Categorical Variables or Qualitative variables:

Categorical Variable Definition – What is a Categorical Variable?

Categorical variables are variables that belong to a particular category. Categorical variables, often known as “Qualitative” variables, are variables that have names, symbols, labels or number codes, and may be classified into groups. These variables categorise a person or thing. In other words, variables that take those values that are names or labels are known as categorical variables or qualitative variables. Categorical variables represent several types of groups, and so categorical variables are classified as either nominal or ordinal variables.

That is, categorical variables are not measurement variables; their values do not come from counting or measuring them. Hence, categorical variables are descriptions of groups or things, such as “gender (male and female)” or “religious preference (Hindu, Jain, Sikh, Muslim, Christian, Jewish, Other, None)”.

For example, if we consider X to be an Indian person’s political party preference, then some examples of X are BJP, Congress, AAP, etc. Hence, the variable X is a categorical variable. It is meaningless to perform math with X values (It makes no sense to calculate an average political party preference).

Examples of Categorical Variables or Qualitative variables:

Eye colour (with categories; “blue,” “green,” or “brown”), Gender (with categories; “male,” “female”), Dating status (with categories; “Yes” and “No”) etc. are all examples of categorical variables because these observations fall into distinct categories.

Categorical Variable Examples – The following examples are also categorical variables.

• Marital status (with categories; “married,” “single,” or “divorced”).
• Dog breed (with categories; “lab,” “bulldog,” “poodle”, etc.).
• Hair colour (with categories; “blond,” “brunette,” “black,” “white,” “grey,” or “brown”).
• Cloud cover (with categories; “cloudy”, “partly cloudy”, or “sunny”).
• Whether it snowed on a particular day (with categories; “Yes” and “No”).
• Religious preference (with categories; “Hindu,” “Jain,” “Sikh,” “Muslim,” “Christian,” “Jewish,” “Other,” “None”).
• Style of housing (with categories; “House,” “Villa,” “Apartment,” “Dormitory,” “Other”).
• Belief in life after death (with categories; “Yes” and “No”).
• In a coin flip (with categories; “Head” and “Tail”).
• In a football game (with categories; “Win” and “Lose”).
• Class in college (e.g. fresher, sophomore, junior, senior).
• Party preference (e.g. Republican, Democrat, Independent).
• Type of pet owned (e.g. dog, cat, rodent, fish).
• Preferred airline (e.g. IndiGo, Air India, SpiceJet, GoAir, AirAsia, Vistara, Other).
• Favourite author (e.g. Stephen King, James Patterson, Charles Dickens).
• Types of hats (e.g. sombrero, beanie, fedora).

Caution:

A variable using numbers as category labels is always a categorical variable and not a quantitative variable.

General rule for Categorical Variables or Qualitative variables: 

You are working with a categorical variable if you can not add something (these variables), or if you can not get a meaningful result by adding or subtracting the values of two variables.

• For example, we can not add cat + dog, or Republican + Democrat, so that means it is categorical.
• Similarly, grades/ranks of A, B, or C, cannot be added together until they are converted to numbers, hence A, B, and C are categorical.

Important Remarks on Categorical Variables:

If each observation belongs to one of a set of several distinct categories, the variable is considered categorical. The categorical variable describes the “types” of something. It is meaningless to perform math with categorical variables.

The major characteristics of a categorical variable are described via graphs and numerical summaries. The relative number of observations in different categories is an important attribute to explain for categorical variables. For instance, what percentage of days in a given year was cloudy?

Observations are the data values that we observe for a variable. In categorical variable, each observation belongs to a category, such as “yes” or “no” for whether it snowed.

Pie charts and bar graphs are used to display data for categorical variables. We provide a frequency table for categorical variables that shows the (relative) frequencies of observations in each category and highlights the categories with the highest frequencies.

Types of Categorical Variables:

Categorical variables represent several types of groups, and so categorical variables are classified as either nominal or ordinal variables. They are sometimes represented by numbers, but the numbers denote categories instead of actual quantities. Hence, there are two types of Categorical variables:

(i) Nominal variables,

(ii) Ordinal variables.

(i) Nominal Variables:

The categories of a nominal variable have no inherent or natural order. Hence, a nominal variable is a categorical variable with two or more categories but no inherent order or rank. It’s worth noting that the different categories of a nominal variable can also be called groups or levels. That is, nominal variables are groups with no rank or order between them.

Examples of Nominal Variables:

For example, it is not possible to state that ‘Green’ is greater than ‘Blue’, so we cannot compare one colour to another, and so the colour of a thing is a nominal categorical variable. The following examples are also nominal variables.

• Marital status (with categories; “married,” “single,” or “divorced”).
• Gender (with categories; “male,” “female”).
• Dog breed (with categories; “lab,” “bulldog,” “poodle”, etc.).
• Hair colour (with categories; “blond,” “brunette,” “black,” “white,” “grey,” or “brown”).
• Cloud cover (with categories; “cloudy”, “partly cloudy”, or “sunny”).
• Whether it snowed on a particular day (with categories; “Yes” and “No”).

(ii) Ordinal Variables:

The categories of an ordinal variable have an inherent or natural order, that is, the ordering of an ordinal variable is clear. Hence, ordinal variables are variables with two or more categories having inherent order or rank. In other words, ordinal variables are groups that are ranked in a specified order. They may, for example, imply superiority.

Examples of Ordinal Variables:

For example, we can easily sort the clothing brands’ sizes according to their name tags in the order of small < medium < large, so the clothing brands’ sizes is an ordinal categorical variable with ordered categories which are; small, medium, large. Similarly, the temperature is an ordinal categorical variable with three orderly categories; low, medium and high. The following examples are also ordinal variables.

• Economic status: (with categories; low, medium, high).
• Letter grades: (with categories; A, B, C, D, E, etc.)
• Rank in a competition: (with categories; First, Second, Third)
• Educational background: (with categories; 10th, 12th, Graduate, Post Graduate, etc.)
• Time of day: (with categories; Morning, Noon, Night)
• The severity of the bug in the software: (with categories; critical, medium and low)

Read Also – Quantitative Variables or Numeric Variables, Discrete variables and Continuous variables

(Source – Various books from the college library)

Tags: categorical variable examples, categorical variables examples, nominal ordinal, Nominal and ordinal variable examples

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