There are four measurement scales (or types of data): nominal, ordinal, interval and ratio. These are simply ways to categorize different types of variables. This topic is usually discussed in the context of academic teaching and less often in the “real world.” If you are brushing up on this concept for a statistics test, thank a psychologist researcher named Stanley Stevens for coming up with these terms. These four measurement scales (nominal, ordinal, interval, and ratio) are best understood with example, as you’ll see below.

**Nominal**

Let’s start with the easiest one to understand. Nominal scales are used for labeling variables, without any quantitative value. “Nominal” scales could simply be called “labels.” Here are some examples, below. Notice that all of these scales are mutually exclusive (no overlap) and none of them have any numerical significance. A good way to remember all of this is that “nominal” sounds a lot like “name” and nominal scales are kind of like “names” or labels.

*Note*: a sub-type of nominal scale with only two categories (e.g. male/female) is called “**dichotomous**.” If you are a student, you can use that to impress your teacher.

Continue reading about types of data and measurement scales: nominal, ordinal, interval, and ratio…

**Ordinal
**With ordinal scales, it is the order of the values is what’s important and significant, but the differences between each one is not really known. Take a look at the example below. In each case, we know that a #4 is better than a #3 or #2, but we don’t know–and cannot quantify–how

*much*better it is. For example, is the difference between “OK” and “Unhappy” the same as the difference between “Very Happy” and “Happy?” We can’t say.

Ordinal scales are typically measures of non-numeric concepts like satisfaction, happiness, discomfort, etc.

“Ordinal” is easy to remember because is sounds like “order” and that’s the key to remember with “ordinal scales”–it is the *order* that matters, but that’s all you really get from these.

*Advanced note*: The best way to determine *central tendency* on a set of ordinal data is to use the mode or median; the mean cannot be defined from an ordinal set.

**Interval
**Interval scales are numeric scales in which we know not only the order, but also the exact differences between the values. The classic example of an interval scale is Celsius temperature because the difference between each value is the same. For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees. Time is another good example of an interval scale in which the increments are known, consistent, and measurable.

Interval scales are nice because the realm of statistical analysis on these data sets opens up. For example, *central tendency* can be measured by mode, median, or mean; standard deviation can also be calculated.

Like the others, you can remember the key points of an “interval scale” pretty easily. “Interval” itself means “space in between,” which is the important thing to remember–interval scales not only tell us about order, but also about the value between each item.

Here’s the problem with interval scales: they don’t have a “true zero.” For example, there is no such thing as “no temperature.” Without a true zero, it is impossible to compute ratios. With interval data, we can add and subtract, but cannot multiply or divide. Confused? Ok, consider this: 10 degrees + 10 degrees = 20 degrees. No problem there. 20 degrees is not twice as hot as 10 degrees, however, because there is no such thing as “no temperature” when it comes to the Celsius scale. I hope that makes sense. Bottom line, interval scales are great, but we cannot calculate ratios, which brings us to our last measurement scale…

**Ratio**

Ratio scales are the ultimate nirvana when it comes to measurement scales because they tell us about the order, they tell us the exact value between units, AND they also have an absolute zero–which allows for a wide range of both descriptive and inferential statistics to be applied. At the risk of repeating myself, everything above about interval data applies to ratio scales + ratio scales have a clear definition of zero. Good examples of ratio variables include height and weight.

Ratio scales provide a wealth of possibilities when it comes to statistical analysis. These variables can be meaningfully added, subtracted, multiplied, divided (ratios). Central tendency can be measured by mode, median, or mean; measures of dispersion, such as standard deviation and coefficient of variation can also be calculated from ratio scales.

**Summary**

**nominal**variables are used to “

*name*,” or label a series of values.

**Ordinal**scales provide good information about the

*order*of choices, such as in a customer satisfaction survey.

**Interval**scales give us the order of values + the ability to quantify

*the difference between each one*. Finally,

**Ratio**scales give us the ultimate–order, interval values, plus the

*ability to calculate ratios*since a “true zero” can be defined.

That’s it! I hope this explanation is clear and that you know understand the four types of data measurement scales: nominal, ordinal, interval, and ratio!

Time is in fact a ratio scale.

20 seconds is twice as long as 10 seconds. You can multiply and divide time. The absolute 0 doesn\’t have to be attainable for the scale to be ratio. To borrow from your example: there is no such thing as \”no height\”, yet you\’ve classified height as ratio.

Thanks for the excellent comment, LJ. I have edited the article based on your comment. Time is a tricky one. This article from UC Davis explains how time, depending on how it is presented, can be categorized as any of these types of scales. http://psychology.ucdavis.edu/sommerb/sommerdemo/scaling/levels.htm

Thanks for this informative text. Now I became clearer between these four terms.

Thanks for that brilliantly written info. Really helped clear all of my confusion regarding scales, especially the difference between interval and ratio. Thanks again.

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Thank you so so much. Im doing a BA in Psychotherapy and one of our modules is Psychology so we only touch on it in one class so Im not au fait at all. You have explained to me in 10 minutes what I could not understand from our lecturer in a 2 hour long lecture. Feel more confident about the exam for this module next Monday!

Thanks so much,since now i understand those scales especial to differentiate them.

Very formative article, thanks to author for such a great job!

Brilliant article though, however I had one doubt regarding oil prices in exact USD figure over a monthly period. On which scale should these values lie. Appreciate your inputs.

That would be a ratio scale. $0 is a meaningful number, and the intervals between values are equal (i.e. the difference between $1 and $2 is the same as the difference between $99 and $100). A clear indication of this fact is that you can easily multiply and divide monetary values. E.g. 1 barrel of oil costs $100, then 2 barrels will cost 2X as much, or $200.

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Celsius is not really a good example for a true zero, as people experience 0 degrees Celsius quite often. A better example would be 0 degrees Kelvin. Semantics, I know, but it\’s easier to understand if phrased in K.

Great explanations otherwise.

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This explanations kinda help. I wish can get more verbal explanations.

Your explanations were very explicit and illustrative. My knowledge has greatly improved on the 4 levels of measurements

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Thanks … It helped me a lot to understand the measurement scales.

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quiz of basic statistics

are the following nominal, ordinal, interval, or ratio data??,Explain your answers

1)Temperature measuring on a kelvin scale.

2)military ranks

3)HIV/AIDS status

4)Coli form bacteria counts in drinking water supplies

I am doing a make up research in clinic no show rates. Taking the amount of patients scheduled on a given day, and the amount of patients that actually show. What type is this?

This article has helped me understand what I am studying, different types of vocational testing. I needed to understand the basic concept. Very helpful. Thank you

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it was more informative to me and ur way of examples in each types scale was outstanding and easily to understabke thank you so much……..

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Being a Quality Engineer. Its very important to know all the scales. This article was very informative..

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I think 0 is the same as 24 so we can\’t count time as ratio data even on the 24 hour clock unless you remove 24 from the data set and end at 23.

Thank you so much sir and ma\’am, this serves as my nirvana about scale of measurement. 🙂

So, Nominal & ordinal are qualitative and interval & ratio are quantitative variable. These are scale of data measurement. But ordinal can be both qualitative and quantitative. Can it?

thanks this is wonderful work.#kevin, but how would you classify the teachers job groups in a staff?

Thank you for the great job. I like the bit on how to remember, nominal is like name, ordinal is like order. That was creative. Keep it up!

Brilliant article! A very QQ: why do you classify temperature as being interval. I agree there if nothing called \\”no temperature\\” , but isn\\’t 20°c twice as hot as 10°c or am I wrong? Please clarify. Also, another ex of ratio scales would be very very helpful.

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Thanks for such clear and understandable explanation

What of binary scale?

Wow! Those examples simply nailed the explanations inside my memory. Thanks a lot.

To make things clearer, pls don’t confuse ‘true zero’ to mean that zero is a valid number on a scale.for example, the height of an individual being 0cm. ‘true zero’ means there are no negative values for the scale being considered, as in the height of a person being -100cm which is invalid. The Celsius scale is said to have ‘no true value’ because negative values are actually valid for the Celsius temperature scale. For instance , the temperature of ice could be -4 degrees Celsius. So weight and height have a true zero.

The ‘no true value’ should be ‘no true zero’ , sorry

Good clarification. thanks!

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simplify and brief

what about these? Is the following nominal, ordinal, interval, or ratio scale?

A score of 90 out of a 100 on a test

A salary of $32.000

Ratio

thanks for such a clear explanation

You cannot multiply or divide with scores or $ eg $32 x $32, 90% / 70% – no mathematical or statistical meaning on these. Hence the example should be Interval.

Quantity of sand minned daily e.g 1-5, 6-10 trucks per day. What measurement scale is that? How can it be analyzed?

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Brilliant explanation of an otherwise mixed up knowledge of measurement scales in some textbooks. Thanks a Lot.

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Thank you very much. Very helpful to clear my mind on measurement scales.

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i would also like to know in situations where interval or ordinal data is taken as nominal data.

thanks for providing such a information about better understanding of scales for measurement.

its really helpful and clear out the confusions between these scales.

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BC Canada

5. Researchers at Princess Margaret Hospital measure patients’ pain using the Pain Survey where 0 = no pain and 10 = excruciating pain. What level of measurement is their survey? What measure of central tendency (mean, median, mode) can they report?

Can anyone help me with this question here, i\\’m a bit stuck

Ordinal. The best way to determine central tendency on a set of ordinal data is to use the mode or median; the mean cannot be defined from an ordinal set.

The best explanation I ever had. You are super! I wish you could be my statistic professor.

This was exactly what I needed to read. This was simple and clearly differentiated the terms quite nicely. I’m ready for my text today.

Thank you very much, I got more detail about measurment scale . I am preparing Master in Development Studies

For the question, \\\”How many courses have you taken in this year?\\\” is nominal or ratio scale?

Sounds like a ratio scale to me. Absolute zero, known order and values.

I am research scholar,i need standred scale for labour welfare measures.

Hi

I am conducting a study with four variables and in one of them, the scores are as decimals (e.g. 4.3, 5, 3.2…\”) all four variables were measured with Likert scale questionnaires, would the data still be ordinal?

Good article. On nominal/categorical data, I think you can calculate/determine the mode. Mode is the most common value in a dataset e.g. In an experiment, note what colour of shoes each participant is wearing on a particular day. Results Yellow = 5, Blue = 13 Read = 7, black = 27. Hence the mode is black since its the most occurring colour of shoes. Therefore amend the table such that you have a row for Mode, and another one for Median. Then have a tick under Ordinal, see below:

Provide Nominal Ordinal Interval Ratio

Mode Yes Yes Yes Yes

Median Yes Yes Yes

Good comment and point. I agree and will update the table. Thanks!

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