Prerequisite: Data Structures in R Programming

**Contingency tables** are very useful to condense a large number of observations into smaller to make it easier to maintain tables. A contingency table shows the distribution of a variable in the rows and another in its columns. Contingency tables are not only useful for condensing data, but they also show the relations between variables. They are a way of summarizing categorical variables. A contingency table that deals with a single table are called a **complex or a flat contingency table.**

#### Making Contingency tables

A contingency table is a way to redraw data and assemble it into a table. And, it shows the layout of the original data in a manner that allows the reader to gain an overall summary of the original data. The

function is used in R to create a contingency table. The **table()**

function is one of the most versatile functions in R. It can take any data structure as an argument and turn it into a table. The more complex the original data, the more complex is the resulting contingency table.**table()**

#### Creating contingency tables from Vectors

In R a vector is an ordered collection of basic data types of a given length. The only key thing here is all the elements of a vector must be of the identical data type e.g homogenous data structures. Vectors are one-dimensional data structures. It is the simplest data object from which you can create a contingency table.

**Example:**

`# R program to illustrate` `# Contingency Table` ` ` `# Creating a vector` `vec ` `=` `c(` `2` `, ` `4` `, ` `3` `, ` `1` `, ` `6` `, ` `3` `, ` `2` `, ` `1` `, ` `4` `, ` `5` `)` ` ` `# Creating contingency table from vec using table()` `conTable ` `=` `table(vec)` `print` `(conTable)` |

**Output:**

vec 1 2 3 4 5 6 2 2 2 2 1 1

In the given program what happens is first when we execute `table()`

command on the vector it sorts the vector value and also prints the frequencies of every element given in the vector.

#### Creating contingency tables from Data

Now we will see a simple example that provides a data frame containing character values in one column and also containing a factor in one of its columns. This one column of factors contains character variables. In order to create our contingency table from data, we will make use of the `table()`

. In the following example, the `table()`

function returns a contingency table. Basically, it returns a tabular result of the categorical variables.

**Example:**

`# R program to illustrate` `# Contingency Table` ` ` `# Creating a data frame` `df ` `=` `data.frame( ` ` ` `"Name"` `=` `c(` `"Amiya"` `, ` `"Rosy"` `, ` `"Asish"` `), ` ` ` `"Gender"` `=` `c(` `"Male"` `, ` `"Female"` `, ` `"Male"` `)` `) ` ` ` `# Creating contingency table from data using table()` `conTable ` `=` `table(df)` `print` `(conTable)` |

**Output:**

Gender Name Female Male Amiya 0 1 Asish 0 1 Rosy 1 0

#### Creating custom contingency tables

The contingency table in R can be created using only a part of the data which is in contrast with collecting data from all the rows and columns. We can create a custom contingency table in R using the following ways:

- Using Columns of a Data Frame in a Contingency Table
- Using Rows of a Data Frame in a Contingency Table
- By Rotating Data Frames in R
- Creating Contingency Tables from Matrix Objects in R

**Using Columns of a Data Frame in a Contingency Table:**With the help of`table()`

command, we are able to specify the columns with which the contingency tables can be created. In order to do so, you only need to pass the name of vector objects in the parameter of`table()`

command.**Example:**`# R program to illustrate`

`# Contingency Table`

`# Creating a data frame`

`df`

`=`

`data.frame(`

`"Name"`

`=`

`c(`

`"Amiya"`

`,`

`"Rosy"`

`,`

`"Asish"`

`),`

`"Gender"`

`=`

`c(`

`"Male"`

`,`

`"Female"`

`,`

`"Male"`

`)`

`)`

`# Creating contingency table by selecting a column`

`conTable`

`=`

`table(df$Name)`

`print`

`(conTable)`

**Output:**Amiya Asish Rosy 1 1 1

From the output, you can notice that the

`table()`

command sorts the name in alphabetically order along with their frequencies of occurrence.**Using Rows of a Data Frame in a Contingency Table:**We can’t create a contingency table using rows of a data frame directly as we did in “using column” part. With the help of the matrix, we can create a contingency table by looking at the rows of a data frame.**Example:**`# R program to illustrate`

`# Contingency Table`

`# Creating a data frame`

`df`

`=`

`data.frame(`

`"Name"`

`=`

`c(`

`"Amiya"`

`,`

`"Rosy"`

`,`

`"Asish"`

`),`

`"Gender"`

`=`

`c(`

`"Male"`

`,`

`"Female"`

`,`

`"Male"`

`)`

`)`

`# Creating contingency table by selecting rows`

`conTable`

`=`

`table(as.matrix(df[`

`2`

`:`

`3`

`, ]))`

`print`

`(conTable)`

**Output:**Asish Female Male Rosy 1 1 1 1

**By Rotating Data Frames in R:**We can also create a contingency table by rotating a data frame in R. We can perform a rotation of the data, that is, transpose of the data using the

command.**t()****Example:**`# R program to illustrate`

`# Contingency Table`

`# Creating a data frame`

`df`

`=`

`data.frame(`

`"Name"`

`=`

`c(`

`"Amiya"`

`,`

`"Rosy"`

`,`

`"Asish"`

`),`

`"Gender"`

`=`

`c(`

`"Male"`

`,`

`"Female"`

`,`

`"Male"`

`)`

`)`

`# Rotating the data frame`

`newDf`

`=`

`t(df)`

`# Creating contingency table by rotating data frame`

`conTable`

`=`

`table(newDf)`

`print`

`(conTable)`

**Output:**newDf Amiya Asish Female Male Rosy 1 1 1 2 1

**Creating Contingency Tables from Matrix Objects in R**A matrix is a rectangular arrangement of numbers in rows and columns. In a matrix, as we know rows are the ones that run horizontally and columns are the ones that run vertically. Matrices are two-dimensional, homogeneous data structures. We can create a contingency table by using this matrix object.**Example:**`# R program to illustrate`

`# Contingency Table`

`# Creating a matrix`

`A`

`=`

`matrix(`

`c(`

`1`

`,`

`2`

`,`

`4`

`,`

`1`

`,`

`5`

`,`

`6`

`,`

`2`

`,`

`4`

`,`

`7`

`),`

`nrow`

`=`

`3`

`,`

`ncol`

`=`

`3`

`)`

`# Creating contingency table using matrix object`

`conTable`

`=`

`table(A)`

`print`

`(conTable)`

**Output:**A 1 2 4 5 6 7 2 2 2 1 1 1

#### Converting Objects into tables

As mentioned above, a table is a special type of data object which is similar to the matrix but also possesses several differences.

**Converting Matrix Objects into tables:**We can directly convert a matrix object into table by using the

command. Just pass the matrix object as a parameter to the**as.table()**

command.**as.table()****Example:**`# R program to illustrate`

`# Contingency Table`

`# Creating a matrix`

`A`

`=`

`matrix(`

`c(`

`1`

`,`

`2`

`,`

`4`

`,`

`1`

`,`

`5`

`,`

`6`

`,`

`2`

`,`

`4`

`,`

`7`

`),`

`nrow`

`=`

`3`

`,`

`ncol`

`=`

`3`

`)`

`# Converting Matrix Objects into tables`

`newTable`

`=`

`as.table(A)`

`print`

`(newTable)`

**Output:**A B C A 1 1 2 B 2 5 4 C 4 6 7

**Converting Data frame Objects into tables:**We can’t directly convert a data frame object into table by using the

command. In the case of a data frame, the object can be converted into the matrix, and then it can be converted into the table using**as.table()**

command.**as.table()****Example:**`# R program to illustrate`

`# Contingency Table`

`# Creating a data frame`

`df`

`=`

`data.frame(`

`"Name"`

`=`

`c(`

`"Amiya"`

`,`

`"Rosy"`

`,`

`"Asish"`

`),`

`"Gender"`

`=`

`c(`

`"Male"`

`,`

`"Female"`

`,`

`"Male"`

`)`

`)`

`# Coverting data frame object to matrix object`

`modifiedDf`

`=`

`as.matrix(df)`

`# Converting Matrix Objects into tables`

`newTable`

`=`

`as.table(modifiedDf)`

`print`

`(newTable)`

**Output:**Name Gender A Amiya Male B Rosy Female C Asish Male