In the previous sections, you learned about the different types of variables. Specifically, you learned that there are two main types of variables you will encounter in statistics: qualitative and quantitative variables. While quantitative variables are numerical, qualitative variables tell us about the properties of any unit, individual or object.

While in the previous section you may have learned about the two types of quantitative variables, discrete and continuous variables, in this section you will be introduced to the two types of qualitative variables: ordinal and nominal.

 

Types of Qualitative Variables

Every few years, in a massive effort of coordination, the European Commission publishes the results of a survey called the Eurobarometer. This survey, which started almost 50 years ago, touches upon many aspects of the lives of people living in Europe: culture, health, climate change, poverty and more.

While quantitative information about populations is very important, such as the average income of the elderly or the number of people in a country, many decision-makers often need qualitative data instead. Surveys like the Eurobarometer are the perfect example of the different types of qualitative data that can be gathered from a population. These include questions like the items and electronics people have available at home or tasks like rating life satisfaction.

Understanding the differences between different qualitative variables is important for understanding the data and interpreting its meaning. Let’s start by understanding the two types of qualitative variables.

 

Ordinal and Nominal Variables

A nominal variable is another name for qualitative, or categorical, data. Nominal variables have two or more categories to describe a person or thing and do not fall under any kind of order. Meaning, nominal variables are not ordered according to any sort of preference, satisfaction or worth. For example, in our eye colour example we had a nominal variable with five different categories:

  • Brown
  • Blue
  • Green
  • Hazel
  • Grey

These categories are mutually exclusive, which means that someone with brown coloured eyes has only brown coloured eyes and not any other colour in any other category. Someone with blue eyes doesn’t have grey eyes, just like someone with hazel eyes doesn’t have green eyes. If something is mutually exclusive, it can either be one thing or another, but it can’t be both. Nominal variables don’t have any intrinsic order, which means that they do not have a predetermined order based on worth or preference.

If this is confusing, it might be helpful to think of the opposite situation, which is captured in ordinal variables. Ordinal variables are qualitative, or nominal, variables that have a predetermined order. This can be something like level of satisfaction, ordered into three simple categories:

  • Very happy
  • Okay
  • Very unhappy

These categories are also mutually exclusive, but in this case they do reflect a certain order. Order, in this case, can be misleading because it doesn’t mean that changing the order of our three categories will change their meaning. A better word to use when thinking about ordinal variables is “scale.” On a scale of satisfaction, we have three different levels that have a predetermined order, or a predetermined place on this scale.

 

ordinal variable

 

This scale, going from left to right, reflects the order of our categories. Either someone is very happy, high on the scale, okay, at the midpoint of the scale, or very unhappy, which is at the lowest part of the scale. Thought about in this way, we can see that nominal and ordinal variables are very different. Here are some other examples to help you get a better picture of these differences.

 

Superprof

Nominal Variables

VariableCategories
Eye Colour
  • Brown
  • Blue
  • Green
  • Hazel
  • Grey
Gender
  • Male
  • Female
  • Other
Dog breed
  • Terrier
  • Golden retriever
  • Border collie

Here, each variable is a nominal variable. Meaning, the categories within each variable are not ordered on a specific scale. From brown to grey, eye colour does not have any intrinsic order - meaning, we cannot rate eye colour on a scale based on any predetermined value. In other words, brown eye colour isn’t automatically better or worse, preferred or not preferred, or valued at any worth.

 

Ordinal Variables

VariableCategories
Happiness: How happy were you with the movie?
  • Very Happy
  • Happy
  • Okay
  • Unhappy
  • Very Unhappy
Education level: What grade are you in?
  • Elementary school
  • Middle school
  • High school
  • University
Income: What is their income level?
  • Low income
  • Lower middle income
  • Middle income
  • Higher middle income
  • High income

 

Here, each variable is an ordinal variable. This means that each category within each variable can be ordered on a specific scale. An easy way to determine whether or not a variable is an ordinal variable is to ask yourself if it can be ordered on a scale based on:

  • Preference: is one category preferred over another? For example, do you prefer someone to be very happy or very unhappy?
  • Worth: can one category be valued over another? For example, can a high income level be determined by a higher salary than that of a low income level?
  • Greatness: is one category better than another? For example, if a business wanted to hire an employee, which education level would be best and which one would be worse strictly from their point of view?

 

Problem 1: Categorical and Quantitative Variables

In this chapter, we learned the basics of data and the variables that it can measure, including quantitative variables and qualitative variables. We learned about the two main types of qualitative variables, ones with order and ones without order. Here, we’ll test what you’ve learned in this section - feel free to go back through the lesson to refresh your memory.

The following questions are given out during the first day of university in order to understand more about the types of students that choose particular classes.

QuestionAnswer
1: How old are you?
2: What year are you in?
  • Year 10
  • Year 11
  • Year 12
  • Year 13
3: What is your field of study?
4: How satisfied are you with your courses?
  • Very Satisfied
  • Somewhat Satisfied
  • Neutral
  • Somewhat Unsatisfied
  • Very Unsatisfied
5: How often do you work on homework outside of class?
  • Daily
  • A few times a week
  • Once a week
  • Never

 

For each question, state whether they are qualitative or quantitative. If quantitative, please specify whether they are nominal or ordinal. Afterwards, check your answers with the solution below.

 

Solution Problem 1

Here, we were asked to identify what type of variable each question is. Below, we’ve identified the answers.

QuestionVariableType of Variable
1: How old are you?QuantitativeDiscrete
2: What year are you in?QualitativeOrdinal
3: What is your field of study?QualitativeNominal
4: How satisfied are you with your courses?QualitativeOrdinal
5: How often do you work on homework outside of class?QualitativeOrdinal

 

Recap of Quantitative and Qualitative Variables

Data

A collection of observations, measurements or ideas on specific variables
QuantitativeQualitative
Numeric information about a place, person or thingDescriptive information about a place, person or thing
OrdinalNominal
Ordered based on a specific scaleNot ordered on a scale

In the next chapter, we will go more in depth on quantitative variables and discuss how you can illustrate both categorical and numerical variables.

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Danica

Located in Prague and studying to become a Statistician, I enjoy reading, writing, and exploring new places.

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