A two way table in statistics is a way to summarize data involving two variables in a compact tabular form. We display one of the categories along the rows and the other category along the columns. We then show the corresponding frequencies for each block.
The advantage of a two-way table is that the data becomes much easier to understand when it is displayed in a visual form. Let us understand this by looking at some examples.
Suppose that in a group of 100 people, there are 50 males and 50 females. We are given the following data about the distribution of eye color vs gender.
- 15 males have black eye color.
- The remaining 35 males have blue eye color.
- 20 females have black colored eyes.
- The remaining 30 females have blue eyes.
We can represent this data in the form of a two-way table as shown below.
The rows represent the eye color of the individuals and the columns represent the gender of the individual.
Of course, the data becomes much easier to understand when presented in such a tabular form. We can also use the two-way table to find the marginal frequencies. By marginal frequency, we mean the total frequency for each row and each column.
If we add up the frequencies of the first row, we conclude that 15 + 20 = 35 people have a black eye color. If we sum the frequencies of the second row, we see that 35 + 30 = 65 people have a blue eye color.
Suppose that we are given data about the gender and age distribution of the employees working for a company as follows:
- 32 males and 18 females are below the age of 25.
- 40 males and 27 females are between the ages of 25 and 35.
- 25 males and 18 females are between the ages of 35 and 45.
- 10 males and 5 females are between the ages of 45 and 55.
- 5 men are more than 55 years old.
We can represent this data in a much more visual form as shown below.
The TOTAL column on the right-hand side of the table shows the marginal frequency distribution for the age. For instance, we can see that 43 employees of the organization are between the ages of 35 and 45.
The TOTAL row at the bottom of the table shows the marginal frequency distribution for the gender of the employees. There are a total of 112 men and 68 women working for the company.
Consider the following two way frequency table showing the number of people in a town who are coffee drinkers categorized according to their gender.
We can see from the above table that there are a total of 25 coffee drinkers in Town X. The remaining 75 people do not drink coffee.
According to the above table, 52% of the town’s population is male and 48% of the population of the town is female. In absolute numbers, the number of people who drink coffee is higher in males compared to females.