13

Objectives

By the end of this section, you should be able to:

Explain the concept of indexing in R and why it is useful.
Use the which() function to identify elements that satisfy a condition.
Perform subsetting on vectors, matrices, and data frames.
Apply the aggregate() function to summarise data efficiently.

The concept of indexing

In R, indexing is how we locate and extract elements from data structures. Think of it like house numbers on a street: every house has a unique number (its “index”), and if you know the number, you can directly access that house.

This same idea applies to vectors, matrices, and data frames in R. Instead of manually searching through your data, you use indices to point to exactly the values you want. This is one of the most powerful features of R, because it allows you to extract, modify, and analyse subsets of data without rewriting or duplicating it.

Indexing with vectors

A vector is the simplest type of data structure in R: a one-dimensional collection of values. Every element in a vector has a position (its index), starting at 1 (unlike Python, which starts at 0).

For example:

my_vector <- c(11.3, 11.2, 10.4, 10.4, 8.7, 10.8, 10.5, 10.3, 9.7, 11.2)
my_vector

 [1] 11.3 11.2 10.4 10.4  8.7 10.8 10.5 10.3  9.7 11.2

To extract elements, we place indices in square brackets:

my_vector[1]      # first element

[1] 11.3

my_vector[3:5]    # third to fifth elements

[1] 10.4 10.4  8.7

my_vector[c(2,4)] # second and fourth elements

[1] 11.2 10.4

If you leave the square brackets empty, R returns the whole vector:

my_vector[]

 [1] 11.3 11.2 10.4 10.4  8.7 10.8 10.5 10.3  9.7 11.2

This is useful when you want to check the full content.

Indexing with matrices

A matrix is a two-dimensional data structure in R (rows × columns). Indexing works in a similar way to vectors, but now you have to specify both row and column positions.

For example:

my_matrix <- matrix(
  data = c(2, 3, 4, 5, 6, 6, 6, 6), 
  nrow = 2, 
  byrow = TRUE
)

my_matrix

     [,1] [,2] [,3] [,4]
[1,]    2    3    4    5
[2,]    6    6    6    6

To extract data, use the format matrix[row, column]:

my_matrix[1, 2]     # element in row 1, column 2

[1] 3

my_matrix[1:2, 3:4] # rows 1–2, columns 3–4

     [,1] [,2]
[1,]    4    5
[2,]    6    6

This is like reading a spreadsheet: first locate the row, then the column.

Using `which()` and subsetting

Sometimes you don’t know the exact position of the element you want — you only know a condition it must satisfy. The function which() is designed for this situation.

It tells you the index (or indices) of elements that meet a condition:

vector_a <- c(4, 7, 2, 9, 6)

which(vector_a > 5)   # returns positions of elements greater than 5

[1] 2 4 5

which.min(vector_a)   # position of the smallest value

[1] 3

which.max(vector_a)   # position of the largest value

[1] 4

Notice that which() does not return the values themselves, but their positions. You can then use those positions to extract the actual elements if you want:

vector_a[which(vector_a > 5)]

[1] 7 9 6

Selection on `data.frame` objects

A data frame is a two-dimensional structure similar to a matrix, but with one key difference:
- In a matrix, every element must have the same data type (all numbers, or all characters).
- In a data frame, each column can be of a different type (e.g. one column numeric, another character, another factor).

This makes data frames much more flexible for real-world datasets.

Accessing data frames follows similar rules to matrices:
- df[row, column] extracts specific cells.
- df$column_name extracts an entire column.

For example:

head(OrchardSprays)

  decrease rowpos colpos treatment
1       57      1      1         D
2       95      2      1         E
3        8      3      1         B
4       69      4      1         H
5       92      5      1         G
6       90      6      1         F

OrchardSprays[1:3, "treatment"] # first three rows of treatment column

[1] D E B
Levels: A B C D E F G H

OrchardSprays$treatment         # entire column

 [1] D E B H G F C A C B H D E A F G F H A E D C G B H A E C F G B D E D G A C B
[39] H F A C F G B D E H B G C F A H D E G F D B H E A C
Levels: A B C D E F G H

Think about this question: what are the advantages of a data frame over a matrix when analysing survey or experimental data?

Slicing data

Slicing means selecting rows that satisfy certain conditions. This is where indexing combines with logical operations.

For example, using the built-in OrchardSprays dataset:

OrchardSprays$treatment == "D"

 [1]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE
[25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE FALSE
[37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
[49] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE
[61] FALSE FALSE FALSE FALSE

This returns a logical vector (TRUE or FALSE) for each row, depending on whether the treatment is equal to "D".

You can use this logical vector directly to filter the data:

OrchardSprays[OrchardSprays$treatment == "D", ]

   decrease rowpos colpos treatment
1        57      1      1         D
12       36      4      2         D
21       22      5      3         D
32       51      8      4         D
34       28      2      5         D
46       27      6      6         D
55       20      7      7         D
59       39      3      8         D

This gives you only the rows where treatment equals D.

Using `aggregate()`

The aggregate() function is very useful for summarising data. It allows you to group data by one or more factors (e.g. treatment groups) and apply a function (e.g. mean, sum, standard deviation) to each group.

For example, to calculate the average decrease by treatment group in the OrchardSprays dataset:

aggregate(
  x = OrchardSprays$decrease,
  by = list(treatment = OrchardSprays$treatment),
  FUN = mean
)

  treatment      x
1         A  4.625
2         B  7.625
3         C 25.250
4         D 35.000
5         E 63.125
6         F 69.000
7         G 68.500
8         H 90.250

Here, x is the variable to summarise, by defines the grouping factor, and FUN specifies the summary function.

This gives you a quick way to compute group statistics without manually splitting your data.

Summary

Indexing is the foundation of working with data in R. Whether you are pulling out a single value from a vector, slicing a matrix, filtering rows of a data frame, or summarising groups with aggregate(), the same principles apply:
- Data are stored in structures.
- Structures have indices.
- You can use indices and conditions to extract, analyse, and summarise data efficiently. ````

Objectives

The concept of indexing

Indexing with vectors

Indexing with matrices

Using which() and subsetting

Selection on data.frame objects

Slicing data

Using aggregate()

Summary

Practice makes perfect

Using `which()` and subsetting

Selection on `data.frame` objects

Using `aggregate()`