# Nominal, ordinal, interval and ratio data: How to Remember the differences

Quantitative researchers measure variables

to answer their research question. The level of measurement that is used to measure

a variable has a significant impact on the type of tests researchers can do with their

data and therefore the conclusions they can come to. The higher the level of measurement

the more statistical tests that can be run with the data. That is why it is best to use

the highest level of measurement possible when collecting information.

In this video nominal, ordinal, interval and ratio levels of data will be described in

order from the lowest level to the highest level of measurement. By the end of this video

you should be able to identify the level of measurement being used in a study. You will

also be familiar with types of tests that can be done with each level.

To remember these levels of measurement in order use the acronym NOIR or noir.

The level of measurement of a variable depends on the nature of that variable as well as

how the researcher collects the data. For example, some variables like gender can only

be measured in a nominal way. Other variables like household income can be measured at multiple

levels depending on how the question is asked. The nominal level of measurement is the lowest

level. Variables in a study are placed into mutually exclusive categories. Each category

has a criteria that a variable either has or does not have. There is no natural order

to these categories. The categories may be assigned numbers but

the numbers have no meaning because they are simply labels. For example, if we categorize

people by hair color people with brown hair do not have more or less of this characteristic

than those with blonde hair. Nominal sounds like name so it is easy to

remember that at a nominal level you are simply naming categories.

Nominal data may be considered dichotomous or categorical. Dichotomous data falls into

one of two categories like Male/female or yes/no. Categorical data have more than two

possible values such as marital status or group membership.

Sometimes researchers refer to nominal data as categorical or qualitative because it is

not numerical. Since nominal data is simply categorical it

allows for the fewest statistical tests. It makes sense to report the number or percentage

of people who are male or female in a particular group. This data is often presented in bar

or pie charts. The only measure of central tendency that makes sense with nominal data

is the mode. Many other statistical tests just do not make sense for nominal data.

For example, since there is no natural way to order nominal data you cannot find a median

or middle number. Likewise, you cannot calculate a mean gender since no numerical value for

the data exists. Ordinal data is also considered categorical.

The difference between nominal and ordinal data is that the categories have a natural

order to them. You can remember that because ordinal sounds like order.

Numbers are assigned to categories but they are arbitrary — They are simply used to establish

a ranking and there is no absolute zero. While there is an order, it is also unknown

how much distance is between each category. The intervals between each number are therefore

not necessarily equal. Ordinal scales are often used to measure attitudes

and perceptions. For example, a survey may ask how satisfied a customer is on a scale

from very dissatisfied to very satisfied. Nurses often use an ordinal scale to get patients

to rank their pain on a scale from 1 to 10. This data is ordinal since it is unknown whether

the intervals between each value are equal. On a 10 point scale, the difference between

a 9 and a 10 is not necessarily perceived to be the same as the difference between a

3 and a 4. All we know is that if the patient rates their pain as an 8 now and a 4 after

receiving pain medication the pain has decreased. We cannot accurately measure how much the

pain has decreased since we do not know the difference between the points on the scale.

It would be inaccurate to claim that the patient was in twice as much pain before receiving

the medication. Likewise you cannot say that one patient is in twice as much pain as another

using this scale. Remember that the values in an ordinal scale

simply express an order. All nominal level tests can be run on ordinal

data. Since there is an order to the categories

the numbers assigned to each category can be compared in limited ways beyond nominal

level tests. It is possible to say that members of one category have more of something than

the members of a lower ranked category. However, you do not know how much more of that thing

they have because the difference cannot be measured.

To determine central tendency the categories can be placed in order and a median can now

be calculated in addition to the mode. Since the distance between each category cannot

be measured the types of statistical tests that can be used on this data are still quite

limited. For example, the mean or average of ordinal data cannot be calculated because

the difference between values on the scale is not known.

Interval level data is ordered like ordinal data but the intervals between each value

are known and equal. Therefore, the difference between two values is meaningful for interval

variables. The zero point is arbitrary since a score of zero does not actually mean that

the variable does not exist. Zero simply represents an additional point of measurement.

For example, tests in school are interval level measurements of student knowledge. If

you scored a zero on a math test it does not mean you have no knowledge. Yet, the difference

between a 79 and 80 on the test is measurable and equal to the difference between an 80

and an 81. Temperature if measured in degrees Fahrenheit

or Celsius is another good example of interval measurement. On the Fahrenheit scale the difference

between a temperature of 37 degrees and 38 degrees is the same difference as between

89 degrees and 90 degrees. The 0 is arbitrary since a temperature of 0 degrees does not

mean that there is no temperature. With interval level scales there is direct,

measurable quantity. In addition, zero does not represent the absolute lowest value. Instead,

it is point on the scale with numbers both above and below it.

If you know that the word interval means space in between it makes remembering what makes

this level of measurement different easy. Interval scales not only tell us about order,

but also about the value between items on a scale.

Since the distance between points on the scale is measurable and equally split it is possible

to do more statistical tests with the data. The mean, median and mode can all be calculated

with interval data. The standard deviation can also now be calculated.

However, the problem with performing statistical tests on interval scales is that they don’t

have a “true zero.” Therefore it is impossible to multiply, divide or calculate ratios.

Ratio measurement is the highest level possible for data. Like interval data, Ratio data is

ordered, with known and measurable intervals between each value. What differentiates it

from interval level data is that the zero is absolute. The zero occurs naturally and

signifies the absence of the characteristic being measured. Remember that Ratio ends in

an o therefore there is a zero. Typically this level of measurement is only

possible with physical measurements like height, weight and length.

Any statistical tests can be used with ratio level data as long as it fits with the study

question and design. It is possible to compare amounts of the variable and make a claim that

one is twice as much as the other. Remember that when working with ratio variables, but

not interval variables, you can look at the ratio of two measurements.

Remembering the basic differences can help you remember the levels of measurement. Nominal

is named. Ordinal is ordered. Interval has a known interval or difference. Ratio has

a true zero. To decide what level of measurement a particular

variable is ask yourself these questions in order:

First, Is the variable ordered? If not, the variable is nominal.

If it is ordered, ask yourself if there are equal distances between values.

If not, the variable is ordinal. If values are equally spaced, ask yourself

If a value of zero actually means that the variable being measured does not exist.

If not, the variable is interval. If zero does mean none, the variable is ratio

because the zero is absolute. The level of measurement dictates the appropriate

statistical tests that can be used. One of the reasons for learning about levels of measurement

is so you know what statistical tests can be performed on different types of data. That

way you can avoid making mistakes in your own work and critique the work of others.

Be aware that Some people gather ordinal level data and treat it like interval data once

numbers are assigned to it. Researchers need to be careful not to make interval and ratio

claims about ordinal data. Be careful not to claim that something is twice as much as

something else if the data were not collected at the appropriate level.

Classifications of some forms of data are debated. For example, some researchers treat

the measurement of intelligence as ordinal while others treat it as interval. Likewise,

money in a bank account may be considered ratio since having a balance of 0 means you

don’t have any money. However, others argue it is interval since it is possible to have

a negative balance, which makes the 0 point simply another point of measurement. So, what

level do you think it is? Can you think of any other controversial examples? Comment

below to start a discussion. What is important to know when reviewing an

article is how the data was collected so you can identify if the appropriate statistical

tests were used to analyze the data. If you are doing research try to collect data in

the highest form possible so a wider variety of tests can be preformed on it. Sometimes

how you ask the question will determine what level your data is at. Knowing the level of

measurement for your data will help you avoid mistakes like taking the average of people’s

marital status. To help you remember what you need to know

about the levels of measurement try making a simple study table to include in your notes.

It is helpful to include an example in the chart that will help you remember each level.

For more you can check out some of my related videos or website. You are also welcome to

subscribe for regular updates. If there is something specific you are looking for or

would like created please comment and let me know. Thank you for watching.

Thank you for the video. It clarified some important information for me.

A list of the number of traffic accidents that occur every year. What measure would that be? Nominal?

thank you

Hi! My student and I are wondering if the income class of the population is ordinal or ratio? There is a range in the choices like 1000-5000,6000-10000. you're video is a great help for us in the school here in the Philippines. thank you!

First rate (interval, right?) explanation, thank you!

thank you very much……very helpful and quite easy to understand. keep it up

Nice and simple explanation.

your lovely, this i far better then what i am getting at uni. I totely understand now. i have dyslexia and my uni doesn't accommodate for my course as it is distance learning.

Thx !

Thank you,

This is the best summary of scales of measurement I have ever come across well DONE your clear succinct presentation style and logical flow is formula perfect! ………….truely a work of Art! thx so much for posting!

i loved your explanation. thanks !

You explained this so well. I will be able to do wonderfully on a quiz.

thanks so much, I finally understood these terms, having dyspraxia makes studying stats without an easy to follow description really hard, thanks again, I look forward to checking out your other videos

awesome video thank you so much!

– a confused stats student

thanks for such a good learning video

Hie this was helpful in preparing for my exams

Hi, very nice and valuable video I would like to ask which statistical software you recommend for medical research.

Thanks

Abdulhadi Alrubaie

Surgeon

How is time an example of ratio data?

Thanks for simplifying the concept to make understand

thank you, i will recommended to my friends this video. good luck

thank you for posting

Can anyone answer this..?? Help me pls..1) social security system numbers

2) the number of LRT passengers from recto to santolan..

3) courses offered in university belt..

4) intelligent quotient of employees

5) political affiliations of politician's in the Philippines

6) time required for engineers to do a certain projects…

Help me pls to answer this… where is ordinal, nominal , ratio or interval

Thanks a million, simple explanation

Excellent presentation

really helpful 🙂

how can you have zero weight? if zero isn't arbitrary and ratios can have zero, how does weight and height factor into that? How can you have zero height or weight?

This is very informative. I love the way you summarize the concepts in the scale of measurements

Could you explain why it is best to collect data at the highest level of measurement?

Excellent, very well explained, Thankyou

Good

pls, madam what type variables are these? 1.Date of diagnosis 2.Town of residence

3.age(years) 4. Highest alanine transferase. your lectures are wonderful

Very thoroughly explained!! Thanks a lot!

So is it safe to say that the zero in interval actually represents a baseline (starting point) in the data? It's what it sounds like to me, but if I'm wrong, please let me know.

you are waaaay better than my stat teachers!

This is exactly what i was looking for. Thank you for your help.

Thank you for the video, it was really helpful!! But, I can't fully understand what is interval variables and ratio variables. I'm sorry, but can you please explain these two in a much simpler way.

So easily explained! Glad I found your channel

thumb up if nathan sent you

Thank you this helped a lot

Looking for scale evaluation

Thanks for your explanation. It helped me.

Thank you so much for posting this video. It easy to understand and the visual charts simple and extremely helpful! Thnx

@nursekillam I am working on an assignment, watched this video and few others and i still dont know what measurement scale is used when describing happiness, openness, extraversion, etc. ORDINAL? help. please and thank you

I suck at remembering things, and for my "Data-driven Design and Development" course for my MSc in IT, I had to memorize these. You helped a lot! You're not just helping nurses here 🙂

For drug testing, the minimum inhibition concentration increase by 2 times to test the growth or not growth of bacterium. Is the MIC ordinal or ratio?

Thank you very much for such a nice explanation of data types and their levels.

Thank you for this. I was looking for a review on this topic for my Psychology Quantitative Research Methods students when I have to be away from class. This fits the bill very well!

One note: In personality psychology and many areas of social and behavioral sciences, we treat Likert-scaled data as interval data, but with the caveat that scales are made up of multiple items, not just one like the pain scale and that data are checked for normality. Some researchers have done comparisons by running the data both ways and have not found any meaningful differences.

Awesome

+NurseKillam bravo, beautifully done! your video makes so much more sense than the other sources i've looked at. so thank you for a job well done!

In a week, I am giving a 15 minute speech about the statistics in Nursing. Would this be a valuable video to play for my audience?

Thank you NurseKillam, very helpful video for review. Good job.

is very helpful.10q

wow OMG so interesting 10q

Thank you, this is very helpful

OMG! You teach better than my stats prof! Thank you veryyyy much! This is a great video!

Wish you could make videos for all the StatsA01

Great! Thank you.

so much more clearer than my statistics professor

Thank you for teaching!

Does this mean that yelp scores and other average ratings like on google maps are bologna?

This video, actually – all of your videos, are extremely helpful and accessible. Thank you so much for making them!

i dont get this at all…

Thanks for this! It really helped

Thank you for your video. It has helped me more than my college professor.

PSYC 311 ITS LIT

Please tell me more, modal percentage,range and frequency distribution are possible measures to nominal scale,,, I think only counting is possible measures

Please clarify my doubt

Thank you, so helpful.

Thx a lot

Veryyy helpfulllllllll

I am from pakistan,you are wonderful but improve your english speaking style so international people could understand it easity

Brilliant delivery of this information, it was a pleasure to watch it and learn these concepts in such a straightforward explanation, Thank you

Thank you for doing this video! It helped so much.

very helpfull. Thank you

There are 10 avatars of lord Vishnu in Hinduism which is believed to have occurred at various points in time. Is it nominal or ordinal ?

hot blonde at 4:09

Beautiful! That was brilliantly explained! Very clear, very crisp!

I am wondering why pain scale considered as an interval data and not a ratio since zero in pain scale means there is no pain at all?

Thank you for the knowledge sharing. It is extremely helpful.

thank you!! it help a lot.

Wow. Amazing explanation and nice video. Thanks a lot. Love.

This is so helpful thank you!!!!!!!

Very easy and clearly presented,

Thanks sooooo much. I love the chart at the end. Excellent.

HOw do you know when to add or subtract or divide

thanks so much, I still have a question about discrete and continuous variables?

Thank you!! I got a 100% on my behavioral stats test because on you!!

Informative, just wish you’d slow down a little when you talk.

Thank you very well done.

Thank you for explaining this in a simple way.

Thank you! This is very helpful!

Really Helpful!

Thank you! Way better than the stat book I have. I Like the NOIR acronym and all the examples you gave. Thank you!!!!

Yay! This is a great explanation and definitely helped me understand the concepts better! How would you explain moderating and mediating variables?

love you

brilliant

do you have any video explaining z scores, t scores and standard deviation

Such a beautiful and soothing voice, lmao I almost slept watching it. Thanks a million

so helpful

Very well explained with good examples

Can you help me with my exam