Scales of Measurement: Nominal, Ordinal, Interval & Ratio

Variables

Imagine that you are a psychologist, and you want to do a study to see whether eating breakfast will help kids focus. You think that the students who eat a healthy breakfast will do best on a math quiz, students who eat an unhealthy breakfast will perform in the middle and students who do not eat anything for breakfast will do the worst on a math quiz.

So, how do you do your study? Where do you even begin?

In research, one of the first things that you have to do is identify your variables, or factors that can change. For example, whether a person eats breakfast or not is a variable - it varies from person to person and perhaps from day to day. A person can eat a healthy breakfast, eat an unhealthy breakfast or not eat breakfast at all. If eating breakfast did not vary, every single person would eat the exact same thing for breakfast every single morning.

Likewise, performance on a math test is a variable because it varies from person to person. Susie might do great on a math quiz, while Jonas fails it. Or, Susie might do well today but not as well tomorrow. Whatever the reason, scores on a math quiz change, and therefore, they are variables.

So, we know that our variables are eating breakfast and math performance. But, how do we measure them? There are four major scales (or types) of measurement of variables: nominal, ordinal, interval and ratio. The scale of measurement depends on the variable itself. Let's look closer at each of the four scales and what types of variables fall into each category.

Nominal

You might have noticed a difference in our two variables. While scores on a math test are reported as numbers, eating breakfast isn't numeric. A person eats a healthy breakfast, an unhealthy breakfast or no breakfast at all. These are not numbers but categories.

A nominal scale of measurement deals with variables that are non-numeric or where the numbers have no value. In other words, we can put them in any order and it wouldn't matter. Think about the numbers on the jerseys of football players. Is the player wearing number 1 a better player than the player wearing number 82? Maybe, but that doesn't have anything to do with the numbers they wear.

Jersey numbers have no value as far as telling us anything about the ability of the players; it's just a way to identify them. Other examples of variables measured on a nominal scale include gender, race and the number on pool balls.

Sometimes for statistical analysis, a researcher will give non-numeric variables numeric values. For example, we might say that students who eat a healthy breakfast are -1, the students who eat an unhealthy breakfast are 0, and the students who do not eat breakfast are +1. These numbers are just a way to mark who is in which group but don't really have value.

Ordinal

Let's say that, instead of looking at grades on a specific math quiz, we want to look at the letter grades overall for the course for each student. So, Susie has an A, and Jonas has a D, and there are other students with Bs and Cs and Fs. In this case, the letters are not completely meaningless. Unlike football player jerseys, for example, we know that Susie is doing better than Jonas. But, how much better?

An ordinal scale of measurement looks at variables where the order matters but the differences do not matter. When you think of 'ordinal,' think of the word 'order.' In the case of letter grades, we don't really know how much better an A is than a D. We know that A is better than B, which is better than C, and so on. But, is A four times better than D? Is it two times better? In this case, the order is important but not the differences.

Have you ever filled out one of those customer service surveys that companies send out? They might ask a question like, 'How was your experience today?' and ask you to rate it on a scale of 1-10. Those, too, are ordinal. Other examples of variables measured on an ordinal scale include difficulty (hard, medium, easy) and the order of finishing a race (first place, second place, and so on).