Categorical Variable

A categorical variable in statistics represents a variable with set or limited numerical values. It mainly represents qualitative data and not quantitative (numerical); thus, it is a qualitative variable. These variables assign data in different sets or categories; each variable is treated as a level or identity bracket.

The probability distribution linked to such variables is called categorical distribution. In scenarios where the categorical variable is expressed in a numerical value, it still represents a group or category; therefore, an analyst can not use that data in any form of calculation. Such variables are mainly expressed in two forms, strings or categories, although they have different encoding methods.

Categorical variables are data grouped in unique labels. The only purpose of such variables is to separate and filter the data, putting each one in a different group. Now, there can be n number of categories, and the dataset can be huge. However, the key aspect of such variables is that they cannot be measured because even if they denote a data set in quantitative value, they represent a qualitative aspect, a feature or characteristic based on which the data is grouped.

The categorical variable definition states that it helps identify the data in statistics and put them in columns not for calculation purposes but for collating them. A group of people categorized based on gender has no inherent order. It cannot be further measured, but the same group of people used as a data set for denoting different heights of people can be further calculated for mean, average height, median and other different arithmetic operations.

The main advantages of categorical data are that they are unique with no statistical analysis, they offer simple and direct results with no interval scale and no change in response or options. The data is useful because of its concreteness and not leaving the topic with subjective, open-ended questions.

There are three types of categorical variables -

1. Nominal categorical variables - such variables define data qualities, features and functionality but without any order or ranking. Nominal variables divide data into distinct categories, yet no hierarchy is followed, such as gender, religion, race, etc.
2. Ordinal categorical variables - these variables are ordered and positioned according to their value. It also categorizes the data, but then those data are aligned accordingly. Such variables are observed in surveys, market research, questionnaire responses, income brackets, education level, etc.
3. Binary variables - these are also called dichotomous variables and are used to represent any number of categorical variables in the form of binary values. The categorical variables are transformed into binary values to simplify the process. Although it may look similar to ordinal variables, only use 0 and 1 to represent categories.

Below are two hypothetical examples of categorical variables -

Example #1

Suppose there is a huge strength of students, and the management decides to create three houses, each with a different color, red, yellow and green, and divide the students into them. Doing so is a simple categorical variable example because the data is grouped according to the color variable. Similarly, if the management groups the Yellow House students based on gender, it is another example of categorical variables, gender playing the key role.

Now, the management conducts a small survey regarding students' views and perceptions about the current education system and was given a questionnaire with different statements and options such as agree, strongly agree, disagree, and strongly disagree. Now, it is again an example of a categorical variable. But the key difference is that the former was a nominal variable distinction, and the latter was an ordinal variable grouping.

Example #2

For another example, suppose a teenager who wants to know how many people in his locality have a pet; since he is good with computers, he wrote a small computer program to divide the society members into two categories and denoted two categories through 0 and 1. Those who do not have a pet are assigned 0, and those families with a pet of any kind are given 1.

The teenager shares the link to the computer program with everyone in his locality, and people respond in 0 or 1. This way, the boy can collect and group data into two unique categories. It is a binary categorical variable example.

The key differences between categorical, continuous and numerical variables are -

• Categorical variables represent data in group sets; continuous variables have a minimum and maximum value, whereas numerical variables are general values that can be measured.
• Categorical variables represent datasets divided into separate groups, and continuous variables define a range in which data can be any value, but numerical variables reflect characteristics through quantifiable numbers.
• Category variables are departments, religion, and grades, and continuous variables are temperature, BMI, birth weight, etc. In comparison, numerical variables are age, height, heart rate, and rainfall measured in inches.