A two-way table is used to explain two or more categorical variables at the same time. The difference between a two-way table and a frequency table is that a two-table tells you the number of subjects that share two or more variables in common while a frequency table tells you the number of subjects that share one variable.

For example, a frequency table would be gender. In such a table, you only know how many subjects are male or female. The only variable involved is gender. In a frequency table, you would learn some of the following

• Total number of men
• Total number of women
• Total number of subjects in the study

In a two-way table, you might look at gender and marital status. In such a table you would be able to learn several things

• Total number of men are married
• Total number of men are single
• Total number of women are married
• Total number of women are single
• Total number of men
• Total number of women
• Total number of married subjects
• Total number of single subjects
• Total number of subjects in the study

As such, there is a lot of information in a two-way table. In this post, we will look at the following

• How to create a table
• How to add margins to a table
• How to calculate proportions in a table

Creating a Table

In the example, we are going to look at two categorical variables. One variable is gender and the other is marital status. For gender, the choices are “Male” and Female”. For marital status, the choicest are ‘Married” and “Single”. Below is the code for developing the table.

Marriage_Study<-matrix(c(34,20,19,42), ncol = 2)
colnames(Marriage_Study) <- c('Male', 'Female')
rownames(Marriage_Study) <- c('Married', 'Single')
Marriage_table <- as.table(Marriage_Study)
print(Marriage_table)

There has already been a discussion on creating matrices in R. Therefore, the details of this script will not be explained here.

If you type this correctly and run the script you should see the following

        Male Female
Married   34     19
Single    20     42

This table tells you about married and single people broken down by their gender. For example, 34 males are married.

Adding Margins and Calculating Proportions

A useful addition to a table is to add the margins. The margins tell you the total number of subjects in each row and column of a table. To do this in R use the ‘addmargins’ function as indicated below.

> addmargins(Marriage_table)
        Male Female Sum
Married   34     19  53
Single    20     42  62
Sum       54     61 115

We now know the total number of Married people, Singles, Males, and Females. In addition to the information we already knew.

One more useful piece of information is to calculate the proportions. This will allow us to know what percentage of each two-way possibility makes up the table. To do this we will use the “prop.table” function. Below is the script

> prop.table(Marriage_table)
             Male    Female
Married 0.2956522 0.1652174
Single  0.1739130 0.3652174

As you can see, we now know the proportions of each category in the table.

Conclusions

This post provided information on how to construct and manipulate data that is in a two-way table. Two-way tables are a useful way of describing categorical variables.