Types of Variables in Statistics: A Comprehensive Overview

Summary: This blog upholds the different types of variables along with their examples. Knowledge of variables is crucial for data scientists and data analysts as it helps them in data analysis of data 

Introduction

If you have been working on statistics, you would come across a common term called a variable. To simplify, a variable is a characteristic that can have different values. For example, height, age, and income of different individuals are examples of variables. These are primarily divided into two key categories: categorical and numeric. 

As a data scientist, having a deep understanding of statistical tools and their analysis is crucial. To use the statistical tool optimally, it is crucial to understand all the core aspects of statistics. This blog breaks down all the different types of variables and their key features.

What is a Variable in Statistics?

To understand a variable, consider it as a characteristic that can be measured or counted like a number. The reason it is called a variable is that the value can change or vary among individuals over time. For example, if you are studying a group of individuals for their demographics like age, gender, eye colour, etc. 

Two Key Components of Variables: Qualitative and Quantitative Variables

The first major distinction to understand is the difference between qualitative and quantitative variables.

Qualitative Variables: The Describers

These are also known as categorical variables. As evident from the name, it highlights the quality or characteristics. It deals with variables that cannot be measured in numbers; rather, they fall under different categories. 

Examples of qualitative variables include:

• Eye colour: Blue, brown, green
• Gender: Male, female, non-binary
• Type of pet: Dog, cat, fish, bird

There are two main types of qualitative variables:

Qualitative variables can further be dissected into two different categories:

Nominal Variables

These types of variables have no natural order or ranking. These are just labels, for example: blood type (A, B, AB, O). There is no order in this. These are categories that do not have a natural order or ranking. Think of them as just labels. For example, blood type (A, B, AB, O) is a nominal variable because there’s no inherent order to these categories.

Ordinal Variables

These are categories that have a natural order or ranking. You know the order, but you don’t know the exact difference between the categories. For example, a satisfaction survey with options like “Very Dissatisfied,” “Dissatisfied,” “Neutral,” “Satisfied,” and “Very Satisfied” is an ordinal variable. You know “Very Satisfied” is better than “Satisfied,” but you can’t say it’s exactly twice as good.

Quantitative Variables: The Countable Parameters

Quantitative variables, also called numeric variables, represent a measurable quantity. These are your numbers-based variables.

Examples of quantitative variables include:

• Height
• Weight
• Age

Quantitative variables can be further broken down into two types:

Discrete Variables

These are variables that can only take on a specific, countable number of values, often whole numbers. Think of things you can count in whole units. For example, the number of children in a family can be 2 or 3, but not 2.5.

Continuous Variables

These are variables that can take on any value within a given range. These are things you measure. For example, a person’s height can be 65 inches, 65.5 inches, or even 65.52 inches, depending on the precision of the measurement.

Types of Variables in Biostatistics

The use of statistics is not limited to a certain domain; it has a universal application. Biostatistics uses statistical methods to analyse biological and health data. Here are some of the key examples of the same:

• Qualitative (Categorical) Variables
  • Nominal: Blood type (A, B, AB, O), Sex (male, female), Presence of a disease (yes, no).
  • Ordinal: Disease severity (mild, moderate, severe), Pain level (none, mild, moderate, severe)

• Quantitative (Numerical) Variables
  • Discrete: The number of hospital visits in a year, the number of medications a patient is taking.
  • Continuous: Blood pressure, cholesterol level, body weight, age.

Having an understanding of the different types of variables helps in statistical analysis. It is the first step of the data analysis journey, hence one should be well-acquainted with the types of variables that eventually help in the accuracy of the analysis. 

Why Does the Variable Type Matter?

Having the right knowledge about the different types of variables is crucial, as it impacts the choice of statistical methods by the data scientists as well as the analysts. 

Accurate Description of Data

Data is the king, and it impacts the strategic decisions. Hence, accurate description, screening, and filtering of the data are crucial. For example, if you use percentages and frequencies for categorical data (e.g., 60% of patients were female), while for continuous data, you would use measures like the mean or median (e.g., the average blood pressure was 120/80 mmHg).

For Statistical Testing

There are different statistical tests designed for different types of variables. For example, the chi-squared test is used to compare two categorical variables, whereas the t-test is used to compare the means of a continuous variable between groups. 

Closing Thoughts

In conclusion, a clear understanding of nominal, ordinal, discrete, and continuous variables is essential for anyone working with data. This knowledge forms the foundation for conducting meaningful statistical analysis and drawing accurate conclusions to advance knowledge.

Frequently Asked Questions

Can I calculate the average (mean) satisfaction score from a 5-point scale?

You should be cautious. This is an ordinal variable, meaning the intervals between points are not guaranteed to be equal. Calculating a mean is misleading. It’s more accurate to use the median, mode, or frequencies to summarise the central tendency and distribution of this type of data.

What are my variable types when comparing three drugs’ effects on blood pressure, and which test should I use?

Your “drug type” is a nominal independent variable, and “blood pressure” is a continuous dependent variable. To compare the mean blood pressure across three or more groups, the correct statistical test is an Analysis of Variance (ANOVA), which is designed for this specific combination of variable types.

Is ‘number of emergency room visits’ a discrete or continuous variable, and does it matter?

The number of ER visits is a discrete variable because it is counted in non-negative whole numbers. This matters because it determines the correct analysis. You should use statistical models designed for count data, like a Poisson regression, not models intended for perfectly continuous data.