surveys | February 13, 2020

# Levels of Measurement: Nominal, Ordinal, Interval, and Ratio Scales Daniel Ndukwu

When you’re collecting qualitative and quantitative data through different types of surveys and research instruments 4 data measurement scales are often used. They’re referred to as nominal, ordinal, interval, and ratio scales.

Each of the measurement scales builds on the other. Scaled questions, no matter what they are, derive from these four measurement scales. For example, a Likert scale is a type of ordinal scale used to measure sentiment (and at times frequency).

The classifications are important because they determine the type of statistical analysis you can do with the survey data you collect. In this article, you’ll get an in-depth rundown of the different types of scales, how they can be used, and when to use them in your research.

### What are the nominal, ordinal, interval, ratio scales really?

Nominal, ordinal, interval, and ratio scales can be defined as the 4 measurement scales used to capture and analyze data from surveys, questionnaires, and similar research instruments. All of the scales use multiple-choice questions.

Psychologist Stanley Smith Stevens created these 4 levels of measurement in 1946 and they’re still the most popular. Here’s a quick table showing you the kind of calculations each one can be used for.

Calculation

Nominal

Ordinal

Interval

Ratio

Frequency distribution

Yes

Yes

Yes

Yes

Mode

Yes

Yes

Yes

Yes

Median

No

Yes

Yes

Yes

No

No

Yes

Yes

Mean, standard deviation

No

No

Yes

Yes

Multiplication and division

No

No

No

Yes

Ratios, coefficient of variation

No

No

No

Yes

Geometric mean

No

No

No

Yes

Let’s look at each one in turn.

## Nominal scale

Nominal scales (also known as a categorical variable scale) refer to variables, categories, or options that don’t have a regular order or ranking that has universal application. For example, male and female are both categories but neither one can be ranked as number one or two in every situation.

In research, nominal data can be given a numerical value but those values don’t hold true significance. If you use the assigned numerical value to calculate other figures like mean, median, etc. it would be meaningless.

Imagine using a nominal scale and giving male a value of 2, female a value of 4, and transgender a value of 6. If you were to calculate the mean, median, mode, etc. using those values it would have no real implication.

A simple way to think about nominal data is to consider them labels for the information you want to collect. Each label is exclusive, doesn’t have any overlap, and lacks numerical significance on their own.

### Example of nominal scales

What phone brands have you used in the past?

• Samsung
• Apple
• Nokia
• Blackberry
• HTC

• Male
• Female
• Transgender
• Non-Binary
• Prefer not to say

What is your highest level of education?

• Some high school
• High school
• Associates degree
• Bachelor’s degree
• Master’s degree
• Ph.D. degree

In the nominal scale examples above, only the names of options (the nominal variables) hold any significance to the researcher. For the survey question presented, it wouldn’t matter if Samsung, Apple, or Nokia were first or last on the scale. What matters is the number of respondents that select each option.

Nominal scales can, to an extent, overlap with ordinal scales because a few of them have order. For example, very short, short, tall, very tall could be considered a nominal scale with an order.

Nominal data can be collected with an open-ended or multiple choice question but the open-ended approach is frowned upon. The latter option is more common and arguably more accurate. Though they appear simple, nominal data is the foundation of quantitative research and is among the most used measurement scale.

## Ordinal scale

The ordinal scale is the second level of data measurement and encompasses the nominal scale. With an ordinal scale, the order of the values (ordinal variable) is important but the difference between values is inconsequential.

That’s because, due to the nature of the options presented on the scale, there’s often no way of knowing the degree of difference between them. Even when the difference between options is quantifiable, it doesn’t yield much insight when compared to the order of the values.

For example, an ordinal scale around income may have the options:

• Less than 25,000
• 25,000 – 50,000
• 50,000 – 100,000
• Above 100,000

The difference between “25,000 – 50,000” and “50,000 – 100,000” is quantifiable but not uniform. A direct comparison isn’t as valuable as the order of the values.  Let’s look at an example where the difference between values isn’t quantifiable.

• Very good
• Good
• Average
• Poor
• Very poor

In the above example, there’s a clear difference between good and very good but how would you measure that? Is there an objective way to say that very good is x units better than good? No, there isn’t.

These scales are used to understand and quantify categories that don’t have a mathematical aspect such as frequency, happiness, satisfaction, degree of feeling, etc. It’s easy to remember because ordinal sounds like order and the ordinal data gains its significance from the order of the items being measured.

Both ordinal scales and nominal scales have descriptive qualities. The key difference is the fact that there’s a relative position of labels. Even though we can’t quantify the difference between ordinal variables, we know one is higher or better than the other.

Keep in mind that ordinal data sets don’t have an origin of scale so we can’t, with certainty, say where the scale truly starts or ends.

### Ordinal scale examples

How was your recent customer service experience?

• Very good
• Good
• neutral
• Poor
• Very poor

How often do you go to the gym?

• Very often
• Often
• Regularly
• Seldom
• Very seldom

Ordinal data is represented and analyzed in a number of ways. The most popular of which are graphs that break down the percentage of answers options selected. Additionally, these graphs can show the absolute number of respondents.

Note: central tendency can be calculated for ordinal scales and they’re susceptible to central tendency bias.

### Nominal scale vs ordinal scale

To recap, nominal scales only take into consideration the label of the options while ignoring order. Ordinal scales take the label of the options into consideration as well as the order of those options. Both scales ignore the value of variables.

Because of this, ordinal scales have more applications than a nominal scale. Nominal scales can have as few as two options (dichotomous question) and can also work as a demographic question (what is your gender). Ordinal scales usually have more than two options to establish order.

## Interval scale

It’s a numerical scale in which the order is known and the difference between the values has meaning. The interval scale is the third level of measurement and encompasses both nominal and ordinal scales. This scale can also be referred to as an interval variable scale (interval variable is used to describe the meaningful nature of the difference between values).

Examples of this would be time, temperature (Celsius, Fahrenheit), credit score, and more. In each of these examples, the difference in value is known and easily calculated. Someone with a credit score of 720 has a higher score than someone with 650.  We know one is greater than the other and we know EXACTLY how much larger the value is.

Note: There’s a difference between time and duration. Time is an interval scale because there’s no meaningful zero. Can you say when time started? Duration is a ratio scale because there’s a meaningful zero and a starting point can be defined. 5 days is twice as long as 10 days.

This is the first scale where you can do true statistical analysis. Like the ordinal scale, the interval scale doesn’t have a starting point that’s already been decided or true zero. For example, credit score is an interval scale but it starts at 300.

With that being said, every point on the scale is equidistant from the next.

• On a Celsius scale, each unit is the same size or has the same value. We can, without a doubt, quantify the difference between 5 Celsius and 6 Celsius.
• There is no true zero because temperature can go into the negatives. Zero is just another point of measurement.

### Example of an interval scale

How likely are you to recommend us to a friend or colleague?

• 1 (very unlikely)
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10 (very likely)

The major challenge with interval data is that there’s no true zero so deeper statistical analysis is impossible. This is where the ratio scale comes into play.

## Ratio scale

Ratio scales are the cream of the crop when it comes to statistical analysis because they have everything you need. A ratio scale has an order, a set value between units, and absolute zero. It’s an interval scale with a true zero.

Examples of ratio scales include concentration, length, weight, duration, and more. Because there’s a zero position, it opens up the doors for inferential and descriptive analysis techniques. Use ratio scales to understand the size of the market, market share, revenue, pricing, etc.

You can only find mode with nominal scales, you can find median with ordinal scales, interval scales lend themselves to mean, mode, and median. Ratio scales can use all of that plus other methods such as geometric mean and coefficient of variation. Arguably, ratio data is the most versatile.

Note: The proportion between two units of a ratio scale is meaningful. On an interval scale, they’re not. For example, 20 pounds is twice the weight of 10 pounds. A credit score of 600 is not twice as good as a credit score of 300 because it’s not a ratio.

### Example of ratio scale question

What is your weight in pounds?

• Less than 70
• 70 – 120
• 121 – 150
• More than 150

• Less than 20
• 20 – 30
• 31 – 40
• 41 – 50
• More than 50

### Interval scale vs ratio scale

These two scales are closely related and it sometimes causes confusion. There are two things that stand out as differences with interval variable scale and ratio variable scale.

1. The interval variable has order and the difference between the variables have meaning but the ratio between them doesn’t have meaning. For example, if you increase the temperature from 10 to 20 degrees Celsius, it’s not twice as hot. With a ratio variable scale, the difference between the variables has meaning and the ratio between them does as well. For example, if you increase height from 10 meters to 20 meters, it’s twice as tall.
2. The second difference between the two scales is that the ratio scale has a true zero. That means if something is zero, it doesn’t exist. If you weigh zero then your weight doesn’t exist. Interval scale may have zero but it’s not absolute. For example, the temperature can go into the negatives and zero is just another measurement on the scale.

## Conclusion

Knowing the type of statistical scale to use in specific situations can help you unlock better data and run a more efficient survey analysis.

To recap, nominal scales have labels, the value and order of options don’t matter. Ordinal scales have labels, the order matters, but the value doesn’t. Interval scales have labels, the order matters, and the values matter but there’s no zero. Ratio scales have labels, the order matters, the value is quantifiable, and there’s a zero which equals nothingness.

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