what is nominal variable in research

Statistics Made Easy

Levels of Measurement: Nominal, Ordinal, Interval and Ratio

In statistics, we use data to answer interesting questions. But not all data is created equal. There are actually four different  data measurement scales that are used to categorize different types of data:

3. Interval

In this post, we define each measurement scale and provide examples of variables that can be used with each scale.

The simplest measurement scale we can use to label variables is a  nominal scale .

Nominal scale: A scale used to label variables that have no quantitative values.

Some examples of variables that can be measured on a nominal scale include:

• Gender:  Male, female
• Eye color:  Blue, green, brown
• Hair color:  Blonde, black, brown, grey, other
• Blood type: O-, O+, A-, A+, B-, B+, AB-, AB+
• Political Preference:  Republican, Democrat, Independent
• Place you live:  City, suburbs, rural

Variables that can be measured on a nominal scale have the following properties:

• They have no natural order. For example, we can’t arrange eye colors in order of worst to best or lowest to highest.
• Categories are mutually exclusive. For example, an individual can’t have  both  blue and brown eyes. Similarly, an individual can’t live  both  in the city and in a rural area.
• The only number we can calculate for these variables are  counts . For example, we can count how many individuals have blonde hair, how many have black hair, how many have brown hair, etc.
• The only measure of central tendency we can calculate for these variables is the mode . The mode tells us which category had the most counts. For example, we could find which eye color occurred most frequently.

The most common way that nominal scale data is collected is through a survey. For example, a researcher might survey 100 people and ask each of them what type of place they live in.

Question: What type of area do you live in?

Possible Answers: City, Suburbs, Rural.

Using this data, the researcher can find out how many people live in each area, as well as which area is the most common to live in.

The next type of measurement scale that we can use to label variables is an  ordinal  scale .

Ordinal scale: A scale used to label variables that have a natural  order , but no quantifiable difference between values.

Some examples of variables that can be measured on an ordinal scale include:

• Satisfaction: Very unsatisfied, unsatisfied, neutral, satisfied, very satisfied
• Socioeconomic status:  Low income, medium income, high income
• Workplace status: Entry Analyst, Analyst I, Analyst II, Lead Analyst
• Degree of pain:  Small amount of pain, medium amount of pain, high amount of pain

Variables that can be measured on an ordinal scale have the following properties:

• They have a natural order. For example, “very satisfied” is better than “satisfied,” which is better than “neutral,” etc.
• The difference between values can’t be evaluated.  For example, we can’t exactly say that the difference between “very satisfied and “satisfied” is the same as the difference between “satisfied” and “neutral.”
• The two measures of central tendency we can calculate for these variables are  the mode  and  the median . The mode tells us which category had the most counts and the median tells us the “middle” value.

Ordinal scale data is often collected by companies through surveys who are looking for feedback about their product or service. For example, a grocery store might survey 100 recent customers and ask them about their overall experience.

Question: How satisfied were you with your most recent visit to our store?

Possible Answers: Very unsatisfied, unsatisfied, neutral, satisfied, very satisfied.

Using this data, the grocery store can analyze the total number of responses for each category, identify which response was most common, and identify the median response.

The next type of measurement scale that we can use to label variables is an  interval  scale .

Interval scale:  A scale used to label variables that have a natural order and a quantifiable difference between values,  but no “true zero” value .

Some examples of variables that can be measured on an interval scale include:

• Temperature: Measured in Fahrenheit or Celsius
• Credit Scores: Measured from 300 to 850
• SAT Scores: Measured from 400 to 1,600

Variables that can be measured on an interval scale have the following properties:

• These variables have a natural order.
• We can measure the mean, median, mode, and standard deviation of these variables.
• These variables have an exact difference between values.  Recall that ordinal variables have no exact difference between variables – we don’t know if the difference between “very satisfied” and “satisfied” is the same as the difference between “satisfied” and “neutral.” For variables on an interval scale, though, we know that the difference between a credit score of 850 and 800 is the exact same as the difference between 800 and 750.
• These variables have no “true zero” value.  For example, it’s impossible to have a credit score of zero. It’s also impossible to have an SAT score of zero. And for temperatures, it’s possible to have negative values (e.g. -10° F) which means there isn’t a true zero value that values can’t go below.

The nice thing about interval scale data is that it can be analyzed in more ways than nominal or ordinal data. For example, researchers could gather data on the credit scores of residents in a certain county and calculate the following metrics:

• Median credit score (the “middle” credit score value)
• Mean credit score (the average credit score)
• Mode credit score (the credit score that occurs most often)
• Standard deviation of credit scores (a way to measure how spread out credit scores are)

The last type of measurement scale that we can use to label variables is a ratio  scale .

Ratio scale: A scale used to label variables that have a natural order, a quantifiable difference between values, and a “true zero” value.

Some examples of variables that can be measured on a ratio scale include:

• Height:  Can be measured in centimeters, inches, feet, etc. and cannot have a value below zero.
• Weight:  Can be measured in kilograms, pounds, etc. and cannot have a value below zero.
• Length:  Can be measured in centimeters, inches, feet, etc. and cannot have a value below zero.

Variables that can be measured on a ratio scale have the following properties:

• We can calculate the mean, median, mode, standard deviation, and a variety of other descriptive statistics for these variables.
• These variables have an exact difference between values.
• These variables have a “true zero” value.  For example, length, weight, and height all have a minimum value (zero) that can’t be exceeded. It’s not possible for ratio variables to take on negative values. For this reason, the ratio  between values can be calculated. For example, someone who weighs 200 lbs. can be said to weigh  two times  as much as someone who weights 100 lbs. Likewise someone who is 6 feet tall is 1.5 times taller than someone who is 4 feet tall.

Data that can be measured on a ratio scale can be analyzed in a variety of ways. For example, researchers could gather data about the height of individuals in a certain school and calculate the following metrics:

• Median height
• Mean height
• Mode height
• Standard deviation of heights
• Ratio of tallest height to smallest height

The following table provides a summary of the variables in each measurement scale:

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Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

19 Replies to “Levels of Measurement: Nominal, Ordinal, Interval and Ratio”

The summary table at the bottom, the Nominal value does not have natural order. Might be a typo

There seems to be a typo in the summary table. Nominal has no natural order.

There’s a discrepancy with the summary table and your post, i.e. Nominal data “have no natural order”

that is a great post the clarity inspires me to incorporate some ideas into my slides for students 🙂

PS. the last table contains one mistake – which is obvious if the whole post is read, i.e. the natural order should not have a plus under nominal measurement (I believe the first line was intended to be “separate categories”)

Summary, Nominal, Has a natural “order” should not be YES

There’s a mistake in the table in the end: nominal variables do not have a “natural” order, so it should be a NO.

And I have to point out that temperature *does* have a true zero (it’s around −273 °C / −460 °F), though it’s true it doesn’t matter much inmost people’s daily life.

Hi Zach, First of all thanks for all these information. Just want to add here that the table at the end, the property, “has natural order” for nominal measure should be “NO”, isn’t it ?

Hi! Thank you for these great and interesting summaries ! Now I can see a big connected picture of the statistics and found answers to all the questions. Short and deep. It seems that in “Nominal” the order is assumed to be “NO”?

Hi there, I think there is a minor typo in the last table. Under Nominal, shouldn’t ‘Has a natural “order”’ be a No instead? 🙂

In summary table, you have mentioned that Nominal has a natural order. Can you please review if that is correct?

Dear Zach , The blog was very useful and I loved reading. But in the summary for nominal data , the natural order is given as yes which is incorrect and kindly change that as NO.

Thank you. Regards, A.Hari babu

Good article. FYI Temperature does have a true 0 (-273C).

Thanks for information you provide. In the summary table there is a trivial mistake: Has a natural “order” property set True for nominal scale. It must be False

There is no natural order in “nominal” variables

Hey, I just found a little problem with your table – “Has natural order” is set as “YES” for Nominal, while it should be “NO”.

In this article last summary table,nominal scale having a natural order but it is not correct

This was the perfect clarification tool for my introduction to statistics study. It refined and clarified the main points from my textbook in an easy-to-understand manner. The way these scales were explained and then demonstrated with examples helped me to grasp the concepts I was struggling with while reading the text.

It is detail explanation. Interesting!

You are awesome! thank you

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Nominal, Ordinal, Interval & Ratio Data

Levels of measurement: explained simply (with examples).

By: Derek Jansen (MBA) | Expert Reviewed By Dr. Eunice Rautenbach | November 2020

If you’re new to the world of quantitative data analysis and statistics, you’ve most likely run into the four horsemen of levels of measurement : nominal, ordinal, interval and ratio . And if you’ve landed here, you’re probably a little confused or uncertain about them.

Don’t stress – in this post, we’ll explain nominal, ordinal, interval and ratio levels of measurement in simple terms , with loads of practical examples .

Overview: Levels of measurement

Here’s what we’ll be covering in this post. Click to skip directly to that section.

• What are levels of measurement in statistics?
• Nominal data
• Ordinal data
• Interval data
• Why does this matter?
• Recap & visual summary

Levels of Measurement 101

When you’re collecting survey data (or, really any kind of quantitative data) for your research project, you’re going to land up with two types of data –  categorical  and/or  numerical . These reflect different levels of measurement.

Categorical data  is data that reflect characteristics or categories (no big surprise there!). For example, categorical data could include variables such as gender, hair colour, ethnicity, coffee preference, etc. In other words, categorical data is essentially a way of assigning numbers to qualitative data (e.g. 1 for male, 2 for female, and so on). 

Numerical data , on the other hand, reflects data that are inherently numbers-based and quantitative in nature. For example, age, height, weight. In other words, these are things that are naturally measured as numbers (i.e. they’re quantitative), as opposed to categorical data (which involves assigning numbers to qualitative characteristics or groups).

Within each of these two main categories, there are two levels of measurement:

• Categorical data – n ominal and o rdinal
• Numerical data – i nterval and r atio

Let’s take look at each of these, along with some practical examples.

Need a helping hand?

What is nominal data?

As we’ve discussed, nominal data is a categorical data type, so it describes qualitative characteristics or groups, with no order or rank between categories. Examples of nominal data include:

• Gender, ethnicity, eye colour, blood type
• Brand of refrigerator/motor vehicle/television owned
• Political candidate preference, shampoo preference, favourite meal

In all of these examples, the data options are categorical , and there’s no ranking or natural order . In other words, they all have the same value – one is not ranked above another. So, you can view nominal data as the most basic level of measurement , reflecting categories with no rank or order involved.

What is ordinal data?

Ordinal data kicks things up a notch. It’s the same as nominal data in that it’s looking at categories, but unlike nominal data, there is also a meaningful order or rank between the options. Here are some examples of ordinal data:

• Income level (e.g. low income, middle income, high income)
• Level of agreement (e.g. strongly disagree, disagree, neutral, agree, strongly agree)
• Political orientation (e.g. far left, left, centre, right, far right)

As you can see in these examples, all the options are still categories, but there is an ordering or ranking difference between the options . You can’t numerically measure the differences between the options (because they are categories, after all), but you can order and/or logically rank them. So, you can view ordinal as a slightly more sophisticated level of measurement than nominal.

What is interval data?

As we discussed earlier, interval data are a numerical data type. In other words, it’s a level of measurement that involves data that’s naturally quantitative (is usually measured in numbers). Specifically, interval data has an order (like ordinal data), plus the spaces between measurement points are equal (unlike ordinal data). 

Sounds a bit fluffy and conceptual? Let’s take a look at some examples of interval data:

• Credit scores (300 – 850)
• GMAT scores (200 – 800)
• The temperature in Fahrenheit

Importantly, in all of these examples of interval data, the data points are numerical , but the zero point is arbitrary . For example, a temperature of zero degrees Fahrenheit doesn’t mean that there is no temperature (or no heat at all) – it just means the temperature is 10 degrees less than 10. Similarly, you cannot achieve a zero credit score or GMAT score. 

In other words, interval data is a level of measurement that’s numerical (and you can measure the distance between points), but that doesn’t have a meaningful zero point – the zero is arbitrary. 

Long story short – interval-type data offers a more sophisticated level of measurement than nominal and ordinal data, but it’s still not perfect. Enter, ratio data…

What is ratio data?

Ratio-type data is the most sophisticated level of measurement. Like interval data, it is ordered/ranked and the numerical distance between points is consistent (and can be measured). But what makes it the king of measurement is that the zero point reflects an absolute zero (unlike interval data’s arbitrary zero point). In other words, a measurement of zero means that there is nothing of that variable.

Here are some examples of ratio data:

• Weight, height, or length
• The temperature in Kelvin (since zero Kelvin means zero heat)
• Length of time/duration (e.g. seconds, minutes, hours)

In all of these examples, you can see that the zero point is absolute . For example, zero seconds quite literally means zero duration. Similarly, zero weight means weightless. It’s not some arbitrary number. This is what makes ratio-type data the most sophisticated level of measurement. 

With ratio data, not only can you meaningfully measure distances between data points (i.e. add and subtract) – you can also meaningfully multiply and divide . For example, 20 minutes is indeed twice as much time as 10 minutes. You couldn’t do that with credit scores (i.e. interval data), as there’s no such thing as a zero credit score. This is why ratio data is king in the land of measurement levels.

Why does it matter?

At this point, you’re probably thinking, “Well that’s some lovely nit-picking nerdery there, Derek – but why does it matter?”. That’s a good question. And there’s a good answer .

The reason it’s important to understand the levels of measurement in your data – nominal, ordinal, interval and ratio – is because they directly impact which statistical techniques you can use in your analysis. Each statistical test only works with certain types of data. Some techniques work with categorical data (i.e. nominal or ordinal data), while others work with numerical data (i.e. interval or ratio data) – and some work with a mix . While statistical software like SPSS or R might “let” you run the test with the wrong type of data, your results will be flawed at best , and meaningless at worst. 

The takeaway – make sure you understand the differences between the various levels of measurement before you decide on your statistical analysis techniques. Even better, think about what type of data you want to collect at the survey design stage (and design your survey accordingly) so that you can run the most sophisticated statistical analyses once you’ve got your data.

Let’s recap.

In this post, we looked at the four levels of measurement – nominal, ordinal, interval and ratio . Here’s a visual summary of each.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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16 Comments

Clear, concise with examples. PLUS in your videos you include other names or terms that could apply to the topic you are reviewing. This is so important! You are fantastic! It has been many, many, many moons ago that these were learned. They are now necessary again as the nursing profession progresses deeper into evidence based practice.

Thanks for the feedback, Diana 🙂

Good explanation.. I came here after giving 5 marks for each question in a quiz n wondering that the data is not continuous and how to analyse it further.. Understood it is ratio and i can use mean/ median accordingly

Glad it helped!

Bloody good! You saved my homework (:

Happy to help 🙂

High quality of education stuff, thank you very much.

great knowledge shared here. I had problem understanding this at the undergraduate school but very clear now. Thanks to GRADCOACH

What type of data would age be? Ratio or interval?

It would be ratio. However, if you are using age ranges (e.g. 18 – 25, 26 – 35, etc.), this wouldn’t be the case.

What is age ranges considered?

What measurement scale is ideal to use when measuring “knowledge” and the acceptable responses are “yes,” “no,” or “not sure”? What kind of analytical test is suitable in this situation?

I watched your youtube tutorial on quantitative analysis and it was really informative.

However, I’m trying to navigate your blog to find the post that discusses the different inferential statistical methods and the data type they support.

Kindly forward this link to my email : [email protected]

Scores from a performance test are ratio data?

It is an excellent discussion about levels of measurement.

Pretty! This was an incredibly wonderful article. Thanks for providing this info.

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Nominal Variable

A nominal variable is a type of categorical variable that can have two or more categories. However, there is no ordering within these categories. A nominal variable does not have any numerical characteristics and is qualitative in nature. If a variable has a proper numerical ordering then it is known as an ordinal variable.

A nominal variable can be coded but arithmetic operations cannot be performed on them. In other words, nominal variables cannot be quantified. In this article, we will learn more about a nominal variable, a nominal scale and several associated examples.

What is a Nominal Variable?

A nominal variable along with a dichotomous and an ordinal variable form the three types of categorical variables. A dichotomous variable is a subtype of a nominal variable that can have only two levels or categories. An ordinal variable on the other hand can have two or more categories, however, these can be ranked or ordered. Apart from categorical variables, other types of variables such as interval and ratio variables are also used.

Nominal Variable Definition

A nominal variable can be defined as a categorical variable in which the categories cannot be ordered. A nominal variable might be numeric in nature but it cannot have any numerical properties. This type of variable is assigned to nominal data as such type of data is non-numerical.

Nominal Variable Examples

An example of a nominal variable is hair color. This is because hair can be of different colors such as blonde, black, brown, red, etc. These categories cannot be ordered and neither can any operations be performed.

An example of a nominal variable is a person being asked if she owns a Macbook. The answer can either be yes or no. Thus, Macbook ownership can be categorized as either yes or no.

Nominal Scale

A nominal scale is a level of measurement where only qualitative variables are used. On such a scale, only tags or labels can classify objects. There are three other scales that are used for measurement levels - ordinal, interval, and ratio. A nominal variable is part of a nominal scale. In case a number is assigned to an object on a nominal scale there is a strict one-to-one correlation between the object and the corresponding numerical value. Thus, the variables in such a scale have no numeric property.

Nominal Scale Examples

An example of a nominal scale is categorizing dogs on the basis of their breeds (E.g. German shepherd, Husky, Samoyed, etc.).

Another example of a nominal scale is putting cities into states. (E.g. Seattle is in Washington).

Characteristics of Nominal Variable

The two main important characteristics of nominal variables are given as follows:

• Even though a nominal variable can take on numeric values, however, they cannot be quantified. In other words, arithmetic and logical operations cannot be performed on a nominal variable.
• The categories under nominal variables cannot be assigned a rank thereby, they cannot be ordered. Thus, a nominal variable is qualitative in nature.

Nominal Variable Types

A nominal variable can be classified either based on the collection technique or based on the numeric property. The nominal variable types are given as follows:

• Open-Ended Nominal Variable - When participants are asked open-ended questions such that they are free to respond in any way they like it is known as a nominal variable. For example, "How can a teacher improve his teaching methods?" is an open-ended nominal variable. Information collected using this variable is usually very detailed.
• Closed-Ended Nominal Variable - When the response of participants to a question has been restricted then such a question forms a closed-ended nominal variable. "How can a teacher improve his teaching methods? a) Acquiring better knowledge, b) Improving communication, c) Demonstrating flexibility. This is an example of a close-ended approach.
• Numeric and Non-Numeric Nominal Variable - A numeric nominal variable can take on a quantitative value but does not have any numeric property. For example, phone numbers. A non-numeric nominal variable neither takes on a numerical value nor does it have any numeric property. For example, an open-ended / closed-ended question.

Nominal Vs Ordinal Variable

A nominal and an ordinal variable are types of categorical variables. Both variables are qualitative in nature. The table given below highlights the main differences between nominal and ordinal variables.

Related Articles:

• Data Handling
• Data Collection
• Categorical Data

Important Notes on Nominal Variable

• A nominal variable is a categorical variable that does not have any intrinsic ordering or ranking.
• Such a variable is qualitative in nature and arithmetic or logical operations cannot be performed on it.
• A nominal variable follows a nominal scale of measurement.
• The types of nominal variables are open-ended, closed-ended, numeric, and non-numeric variables.

Examples on Nominal Variable

Example 1: How can a restaurant service be improved?

a) Improving menu

b) Changing the chef

c) Better Decor

What type of nominal variable is this?

Solution: As the question is in the form of multiple-choice thus, it is a closed-ended nominal variable. Furthermore, as there is no associated numeric value thus, it is a non-numeric nominal variable.

Answer: Close-ended non-numeric nominal variable.

Example 2: How satisfied are you with the course curriculum?

1. Dissatisfied

2. Satisfied

3. Very Satisfied

Is this a nominal variable?

Solution: As the replies to the question can be ranked hence, this is not a nominal variable. It is an ordinal variable.

Answer: Not a nominal variable

Example 3: Is a personal bio-data (name, gender, date of birth) a nominal variable?

Solution: Yes, because the categories cannot be ranked and do not possess numeric properties.

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FAQs on Nominal Variable

A variable consisting of categories that cannot be ranked or ordered is known as a nominal variable. A nominal variable cannot be quantitative.

Is a Nominal Variable a Type of Categorical Variable?

Yes, a nominal variable is a type of categorical variable. Other types of categorical variables are ordinal variables and dichotomous variables.

Is a Nominal Variable Qualitative in Nature?

Yes, a nominal variable is qualitative in nature. This means that arithmetic operations and logical operations cannot be performed on a nominal variable.

What Measurement Level is Followed by a Nominal Variable?

A nominal scale is the level of measurement used by a nominal variable. Such a scale is qualitative in nature and uses labels and tags to categorize data.

What is the Difference Between an Open-Ended and Closed-Ended Nominal Variable?

An open-ended nominal variable lets the participant respond freely while a closed-ended nominal variable is usually in the form of multiple-choice questions and restricts the participant's views.

Can a Nominal Variable Be Numeric?

Yes, a nominal variable can be in the form of a number however, it will not have any quantitative property. Thus, arithmetic operations cannot be performed on such a variable.

What is the Difference Between an Ordinal and a Nominal Variable?

In an ordinal variable the categories can be ranked and ordered however, in a nominal variable no ranking is possible.

4 Levels of Measurement: Nominal, Ordinal, Interval & Ratio

When carrying out any kind of data collection or analysis, it’s essential to understand the nature of the data you’re dealing with.

Within your dataset, you’ll have different variables—and these variables can be recorded to varying degrees of precision. This is what’s known as the level of measurement.

There are four main levels of measurement: nominal , ordinal , interval , and ratio . In this guide, we’ll explain exactly what is meant by levels (also known as types or scales) of measurement within the realm of data and statistics—and why it matters. We’ll then introduce you to the four types of measurements, providing a few examples of each.

If you’d like to get your hands on some datasets already, try this free data analytics short course to get started.

Here’s what we’ll cover:

Why are levels of measurement important?

• Levels of measurement: FAQ
• Key takeaways

Let’s get started!

1. What are levels of measurement in data and statistics?

Level of measurement refers to how precisely a variable has been measured. When gathering data, you collect different types of information, depending on what you hope to investigate or find out.

For example, if you wanted to analyze the spending habits of people living in Tokyo, you might send out a survey to 500 people asking questions about their income, their exact location, their age, and how much they spend on various products and services. These are your variables: data that can be measured and recorded, and whose values will differ from one individual to the next.

When we talk about levels of measurement, we’re talking about how each variable is measured, and the mathematical nature of the values assigned to each variable. This, in turn, determines what type of analysis can be carried out.

Let’s imagine you want to gather data relating to people’s income. There are various levels of measurement you could use for this variable. You could ask people to provide an exact figure, or you could ask them to select their answer from a variety of ranges—for example:

You could ask them to simply categorize their income as “high,” “medium,” or “low.”

Can you see how these levels vary in their precision? If you ask participants for an exact figure, you can calculate just how much the incomes vary across your entire dataset (for example).

However, if you only have classifications of “high,” “medium,” and “low,” you can’t see exactly how much one participant earns compared to another. You also have no concept of what salary counts as “high” and what counts as “low”—these classifications have no numerical value. As a result, the latter is a less precise level of measurement.

Level of measurement is important, as it determines the type of statistical analysis you can carry out. As a result, it affects both the nature and the depth of insights you’re able to glean from your data.

Certain statistical tests can only be performed where more precise levels of measurement have been used, so it’s essential to plan in advance how you’ll gather and measure your data.

3. What are the four levels of measurement? Nominal, ordinal, interval, and ratio scales explained

There are four types of measurement (or scales) to be aware of: nominal , ordinal , interval , and ratio .

Each scale builds on the previous, meaning that each scale not only “ticks the same boxes” as the previous scale, but also adds another level of precision.

Let’s go through each in turn to give you an idea of what they are, and how they interact.

The nominal scale simply categorizes variables according to qualitative labels (or names). These labels and groupings don’t have any order or hierarchy to them, nor do they convey any numerical value.

For example, the variable “hair color” could be measured on a nominal scale according to the following categories: blonde hair, brown hair, gray hair, and so on.

You can learn more in this complete guide to nominal data .

The ordinal scale also categorizes variables into labeled groups, and these categories have an order or hierarchy to them.

For example, you could measure the variable “income” on an ordinal scale as follows:

• medium income
• high income.

Another example could be level of education, classified as follows:

• high school
• master’s degree

These are still qualitative labels (as with the nominal scale), but you can see that they follow a hierarchical order.

Learn more in our guide to ordinal data .

The interval scale is a numerical scale which labels and orders variables, with a known, evenly spaced interval between each of the values.

A commonly-cited example of interval data is temperature in Fahrenheit, where the difference between 10 and 20 degrees Fahrenheit is exactly the same as the difference between, say, 50 and 60 degrees Fahrenheit.

Find out more about interval data in our full guide .

The ratio scale is exactly the same as the interval scale, with one key difference: The ratio scale has what’s known as a “true zero.”

A good example of ratio data is weight in kilograms. If something weighs zero kilograms, it truly weighs nothing—compared to temperature (interval data), where a value of zero degrees doesn’t mean there is “no temperature,” it simply means it’s extremely cold!

You’ll find we’ve made a full guide to ratio data if you want to dive deeper.

4. Another way of thinking about the levels of measurement

Another way to think about levels of measurement is in terms of the relationship between the values assigned to a given variable .

With the nominal scale, there’s no relationship between the values; there’s no relationship between the categories “blonde hair” and “black hair” when looking at hair color, for example. The ratio scale, on the other hand, is very telling about the relationship between variable values.

For example, if your variable is “number of clients” (which constitutes ratio data), you know that a value of four clients is double the value of two clients. As such, you can get a much more accurate and precise understanding of the relationship between the values in mathematical terms.

In that sense, there’s an implied hierarchy to the four levels of measurement . Analysis of nominal and ordinal data tends to be less sensitive, while interval and ratio scales lend themselves to more complex statistical analysis. With that in mind, it’s generally preferable to work with interval and ratio data.

5. Levels of measurement: FAQ

What are the 4 levels of measurement.

The 4 levels of measurement, also known as measurement scales, are nominal, ordinal, interval, and ratio. These levels are used to categorize and describe data based on their characteristics and properties.

What is level of measurement in statistics?

Level of measurement, also known as scale of measurement, refers to the process of categorizing data based on the characteristics and properties of the data. It’s important in statistics because it helps determine the appropriate statistical methods and tests that can be used to analyze the data.

Is age an interval or ratio?

Age is typically considered to be measured on a ratio scale. This is because age has a true zero point, which means that a value of zero represents the absence of age. In addition, it’s possible to perform mathematical operations such as addition, subtraction, multiplication, and division on age values.

Is gender nominal or ordinal?

Gender is typically considered to be measured on a nominal scale. This is because gender is a categorical variable that has no inherent order or ranking. It’s not possible to perform mathematical operations on gender values.

5. Key takeaways

So there you have it: the four levels of data measurement and how they’re analyzed. In this article, we’ve learned the difference between the various levels of measurement, and introduced some of the different descriptive statistics and analyses that can be applied to each.

If you’re looking to pursue a career in data analytics , or even just dabbling in statistics, this fundamental knowledge of the types of measurement will stand you in good stead.

If you enjoyed learning about the different levels of measurement, why not get a hands-on introduction to data analytics with this free, 5-day short course ?

At the same time, keep building on your knowledge with these guides:

• What’s the difference between descriptive and inferential statistics?
• An introduction to multivariate analysis
• What is data visualization and why is it important?

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Levels of Measurement: Nominal, Ordinal, Interval & Ratio

The nominal, ordinal, interval & ratio levels of measurement are scales that allow us to measure and classify gathered data in well-defined variables to be used for different purposes.  

Mainly used for these four scales are:

• Nominal : Used to categorize data into mutually exclusive categories or groups.
• Ordinal : Used to measure variables in a natural order, such as rating or ranking. They provide meaningful insights into attitudes, preferences, and behaviors by understanding the order of responses.
• Interval : Used to measure variables with equal intervals between values. Temperature and time often make use of this type of measurement, enabling precise comparisons and calculations.
• Ratio : Allows for comparisons and computations such as ratios, percentages, and averages. Great for research in fields like science, engineering, and finance, where you need to use ratios, percentages, and averages to understand the data.

Below, we’ll discuss everything you need to know about these measurement levels, characteristics, examples, and how to use them.

Levels of Measurement in Statistics

To perform statistical data analysis , it is important first to understand variables and what should be measured using them.

There are different levels of measurement in statistics, and data measured using them can be broadly classified into qualitative and quantitative data. Let’s discuss the Nominal, Ordinal, Interval, and ratio scales.

First, let’s understand what a variable is. You can measure a variable, which is a quantity that changes across the population. For instance, consider a sample of employed individuals.

The variables for this set of the population can be industry, location, gender, age, skills, job type, paid time off , etc. The value of the variables will differ with each employee spotlight . 

For example, it is practically impossible to calculate the average hourly rate of a worker in the US. So, a sample audience is randomly selected to represent the larger population appropriately.

Then, we calculate the average hourly rate of this sample audience. Using statistical tests, you can conclude the average hourly rate of a larger population. In statistical analysis, distinguishing between categorical data and numerical data is essential, as categorical data involves distinct categories or labels, while numerical data consists of measurable quantities.

A variable’s measurement level decides the statistical test type to be used. The mathematical nature of a variable, or in other words, how a variable is measured, is considered the level of measurement.

What are Nominal, Ordinal, Interval, and ratio?

Nominal, Ordinal, Interval, and ratio are defined as the four fundamental measurement scales used to capture data in the form of surveys and questionnaires , each being a multiple-choice question . 

Each scale is an incremental level of measurement, meaning each scale fulfills the function of the previous scale, and all survey question scales, such as Likert , Semantic Differential , Dichotomous , etc, are the derivation of this these four fundamental levels of variable measurement.

Before we discuss all four levels of measurement scales in detail, with examples, let’s briefly look at what these scales represent.

A nominal scale is a naming scale where variables are simply “named” or labeled with no specific order. The ordinal scale has all its variables in a specific order, beyond just naming them. Interval scale offers labels, order, as well as a specific interval between each of its variable options.

The ratio scale bears all the characteristics of an interval scale. In addition to that, it can also accommodate the value of “zero” on any of its variables.

Here’s more of the four levels of measurement in research and statistics: Nominal, Ordinal, Interval, Ratio.

LEARN ABOUT: Graphic Rating Scale

Nominal Scale: 1 st Level of Measurement

Nominal Scale, also called the categorical variable scale, is defined as a scale that labels variables into distinct classifications and doesn’t involve a quantitative value or order. This scale is the simplest of the four variable measurement scales. Calculations done on these variables will be futile as the options have no numerical value.

There are cases where this scale is used for the purpose of classification – the numbers associated with variables of this scale are only tags for categorization or division. Calculations done on these numbers will be futile as they have no quantitative research significance.

For a question such as:

Where do you live?

A nominal scale is often used in research surveys and questionnaires where only variable labels hold significance.

For instance, a customer survey asking “Which brand of smartphones do you prefer?” Options : “Apple”- 1 , “Samsung”-2, “OnePlus”-3.

• In this survey question , only the names of the brands are significant for the researcher conducting consumer research or netnography . There is no need for any specific order for these brands. However, while capturing nominal data, researchers conduct analysis based on the associated labels.
• In the above example, when a survey respondent selects Apple as their preferred brand, the data entered and associated will be “1”. This helped in quantifying and answering the final question – How many respondents selected Apple, how many selected Samsung, and how many went for OnePlus – and which one is the highest?
• This is the fundamental of quantitative research, and the nominal scale is the most fundamental research scale.

Nominal Scale Data and Analysis

There are two primary ways in which nominal scale data can be collected:

• By asking an open-ended question , the answers of which can be coded to a respective number of labels decided by the researcher.
• The other alternative to collect nominal data is to include a multiple-choice question in which the answers will be labeled.

In both cases, the analysis of gathered data will happen using percentages or mode,i.e., the most common answer received for the question. It is possible for a single question to have more than one mode, as it is possible for two common favorites to exist in a target population.  

Nominal Scale Examples

• Political preferences
• Place of residence

LEARN ABOUT: Average Order Value

Nominal Scale SPSS

In SPSS, you can specify the level of measurement as scale (numeric data on an interval or ratio scale), ordinal, or nominal. Nominal and ordinal data can be either string alphanumeric or numeric.

Upon importing the data for any variable into the SPSS input file, it takes it as a scale variable by default since the data essentially contains numeric values. It is important to change it to either nominal or ordinal or keep it as scale depending on the variable the data represents.

Ordinal Scale: 2 nd Level of Measurement

Ordinal Scale is defined as a variable measurement scale used to simply depict the order of variables and not the difference between each variable . These scales generally depict non-mathematical ideas such as frequency, satisfaction, happiness, a degree of pain, etc. It is quite straightforward to remember the implementation of this scale as ‘Ordinal’ sounds similar to ‘Order,’ which is exactly the purpose of this scale.

Ordinal Scale maintains descriptional qualities along with an intrinsic order but is void of an origin of scale, and thus, the distance between variables can’t be calculated. Descriptional qualities indicate tagging properties similar to the nominal scale, in addition to which the ordinal scale also has a relative position of variables. This scale’s origin is absent, so there is no fixed start or “true zero.”

Ordinal Data and Analysis   

Ordinal scale data can be presented in tabular or graphical formats for a researcher to conduct a convenient analysis of collected data. Also, methods such as the Mann-Whitney U test and the Kruskal–Wallis H test can also be used to analyze ordinal data. These methods are generally implemented to compare two or more ordinal groups.

In the Mann-Whitney U test, researchers can conclude which variable of one group is bigger or smaller than another variable of a randomly selected group. In the Kruskal–Wallis H test, researchers can analyze whether two or more ordinal groups have the same median or not.

Ordinal Scale Examples

Status at the workplace, tournament team rankings, order of product quality, and order of agreement or satisfaction are some of the most common examples of the ordinal Scale. These scales are generally used in market research to gather and evaluate relative feedback about product satisfaction, changing perceptions with product upgrades, etc.

For example, a semantic differential scale question such as:

How satisfied are you with our services?

• Very Unsatisfied – 1
• Unsatisfied – 2
• Neutral – 3
• Satisfied – 4
• Very Satisfied – 5
• Here, the order of variables is of prime importance, and so is the labeling. Very unsatisfied will always be worse than unsatisfied, and satisfied will be worse than very satisfied.
• This is where the ordinal scale is a step above the nominal scale – the order is relevant to the results, and so is their naming.
• Analyzing results based on the order along with the name becomes a convenient process for the researcher.
• If they intend to obtain more information than what they would collect using a nominal scale, they can use the ordinal scale.

This scale not only assigns values to the variables but also measures the rank or order of the variables, such as:

• Satisfaction
• 1- Very Unsatisfied
• 2- Unsatisfied
• 4- Satisfied
• 5- Very Satisfied

LEARN ABOUT: Nominal vs. Ordinal Scale

Interval Scale: 3 rd Level of Measurement

Interval Scale is defined as a numerical scale where the variables’ order is known and the difference between these variables. Variables that have familiar, constant, and computable differences are classified using the Interval scale. It is easy to remember the primary role of this scale, too, ‘Interval’ indicates ‘distance between two entities,’ which is what the Interval scale helps achieve .  

These scales are effective as they open doors for the statistical analysis of provided data. Mean, median, or mode can be used to calculate the central tendency in this scale. The only drawback of this scale is that there is no pre-decided starting point or a true zero value.

The interval scale contains all the properties of the ordinal scale and offers a calculation of the difference between variables. The main characteristic of this scale is the equidistant difference between objects.  

For instance, consider a Celsius/Fahrenheit temperature scale –

• Eighty degrees is always higher than 50 degrees, and the difference between these two temperatures is the same as the difference between 70 degrees and 40 degrees.
• Also, the value of 0 is arbitrary because negative temperature values exist – which makes the Celsius/Fahrenheit temperature scale a classic example of an interval scale.
• Interval scale is often chosen in research cases where the difference between variables is a mandate – which can’t be achieved using a nominal or ordinal scale. The Interval scale quantifies the difference between two variables, whereas the other two scales can solely associate qualitative observation values with variables.
• Unlike the previous two scales, an ordinal scale’s mean and median values can be evaluated.
• In statistics, interval scale is frequently used as a numerical value that can not only be assigned to variables but calculations based on those values can also be carried out.

Even if interval scales are amazing, they do not calculate the “true zero” value, which is why the next scale comes into the picture.

Interval Data and Analysis

All the techniques applicable to nominal and ordinal data analysis are applicable to Interval Data as well. Apart from those techniques, there are a few analysis methods, such as descriptive statistics correlation regression analysis, which is extensively used for analyzing interval data.

Descriptive analysis statistics is the term given to the analysis of numerical data. It helps to describe, depict, or summarize data in a meaningful manner, and it helps in the calculation of mean, median, and mode.

LEARN MORE: Descriptive Research vs Correlational Research

Interval Scale Examples

• There are situations where attitude scales are considered to be interval scales.
• Apart from the temperature scale, time is also a very common example of an interval scale, as the values are already established, constant, and measurable.
• Calendar years and times also fall under this category of measurement scales.
• Likert scale, Net Promoter Score , Semantic Differential Scale, Bipolar Matrix Table , etc., are the most-used interval scale examples.

The following questions fall under the Interval Scale category:

• What is your family income?
• What is the temperature in your city?

Ratio Scale: 4 th Level of Measurement

Ratio Scale is defined as a variable measurement scale that not only produces the order of variables but also makes the difference between variables known, along with information on the value of true zero. It is calculated by assuming that the variables have an option for zero, the difference between the two variables is the same, and there is a specific order between the options.

With the option of true zero, varied inferential statistics and descriptive analysis techniques can be applied to the variables. In addition to the fact that the ratio scale does everything that a nominal, ordinal, and interval scale can do, it can also establish the value of absolute zero. The best examples of ratio scales are weight and height. In market research, a ratio scale is used to calculate market share, annual sales, the price of an upcoming product, the number of consumers, etc.

• The ratio scale provides the most detailed information as researchers and statisticians can calculate the central tendency using statistical techniques such as mean, median, and mode, and methods such as geometric mean, coefficient of variation, or harmonic mean can also be used on this scale.
• The ratio scale accommodates the characteristics of three other variable measurement scales, i.e., labeling the variables, the significance of the order of variables, and a calculable difference between variables (which are usually equidistant).
• Because of the existence of a true zero value, the ratio scale doesn’t have negative values.
• To decide when to use a ratio scale, the researcher must observe whether the variables have all the characteristics of an interval scale along with the presence of the absolute zero value.
• The rati o scale can calculate the mean, mode, and median .

Ratio Data and Analysis

At a fundamental level, Ratio scale data is quantitative in nature, due to which all quantitative analysis techniques, such as SWOT, TURF, Cross-tabulation, Conjoint, etc., can be used to calculate ratio data. While some techniques, such as SWOT and TURF, will analyze ratio data in such a manner that researchers can create roadmaps of how to improve products or services and Cross-tabulation will be useful in understanding whether new features will be helpful to the target market or not.

LEARN ABOUT: Level of Analysis

Ratio Scale Examples

The following questions fall under the Ratio Scale category:

• Less than 5 feet.
• 5 feet 1 inch – 5 feet 5 inches
• 5 feet 6 inches- 6 feet
• More than 6 feet
• Less than 50 kilograms
• 51- 70 kilograms
• 71- 90 kilograms
• 91-110 kilograms
• More than 110 kilograms

Nominal, Ordinal, Interval, Ratio: Main Characteristics

The four data measurement scales – nominal, ordinal, interval, and ratio –  are quite often discussed in academic teaching. The easy-to-remember chart might help you in your statistics test.

LEARN ABOUT: Interval vs. Ratio Scale & Population vs Sample

Understanding the levels of measurement is crucial in research, as it affects the type of analysis that can be performed and the conclusions that can be drawn from the data. By understanding the differences between nominal, ordinal, interval, and ratio data, researchers can make more informed decisions about the appropriate statistical tests to use and how to interpret their results.

Remember that selecting the appropriate level of measurement is a critical step in designing a research study, so take the time to carefully consider the measurement level most appropriate for your research question and data.

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Table of Contents

What is nominal data  , characteristics of nominal data, nominal data analysis, examples of nominal data, nominal vs. ordinal data, frequently asked questions, choose the right program, what is nominal data definition, examples, variables & analysis.

The level of measurement of variables is essential in statistical analysis because it determines how you can analyze your data. The four primary levels of measurement – nominal, ordinal, interval, and ratio provide different levels of detail – nominal provides minuscule detail, while interval and ratio give the maximum detail. 

If you're interested in learning the basics of nominal data, this guide is for you. We'll define what nominal data is, look at the characteristics of nominal data, examples of nominal data, how to analyze nominal data, and nominal vs. ordinal data.   

Nominal data is qualitative data used to name or label variables without providing numeric values. It is the most straightforward type of measurement scale. Nominal variables are labeled into categories that do not overlap. Unlike other data types, nominal data cannot be ordered or measured; it does not have equal spacing between values or a true zero value. 

Nominal data is the foundation of statistical analysis and all other mathematical sciences. They comprise individual pieces of information recorded and used for analysis. 

For instance, the preferred mode of transportation is a nominal variable since we can sort the data into mutually exclusive categories like a car, bus, train, bicycle, etc. Numbers and words may denote nominal variables, but the number labels do not have any numeric value.

The main characteristics of nominal data are:

• Nominal data are categorical, the categories being mutually exclusive without any overlap. 
• The categories of nominal data are purely descriptive, that is, they do not possess any quantitative or numeric value. Nominal data can never be quantified 
• Nominal data cannot be put into any definite order or hierarchy. None of the categories can be greater than or worth more than one another. 
• The mean of nominal data cannot be calculated even if the data is arranged in alphabetical order. 
• The mode is the only measure of central tendency for nominal data. 
• In most cases, nominal data is alphabetical. 

Most nominal data is collected through open or closed-ended survey questions that provide the respondent with a list of labels to choose from. 

Close-ended questions are used if all data can be captured using a few possible labels. 

On the other hand, if the variable selected has many possible labels, an open-ended question is preferred.  

For example, 

What is your ethnicity? __ (followed by a drop-down list of ethnicities)

Nominal data can be organized and visualized into tables and charts. Thereafter, you can get descriptive statistics about your data set to calculate your data's frequency distribution and central tendency. 

The general steps to be taken to analyze nominal data include:

Descriptive Statistics 

In this step, descriptive statistics will enable you to see how your data are distributed. The most common descriptive statistics methods for nominal data are

• Frequency Distribution – frequency distribution table is created to bring order to nominal data. Such a table clearly shows the number of responses for each category in the variable. Thus, you can use these tables to visualize data distribution through graphs and charts. 

Central Tendency 

 it is a measure of where most of the values lie. The most commonly used measures of central tendency are the mean, median, and mode. However, since nominal data is purely qualitative, only one mode can be calculated for nominal data. 

You can find the mode by identifying the most frequently appearing value in your frequency table. 

Statistical Tests

Inferential statistics allow you to test scientific hypotheses about the data and dig deeper into what the data are conveying. Non-parametric tests are used for nominal data because the data cannot be ordered in any meaningful way. 

Nonparametric tests used for nominal data are:

• Chi-square goodness of fit test – this test helps to assess if the sample data collected is representative of the whole data populace. The test is used when data is collected from a single population through random sampling.
• The Chi-square independence test explores the relationship between two nominal variables. Hypotheses testing allows testing whether two nominal variables from one sample are independent. 

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Most nominal data is sorted into categories, where each response fits only into one category. 

Some examples of nominal data are:

1. Which state do you live in? (Followed by a drop-down list of names of states)

2.Which among the following do you usually choose for pizza toppings?

• Extra Cheese
• Which is the most loved breed of dog?
• Doberman - 1
• Dalmatian - 2
• Labrador – 3
• German Shepherd – 4

3. Hair Color (black, brown, grey, blonde)

4. Preferred mode of Public Transport (bus, tram, train)

5. Employment Status (employed, unemployed, retired)

6. Literary Genre (comedy, tragedy, drama, epic, satire)

Ordinal data is a kind of qualitative data that groups variables into ordered categories. The categories have a natural order or rank based on some hierarchal scale. 

The main differences between Nominal Data and Ordinal Data are:

While Nominal Data is classified without any intrinsic ordering or rank, Ordinal Data has some predetermined or natural order. 

• Nominal data is qualitative or categorical data, while Ordinal data is considered “in-between” qualitative and quantitative data.
• Nominal data do not provide any quantitative value, and you cannot perform numeric operations with them or compare them with one another. However, Ordinal data provide sequence, and it is possible to assign numbers to the data. No numeric operations can be performed. But ordinal data makes it possible to compare one item with another in terms of ranking.  
• Example of Nominal Data – Eye color, Gender; Example of Ordinal data – Customer Feedback, Economic Status

1. What is nominal or ordinal data?

There are four main data types or levels of measurement – nominal, ordinal, interval, and ratio. Nominal Data is qualitative data used to name or label variables without providing numeric values. It is the most straightforward form of a level of measurement.

Ordinal data is also qualitative data that groups variables into ordered categories. The categories have a natural order or rank based on some hierarchal scale, like from high to low.

2. What are nominal data statistics?

In statistics, Nominal data is qualitative data that groups variables into categories that do not overlap. Nominal data is the simplest measure level and are considered the foundation of statistical analysis and all other mathematical sciences. They are individual pieces of information recorded and used for analysis. Nominal data cannot be ordered and cannot be measured. 

3. What are nominal and ordinal data examples?

1. Example of Nominal Data – Which state do you live in? (Followed by a drop-down list of names of states)

2. Example of Ordinal data – Rate education level according to:

• High School
• Post-graduate

4. What are the characteristics of nominal data?

5. which is an example of ordinal data.

An organization asks employees to rate how happy they are with their manager and peers according to the following scale:

• Extremely Happy – 1
• Unhappy – 4
• Extremely Unhappy – 5 

6. What is an example of nominal data?

Example of nominal data:

A real estate agent surveys to understand the answer to this question:

Which kind of houses are preferred by the residents of City X?

• Apartments -A
• Bungalows – B

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What is Nominal Data? Definition, Characteristics, Examples

Appinio Research · 23.02.2024 · 32min read

Ever wondered how researchers classify data into different categories? Nominal data holds the key to this classification puzzle. From demographic studies to market research, nominal data helps organize information into distinct groups or labels. But what exactly is nominal data, and why is it essential? In this guide, we'll explore the basics of nominal data, its characteristics, analysis techniques, and real-world applications. Whether you're a student, researcher, or data enthusiast, understanding nominal data is the first step towards unlocking valuable insights from your datasets.

What is Nominal Data?

Nominal data represents categories or labels that cannot be ordered or ranked in a meaningful way. Unlike numerical data, which can be quantified, nominal data is qualitative in nature, describing attributes rather than quantities.

Importance of Nominal Data

Nominal data holds significant importance across a wide range of disciplines and applications. Some key reasons for its importance include:

• Categorization : Nominal data allows for the classification of observations into distinct categories or groups, facilitating organization and analysis.
• Identification of Patterns : By categorizing data, nominal variables enable the identification of patterns , trends, and associations within datasets.
• Decision Making : Nominal data aids decision-making processes by providing insights into group compositions, preferences, and behaviors.
• Communication : Nominal data helps in effectively communicating information, such as demographic characteristics or group memberships, in a concise and understandable manner.

Nominal Data Characteristics and Properties

Nominal data exhibits specific characteristics and properties that distinguish it from other types of data. These characteristics include:

• Non-Numeric : Nominal data consists of categories or labels that cannot be expressed as numerical values.
• Discreteness : Each category in nominal data is discrete and mutually exclusive, with no overlap between categories.
• No Order : Unlike ordinal data, nominal data categories lack any inherent order or ranking.
• Qualitative : Nominal data describes qualitative attributes or characteristics rather than quantities or measurements.

Understanding these characteristics is essential for appropriately handling and analyzing nominal data in research and analysis.

Nominal Data Applications

Nominal data finds diverse applications across various fields and industries. Some common applications include:

• Demographic Analysis : Nominal data is frequently used in demographic studies to classify individuals based on characteristics such as age, gender, ethnicity, and education level.
• Market Research : In market research, nominal data is employed to segment consumers into distinct groups based on preferences, buying behaviors, or demographic profiles.
• Medical Diagnosis : Nominal data is used in medical diagnosis to classify patients into different diagnostic categories, such as disease types or severity levels.
• Sociological Studies : Sociologists utilize nominal data to examine social phenomena, such as group affiliations, cultural identities, or political affiliations.

These applications highlight the versatility and relevance of nominal data in understanding and interpreting various aspects of the world around us.

Understanding Nominal Variables

Nominal variables play a crucial role in data analysis, providing a framework for categorizing information into distinct groups or labels. Let's delve deeper into the concept of nominal variables, exploring their definition, examples, and how they differ from other data types.

What are Nominal Variables?

Nominal variables are categorical variables that represent distinct categories or labels within a dataset. These categories are used to classify data based on qualitative attributes rather than quantitative measurements. Unlike numerical variables, nominal variables do not have a numerical value associated with them. Instead, they serve as identifiers for different groups or characteristics.

For example, if we are conducting a survey on favorite movie genres and the categories include "Action," "Comedy," "Drama," and "Horror," each genre represents a nominal variable.

Examples of Nominal Variables

Nominal variables are prevalent in various fields and research studies. Here are some common examples:

• Gender : Male, Female, Other
• Marital Status : Single, Married, Divorced, Widowed
• Ethnicity : Caucasian, African American, Hispanic, Asian
• Educational Qualification : High School Diploma, Bachelor's Degree, Master's Degree, PhD

These examples illustrate how nominal variables are used to categorize individuals or entities based on non-quantitative attributes.

Differentiating Nominal Data from Other Data Types

Nominal data differs from other types of data, such as ordinal, interval, and ratio data, based on the level of measurement and the characteristics of the data.

• Ordinal Data : While nominal data categorizes information into distinct groups with no inherent order, ordinal data categorizes information into ordered categories where the relative position or ranking matters. For example, rating scales (e.g., "poor," "fair," "good") represent ordinal data.
• Interval Data : Interval data includes numerical values with equal intervals between them but lacks a true zero point. Unlike nominal data, interval data can be subjected to mathematical operations such as addition and subtraction. However, the zero point is arbitrary, as in the case of temperature measured in Celsius or Fahrenheit.
• Ratio Data : Ratio data possesses the properties of interval data with the addition of a true zero point, where zero represents the absence of the measured quantity. Ratio data allows for meaningful ratios and comparisons between values. Examples include height, weight, and income.

Understanding these distinctions is essential for selecting appropriate statistical methods and interpreting the results accurately in data analysis.

Data Collection Methods for Nominal Data

When it comes to collecting nominal data, researchers have several methods at their disposal, each suited to different research contexts and objectives. Let's explore these methods to understand how nominal data is gathered.

Surveys and Questionnaires

Surveys and questionnaires are popular tools for collecting nominal data, particularly in social sciences, market research, and public opinion studies. These instruments involve presenting respondents with a set of questions or statements, each accompanied by a list of predefined response options. Respondents select the option that best corresponds to their views, preferences , or characteristics.

Surveys and questionnaires offer several advantages for collecting nominal data:

• Scalability : Surveys can be administered to large samples of respondents, making them suitable for studying broad populations or demographic groups.
• Standardization : By using standardized questions and response options, researchers can ensure consistency and comparability across respondents.
• Anonymity : Respondents may feel more comfortable providing honest answers to sensitive questions when their responses are anonymous.
• Efficiency : Surveys can be conducted quickly and cost-effectively, allowing researchers to collect data efficiently.

However, surveys and questionnaires also pose some challenges, such as low response rates, response bias, and the potential to misinterpret questions.

Observational Studies

Observational studies involve systematically observing and recording behaviors, events, or phenomena in their natural settings without intervening or manipulating variables. Researchers collect nominal data by categorizing observed behaviors or characteristics into predefined categories or labels.

Observational studies offer several advantages for collecting nominal data:

• Naturalistic Setting : Observing behaviors in real-world settings allows researchers to capture authentic and spontaneous behavior.
• Flexibility : Observational studies can be adapted to various research contexts and objectives, making them suitable for studying diverse phenomena.
• Richness of Data : Observational data can provide rich, detailed insights into complex behaviors or interactions that may be challenging to capture using other methods.

However, observational studies also have limitations, including potential observer bias, lack of control over extraneous variables, and difficulties in generalizing findings to broader populations.

Experimental Studies

Experimental studies involve manipulating one or more independent variables to observe their effects on a dependent variable. While experimental studies are often associated with quantitative research, nominal data can also be collected within experimental designs by categorizing participants into groups or conditions based on qualitative attributes.

Experimental studies offer several advantages for collecting nominal data:

• Control Over Variables : Experimental designs allow researchers to manipulate variables systematically and control for confounding factors, enhancing the internal validity of the study.
• Causality : By manipulating independent variables and observing their effects on dependent variables, experimental studies can establish causal relationships.
• Replication : Experimental designs can be replicated or repeated to verify findings and ensure the reliability of results.

However, experimental studies also have limitations, including ethical constraints, potential artificiality of laboratory settings, and challenges in generalizing findings to real-world contexts.

Case Studies

Case studies involve in-depth examination and analysis of a single individual, group, organization, or event. Nominal data can be collected within case studies by categorizing attributes, characteristics, or outcomes into predefined categories or labels.

Case studies offer several advantages for collecting nominal data:

• Richness of Data : Case studies provide detailed, in-depth insights into specific cases, allowing researchers to explore complex phenomena in depth.
• Contextual Understanding : By examining individual cases within their broader contexts, case studies can provide a rich, nuanced understanding of real-world phenomena.
• Theory Development : Case studies can generate hypotheses or theories that can be further tested and refined in subsequent research.

However, case studies also have limitations, including potential bias in data collection and analysis, limited generalizability of findings, and challenges in establishing causality.

When considering the myriad of data collection methods for nominal data, it's imperative to weigh the pros and cons of each approach to ensure accurate and insightful results. Whether it's through surveys, observational studies, experimental designs, or case studies, the nuances of data collection can significantly impact the outcomes of your research endeavors.

Harnessing the power of tools like Appinio  can streamline this process, allowing you to effortlessly gather real-time consumer insights and make informed decisions with confidence. Dive into the world of data-driven discovery with Appinio and revolutionize the way you conduct research.    Schedule a demo today to experience the seamless integration of consumer insights into your decision-making journey!

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Data Representation and Measurement Scales

In data analysis, it's essential to understand different measurement scales and how they influence data representation and analysis. Let's explore the various measurement scales, including nominal, ordinal, interval, and ratio scales, and discuss their significance in data representation.

Nominal Scale

The nominal scale is the simplest form of measurement, where data is categorized into distinct labels or categories with no inherent order or ranking. Each category represents a unique attribute, but there is no quantitative significance to the labels. Nominal data is qualitative in nature and is often used to classify or categorize information.

In nominal scales:

• Categories are mutually exclusive : Each observation belongs to only one category.
• No inherent order : Categories have no natural order or hierarchy.
• Examples : Gender (male, female, other), marital status (single, married, divorced), and types of vehicles (car, truck, motorcycle).

Nominal data is typically represented using frequency counts or percentages within each category. Standard statistical analyses for nominal data include frequency distributions, chi-square tests, and cross-tabulations.

Ordinal Scale

The ordinal scale ranks data into ordered categories or levels, where the relative position or ranking of categories is meaningful. While the categories have a defined sequence, the intervals between them may not be equal or meaningful. Ordinal data retains the qualitative nature of nominal data but adds a degree of order or hierarchy.

In ordinal scales:

• Categories have a meaningful order : Categories are ranked or ordered based on their position.
• Unequal intervals : The differences between categories may not be equal or measurable.
• Examples : Educational attainment (high school diploma, bachelor's degree, master's degree), Likert scale responses (strongly agree, agree, neutral, disagree, strongly disagree).

Interval Scale

The interval scale measures data with equal intervals between consecutive points but lacks a true zero point. While the intervals between values are equal and meaningful, there is no absolute zero point that represents the absence of the measured quantity. Interval data allows for arithmetic operations such as addition and subtraction but not multiplication or division.

In interval scales:

• Equal intervals : The differences between consecutive values are equal and measurable.
• No true zero point : Zero does not represent the absence of the measured quantity.
• Examples : Temperature measured in Celsius or Fahrenheit, dates on the calendar.

Interval data is typically represented using numerical values, and common statistical analyses include mean calculations, standard deviation, and t-tests.

Ratio Scale

The ratio scale is the most informative measurement scale, featuring equal intervals between values and a true zero point where zero represents the absence of the measured quantity. Ratio data allows for meaningful ratios and comparisons between values, as well as all arithmetic operations.

In ratio scales:

• Equal intervals with a true zero point : Zero represents the absence of the measured quantity.
• Meaningful ratios : Ratios between values are meaningful and interpretable.
• Examples : Height, weight, age, income.

Ratio data is represented using numerical values, and common statistical analyses include mean calculations, standard deviation, correlations, and regression analysis.

Comparing Nominal Data with Other Measurement Scales

When comparing nominal data with other measurement scales, it's essential to recognize the qualitative nature of nominal data and its differences from ordinal, interval, and ratio scales.

• Qualitative vs. Quantitative : Nominal data represents qualitative attributes, while ordinal, interval, and ratio data represent quantitative measurements.
• Order and Hierarchy : Nominal data lacks order or hierarchy, while ordinal data has a meaningful order but unequal intervals.
• Arithmetic Operations : Unlike interval and ratio data, nominal and ordinal data cannot be subjected to arithmetic operations such as addition, subtraction, multiplication, or division.
• Statistical Analyses : Different measurement scales require different statistical analyses. Nominal data is often analyzed using non-parametric tests, while interval and ratio data can be analyzed using parametric tests.

Understanding these distinctions is crucial for selecting appropriate data representation techniques, statistical analyses, and interpretation methods in data analysis.

Data Analysis Techniques for Nominal Data

Analyzing nominal data involves various techniques to summarize, visualize, and interpret categorical information. Let's explore these techniques and understand how they contribute to gaining insights from nominal data.

Frequency Distribution

Frequency distribution is a fundamental technique for analyzing nominal data, providing a summary of the number of occurrences of each category within a dataset. It helps identify patterns, trends, and distributions within the data by counting the frequency of each category.

To Create a Frequency Distribution:

• Identify Categories : Determine the distinct categories or labels within the nominal dataset.
• Count Frequencies : Count the number of observations belonging to each category.
• Tabulate Data : Organize the frequencies into a table format, listing each category along with its corresponding frequency count.
• Visualize Data : Visualize the frequency distribution using bar charts or pie charts to enhance understanding and interpretation.

Frequency distributions provide valuable insights into the distribution of categorical variables, allowing researchers to identify dominant categories, outliers, and patterns of interest.

The mode is a measure of central tendency that represents the most frequently occurring category or value within a dataset. For nominal data, the mode is simply the category with the highest frequency count.

To Calculate the Mode:

• Identify Categories : Determine the distinct categories within the dataset.
• Count Frequencies : Calculate the frequency count for each category.
• Find the Mode : Identify the category with the highest frequency count.

The mode is particularly useful for identifying the most common or prevalent category within a dataset. It provides a simple and intuitive summary of the central tendency of nominal data.

Chi-square Test

The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. It compares the observed frequencies of categories with the expected frequencies under the assumption of independence between the variables.

To Conduct a Chi-square Test:

• Formulate Hypotheses : Define the null hypothesis (no association) and alternative hypothesis (association) based on the research question.
• Calculate Expected Frequencies : Calculate the expected frequencies for each category under the assumption of independence.
• Compute Test Statistic : Calculate the chi-square statistic using the formula: χ^2 = ∑((Oi - Ei)^2 / Ei) Where Oi is the observed frequency, and Ei is the expected frequency for each category.
• Assess Significance : Compare the calculated chi-square statistic with the critical value from the chi-square distribution to determine statistical significance.

The chi-square test is widely used in various fields, including social sciences, market research, and epidemiology, to assess relationships between categorical variables.

Cross-tabulation

Cross-tabulation, also known as contingency table analysis, is a technique for examining the relationship between two or more categorical variables by organizing data into a table format. It allows researchers to compare the distribution of categories across different groups or conditions.

To Conduct Cross-tabulation:

• Identify Variables : Select the categorical variables of interest for cross-tabulation.
• Create Contingency Table : Construct a contingency table with rows representing one variable and columns representing another variable.
• Calculate Frequencies : Count the frequencies of observations for each combination of categories.
• Interpret Results : Analyze the patterns and associations observed in the contingency table to draw conclusions about the relationship between variables.

Cross-tabulation is a powerful tool for exploring interactions and dependencies between categorical variables, providing valuable insights into the underlying structure of the data.

Bar Charts and Pie Charts

Bar charts and pie charts are graphical representations of nominal data, visually displaying the distribution of categories within a dataset. These visualizations help researchers and stakeholders understand the relative frequencies of different categories and identify patterns or trends.

• Bar Charts : Bar charts represent categorical data using rectangular bars of varying lengths, with each bar corresponding to a category and its height proportional to the frequency count.
• Pie Charts : Pie charts display categorical data as a circular diagram divided into slices, with each slice representing a category and its size proportional to the frequency count.

Bar charts and pie charts are effective tools for communicating findings and presenting insights in a visually appealing format. They are widely used in reports, presentations, and publications to convey key messages derived from nominal data analysis.

Interpretation of Nominal Data Analysis

After analyzing nominal data, it's crucial to interpret the results accurately to draw meaningful conclusions and insights. Let's explore the interpretation of nominal data analysis in various contexts, including frequency distributions, cross-tabulations, chi-square test results, and effective communication of findings.

Drawing Conclusions from Frequency Distributions

Frequency distributions provide a summary of the number of occurrences of each category within a dataset. To draw conclusions from frequency distributions:

• Identify Dominant Categories : Determine which categories have the highest frequencies, indicating the most prevalent attributes within the dataset.
• Identify Outliers : Look for categories with unusually high or low frequencies compared to others, which may indicate unique or rare attributes.
• Identify Patterns : Analyze the distribution of categories to identify any patterns or trends, such as clustering or dispersion of data .
• Compare Subgroups : If applicable, compare frequency distributions across different subgroups or conditions to identify differences or similarities.

Interpreting frequency distributions allows researchers to gain insights into the distribution and prevalence of different attributes within the dataset, informing further analysis and decision-making.

Analyzing Patterns in Cross-tabulations

Cross-tabulations provide a means to examine the relationship between two or more categorical variables by organizing data into a table format. To analyze patterns in cross-tabulations:

• Examine Cell Counts : Review the frequencies of observations in each cell of the contingency table to identify patterns or associations.
• Calculate Percentages : Calculate row percentages, column percentages, or total percentages to compare the distribution of categories across different variables.
• Test for Independence : Use statistical tests, such as the chi-square test, to determine whether there is a significant association between variables.

Analyzing patterns in cross-tabulations helps identify relationships and dependencies between categorical variables, providing insights into the underlying structure of the data.

Interpreting Chi-square Test Results

The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. To interpret chi-square test results:

• Compare Observed and Expected Frequencies : Review the calculated chi-square statistic and compare it to the critical value from the chi-square distribution.
• Assess Significance : Determine whether the chi-square statistic is statistically significant at a predetermined level of significance (e.g., p < 0.05).
• Interpret Effect Size : Consider the effect size measures, such as Cramer's V or Phi coefficient, to assess the strength of the association between variables.
• Examine Residuals : Analyze standardized residuals to identify specific cells contributing to the observed association.

Interpreting chi-square test results helps determine whether there is evidence of a significant association between categorical variables and provides insights into the nature and strength of the relationship.

Communicating Findings Effectively

Effective communication of findings is essential for conveying insights derived from nominal data analysis to stakeholders and decision-makers. To communicate findings effectively:

• Use Clear and Concise Language : Present findings in plain language, avoiding jargon or technical terms that may be unfamiliar to the audience.
• Use Visualizations : Utilize graphical representations, such as bar charts, pie charts, or tables, to visually illustrate key findings and trends.
• Provide Context : Offer context for the findings by explaining the significance of the results and their implications for decision-making or further research.
• Tailor Messaging to the Audience : Consider the needs and preferences of the audience when communicating findings, adapting the message to resonate with their interests and priorities.

Effective communication of findings ensures that insights derived from nominal data analysis are understood and utilized to inform decision-making and drive action.

Nominal Data Examples

Understanding nominal data is essential for various fields and industries. Let's delve into some detailed examples to grasp how nominal data manifests in different contexts.

Demographic Data

Demographic studies rely heavily on nominal data to classify individuals based on various attributes:

• Gender : Male, Female, Non-binary
• Education Level : High School Diploma, Bachelor's Degree, Master's Degree, PhD

Product Categories

In retail and market research, products are categorized into distinct groups:

• Apparel : Tops, Bottoms, Dresses, Accessories
• Food : Dairy, Produce, Meat, Frozen Foods
• Electronics : Smartphones, Laptops, Televisions, Headphones

Survey Responses

Survey data often involves nominal variables to categorize responses:

• Preferred Communication Method : Email, Phone, In-person
• Likert Scale Responses : Strongly Agree, Agree, Neutral, Disagree, Strongly Disagree
• Political Affiliation : Republican, Democrat, Independent, Other

Medical Diagnosis

Medical diagnoses are classified using nominal data to distinguish different conditions:

• Disease Status : Infected, Non-infected
• Cancer Subtypes : Breast Cancer, Lung Cancer, Prostate Cancer
• Severity Levels : Mild, Moderate, Severe

Geographic Regions

Geographic data is categorized into regions and zones:

• Continents : Africa, Asia, Europe, North America, South America
• Climate Zones : Tropical, Temperate, Polar
• Administrative Units : Countries, States, Provinces, Cities

Examining these examples gives you a deeper understanding of how nominal data is applied across various domains. Whether it's analyzing demographics, market segments, survey responses, medical conditions, or geographical regions, nominal data provides a versatile framework for classification and interpretation.

Nominal Data Challenges and Considerations

Working with nominal data presents several challenges and considerations that researchers must address to ensure accurate analysis and interpretation. These challenges include:

• Data Quality and Accuracy : Ensuring the quality and accuracy of nominal data is essential for reliable analysis. Common issues include missing values, misclassification, and data entry errors. Implementing data validation checks and cleaning procedures is vital to minimize errors and improve data quality.
• Handling Missing Values : Missing values can introduce bias and affect the validity of analysis results. Researchers must develop strategies for handling missing data, such as imputation techniques, deletion of incomplete cases, or sensitivity analysis to assess the impact of missingness on results.
• Dealing with Large Datasets : Large datasets present challenges in terms of processing power, storage, and analysis techniques. Researchers must develop strategies for efficiently managing and analyzing large volumes of nominal data, such as data sampling , parallel computing, or distributed computing frameworks.
• Addressing Bias and Confounding Factors : Bias and confounding factors can distort analysis results and lead to erroneous conclusions. Researchers must be vigilant in identifying and controlling for potential sources of bias , such as selection bias, measurement bias, or confounding variables. Strategies include randomization, blinding, and statistical adjustment techniques.

Best Practices for Handling Nominal Data

To ensure effective handling and analysis of nominal data, researchers should adhere to best practices throughout the data lifecycle. These best practices include:

• Data Cleaning and Preprocessing : Thoroughly clean and preprocess nominal data before analysis to address missing values, outliers, and inconsistencies. This may involve data validation, transformation, and normalization techniques to improve data quality and consistency.
• Choosing Appropriate Analysis Techniques : Select analysis techniques that are suitable for nominal data, such as frequency distributions, chi-square tests, or cross-tabulations. Consider the research question, data characteristics, and assumptions of the analysis techniques when choosing appropriate methods.
• Ensuring Data Privacy and Security : Protect the privacy and confidentiality of nominal data by implementing appropriate security measures, such as encryption, access controls, and anonymization techniques. Comply with data protection regulations and ethical guidelines to safeguard sensitive information.
• Documenting Data and Analysis Procedures : Maintain comprehensive documentation of nominal data and analysis procedures to ensure transparency, reproducibility, and auditability. Document data sources, variables, coding schemes, and analysis techniques to facilitate replication and validation of results.

Adhering to these best practices helps ensure the reliability, validity, and reproducibility of nominal data analysis, leading to more robust and trustworthy research outcomes.

Conclusion for Nominal Data

Nominal data plays a vital role in data analysis across various fields and industries. By categorizing information into distinct labels or categories, nominal data enables researchers to organize, analyze, and interpret complex datasets effectively. From demographic studies to market research and medical diagnosis, nominal data provides valuable insights into group characteristics, preferences , and behaviors. Understanding the basics of nominal data, including its definition, characteristics, and analysis techniques, empowers individuals to make informed decisions and draw meaningful conclusions from their data. In today's data-driven world, the importance of nominal data cannot be overstated. Whether you're conducting research, making business decisions, or simply exploring patterns in your data, nominal data serves as a fundamental building block for analysis and interpretation. By mastering the concepts and techniques outlined in this guide, you'll be equipped with the knowledge and skills needed to harness the power of nominal data and unlock actionable insights that drive success in your endeavors.

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StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

StatPearls [Internet].

Types of variables and commonly used statistical designs.

Jacob Shreffler ; Martin R. Huecker .

Affiliations

Last Update: March 6, 2023 .

• Definition/Introduction

Suitable statistical design represents a critical factor in permitting inferences from any research or scientific study. [1]  Numerous statistical designs are implementable due to the advancement of software available for extensive data analysis. [1]  Healthcare providers must possess some statistical knowledge to interpret new studies and provide up-to-date patient care. We present an overview of the types of variables and commonly used designs to facilitate this understanding. [2]

• Issues of Concern

Individuals who attempt to conduct research and choose an inappropriate design could select a faulty test and make flawed conclusions. This decision could lead to work being rejected for publication or (worse) lead to erroneous clinical decision-making, resulting in unsafe practice. [1]  By understanding the types of variables and choosing tests that are appropriate to the data, individuals can draw appropriate conclusions and promote their work for an application. [3]

To determine which statistical design is appropriate for the data and research plan, one must first examine the scales of each measurement. [4]  Multiple types of variables determine the appropriate design.

Ordinal data (also sometimes referred to as discrete) provide ranks and thus levels of degree between the measurement. [5]  Likert items can serve as ordinal variables, but the Likert scale, the result of adding all the times, can be treated as a continuous variable. [6]  For example, on a 20-item scale with each item ranging from 1 to 5, the item itself can be an ordinal variable, whereas if you add up all items, it could result in a range from 20 to 100. A general guideline for determining if a variable is ordinal vs. continuous: if the variable has more than ten options, it can be treated as a continuous variable. [7]  The following examples are ordinal variables:

• Likert items
• Cancer stages
• Residency Year

Nominal, Categorical, Dichotomous, Binary

Other types of variables have interchangeable terms. Nominal and categorical variables describe samples in groups based on counts that fall within each category, have no quantitative relationships, and cannot be ranked. [8]  Examples of these variables include:

• Service (i.e., emergency, internal medicine, psychiatry, etc.)
• Mode of Arrival (ambulance, helicopter, car)

A dichotomous or a binary variable is in the same family as nominal/categorical, but this type has only two options. Binary logistic regression, which will be discussed below, has two options for the outcome of interest/analysis. Often used as (yes/no), examples of dichotomous or binary variables would be:

• Alive (yes vs. no)
• Insurance (yes vs. no)
• Readmitted (yes vs. no)

With this overview of the types of variables provided, we will present commonly used statistical designs for different scales of measurement. Importantly, before deciding on a statistical test, individuals should perform exploratory data analysis to ensure there are no issues with the data and consider type I, type II errors, and power analysis. Furthermore, investigators should ensure appropriate statistical assumptions. [9] [10]  For example, parametric tests, including some discussed below (t-tests, analysis of variance (ANOVA), correlation, and regression), require the data to have a normal distribution and that the variances within each group are similar. [6] [11]  After eliminating any issues based on exploratory data analysis and reducing the likelihood of committing type I and type II errors, a statistical test can be chosen. Below is a brief introduction to each of the commonly used statistical designs with examples of each type. An example of one research focus, with each type of statistical design discussed, can be found in Table 1 to provide more examples of commonly used statistical designs. 

Commonly Used Statistical Designs

Independent Samples T-test

An independent samples t-test allows a comparison of two groups of subjects on one (continuous) variable. Examples in biomedical research include comparing results of treatment vs. control group and comparing differences based on gender (male vs. female).

Example: Does adherence to the ketogenic diet (yes/no; two groups) have a differential effect on total sleep time (minutes; continuous)?

Paired T-test

A paired t-test analyzes one sample population, measuring the same variable on two different occasions; this is often useful for intervention and educational research.

Example :  Does participating in a research curriculum (one group with intervention) improve resident performance on a test to measure research competence (continuous)?

One-Way Analysis of Variance (ANOVA)

Analysis of variance (ANOVA), as an extension of the t-test, determines differences amongst more than two groups, or independent variables based on a dependent variable. [11]  ANOVA is preferable to conducting multiple t-tests as it reduces the likelihood of committing a type I error.

Example: Are there differences in length of stay in the hospital (continuous) based on the mode of arrival (car, ambulance, helicopter, three groups)?

Repeated Measures ANOVA

Another procedure commonly used if the data for individuals are recurrent (repeatedly measured) is a repeated-measures ANOVA. [1]  In these studies, multiple measurements of the dependent variable are collected from the study participants. [11]  A within-subjects repeated measures ANOVA determines effects based on the treatment variable alone, whereas mixed ANOVAs allow both between-group effects and within-subjects to be considered.

Within-Subjects Example: How does ketamine effect mean arterial pressure (continuous variable) over time (repeated measurement)?

Mixed Example: Does mean arterial pressure (continuous) differ between males and females (two groups; mixed) on ketamine throughout a surgical procedure (over time; repeated measurement)?  

Nonparametric Tests

Nonparametric tests, such as the Mann-Whitney U test (two groups; nonparametric t-test), Kruskal Wallis test (multiple groups; nonparametric ANOVA), Spearman’s rho (nonparametric correlation coefficient) can be used when data are ordinal or lack normality. [3] [5]  Not requiring normality means that these tests allow skewed data to be analyzed; they require the meeting of fewer assumptions. [11]

Example: Is there a relationship between insurance status (two groups) and cancer stage (ordinal)?  

A Chi-square test determines the effect of relationships between categorical variables, which determines frequencies and proportions into which these variables fall. [11]  Similar to other tests discussed, variants and extensions of the chi-square test (e.g., Fisher’s exact test, McNemar’s test) may be suitable depending on the variables. [8]

Example: Is there a relationship between individuals with methamphetamine in their system (yes vs. no; dichotomous) and gender (male or female; dichotomous)?

Correlation

Correlations (used interchangeably with ‘associations’) signal patterns in data between variables. [1]  A positive association occurs if values in one variable increase as values in another also increase. A negative association occurs if variables in one decrease while others increase. A correlation coefficient, expressed as r,  describes the strength of the relationship: a value of 0 means no relationship, and the relationship strengthens as r approaches 1 (positive relationship) or -1 (negative association). [5]

Example: Is there a relationship between age (continuous) and satisfaction with life survey scores (continuous)?

Linear Regression

Regression allows researchers to determine the degrees of relationships between a dependent variable and independent variables and results in an equation for prediction. [11]  A large number of variables are usable in regression methods.

Example: Which admission to the hospital metrics (multiple continuous) best predict the total length of stay (minutes; continuous)?

Binary Logistic Regression

This type of regression, which aims to predict an outcome, is appropriate when the dependent variable or outcome of interest is binary or dichotomous (yes/no; cured/not cured). [12]

Example: Which panel results (multiple of continuous, ordinal, categorical, dichotomous) best predict whether or not an individual will have a positive blood culture (dichotomous/binary)?

An example of one research focus, with each type of statistical design discussed, can be found in Table 1 to provide more examples of commonly used statistical designs.

(See Types of Variables and Statistical Designs Table 1)

• Clinical Significance

Though numerous other statistical designs and extensions of methods covered in this article exist, the above information provides a starting point for healthcare providers to become acquainted with variables and commonly used designs. Researchers should study types of variables before determining statistical tests to obtain relevant measures and valid study results. [6]  There is a recommendation to consult a statistician to ensure appropriate usage of the statistical design based on the variables and that the assumptions are upheld. [1]  With the variety of statistical software available, investigators must a priori understand the type of statistical tests when designing a study. [13]  All providers must interpret and scrutinize journal publications to make evidence-based clinical decisions, and this becomes enhanced by a limited but sound understanding of variables and commonly used study designs. [14]

• Nursing, Allied Health, and Interprofessional Team Interventions

All interprofessional healthcare team members need to be familiar with study design and the variables used in studies to accurately evaluate new data and studies as they are published and apply the latest data to patient care and drive optimal outcomes.

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Types of Variables and Statistical Designs Table 1 Contributed by Martin Huecker, MD and Jacob Shreffler, PhD

Disclosure: Jacob Shreffler declares no relevant financial relationships with ineligible companies.

Disclosure: Martin Huecker declares no relevant financial relationships with ineligible companies.

This book is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ), which permits others to distribute the work, provided that the article is not altered or used commercially. You are not required to obtain permission to distribute this article, provided that you credit the author and journal.

• Cite this Page Shreffler J, Huecker MR. Types of Variables and Commonly Used Statistical Designs. [Updated 2023 Mar 6]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

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What is the difference between categorical, ordinal and interval variables?

In talking about variables, sometimes you hear variables being described as categorical (or sometimes nominal), or ordinal, or interval.  Below we will define these terms and explain why they are important.

Categorical or nominal

A categorical variable (sometimes called a nominal variable) is one that has two or more categories, but there is no intrinsic ordering to the categories.  For example, a binary variable (such as yes/no question) is a categorical variable having two categories (yes or no) and there is no intrinsic ordering to the categories.  Hair color is also a categorical variable having a number of categories (blonde, brown, brunette, red, etc.) and again, there is no agreed way to order these from highest to lowest.  A purely nominal variable is one that simply allows you to assign categories but you cannot clearly order the categories.  If the variable has a clear ordering, then that variable would be an ordinal variable, as described below.

An ordinal variable is similar to a categorical variable.  The difference between the two is that there is a clear ordering of the categories.  For example, suppose you have a variable, economic status, with three categories (low, medium and high).  In addition to being able to classify people into these three categories, you can order the categories as low, medium and high. Now consider a variable like educational experience (with values such as elementary school graduate, high school graduate, some college and college graduate). These also can be ordered as elementary school, high school, some college, and college graduate.  Even though we can order these from lowest to highest, the spacing between the values may not be the same across the levels of the variables. Say we assign scores 1, 2, 3 and 4 to these four levels of educational experience and we compare the difference in education between categories one and two with the difference in educational experience between categories two and three, or the difference between categories three and four. The difference between categories one and two (elementary and high school) is probably much bigger than the difference between categories two and three (high school and some college).  In this example, we can order the people in level of educational experience but the size of the difference between categories is inconsistent (because the spacing between categories one and two is bigger than categories two and three).  If these categories were equally spaced, then the variable would be an interval variable.

Interval (also called numerical)

An interval variable is similar to an ordinal variable, except that the intervals between the values of the numerical variable are equally spaced.  For example, suppose you have a variable such as annual income that is measured in dollars, and we have three people who make \$10,000, \$15,000 and \$20,000. The second person makes \$5,000 more than the first person and \$5,000 less than the third person, and the size of these intervals is the same.  If there were two other people who make \$90,000 and \$95,000, the size of that interval between these two people is also the same (\$5,000).

Why does it matter whether a variable is categorical , ordinal or interval?

Statistical computations and analyses assume that the variables have a specific levels of measurement.  For example, it would not make sense to compute an average hair color.  An average of a nominal variable does not make much sense because there is no intrinsic ordering of the levels of the categories.  Moreover, if you tried to compute the average of educational experience as defined in the ordinal section above, you would also obtain a nonsensical result.  Because the spacing between the four levels of educational experience is very uneven, the meaning of this average would be very questionable.  In short, an average requires a variable to be numerical. Sometimes you have variables that are “in between” ordinal and numerical, for example, a five-point Likert scale with values “strongly agree”, “agree”, “neutral”, “disagree” and “strongly disagree”.  If we cannot be sure that the intervals between each of these five values are the same, then we would not be able to say that this is an interval variable, but we would say that it is an ordinal variable.  However, in order to be able to use statistics that assume the variable is numerical, we will assume that the intervals are equally spaced.

Does it matter if my dependent variable is normally distributed?

When you are doing a t-test or ANOVA, the assumption is that the distribution of the sample means are normally distributed.  One way to guarantee this is for the distribution of the individual observations from the sample to be normal.  However, even if the distribution of the individual observations is not normal, the distribution of the sample means will be normally distributed if your sample size is about 30 or larger.  This is due to the “central limit theorem” that shows that even when a population is non-normally distributed, the distribution of the “sample means” will be normally distributed when the sample size is 30 or more, for example see Central limit theorem demonstration .

If you are doing a regression analysis, then the assumption is that your residuals are normally distributed.  One way to make it very likely to have normal residuals is to have a dependent variable that is normally distributed and predictors that are all normally distributed; however, this is not necessary for your residuals to be normally distributed.  You can see the following resources for more information:

• Regression with Stata: Chapter 2 – Regression Diagnostics
• Regression with SAS: Chapter 2 -Regression Diagnostics
• Introduction to Regression with SPSS: Lesson 2 – Regression Diagnostics

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• Nominal, Ordinal, Interval & Ratio Variable + [Examples]

• Data Collection

Measurement variables, or simply variables are commonly used in different physical science fields—including mathematics, computer science, and statistics. It has a different meaning and application in each of these fields.

In algebra, which is a common aspect of mathematics, a variable is simply referred to as an unknown value. This meaning is what is adopted in computer science, where it is used to define values when writing in various computer programming languages.

However, variables have a slightly different meaning and use in statistics. Although it also slightly intersects with algebraic meaning, its uses and definition differ greatly.

What is a Measurement Variable?

A measurement variable is an unknown attribute that measures a particular entity and can take one or more values. It is commonly used for scientific research purposes. Unlike in mathematics, measurement variables can not only take quantitative values but can also take qualitative values in statistics.

Statistical variables can be measured using measurement instruments, algorithms, or even human discretion.

How we measure variables are called scale of measurements, and it affects the type of analytical techniques that can be used on the data, and conclusions that can be drawn from it. Measurement variables are categorized into four types, namely; nominal , ordinal , interval and ratio variables. 

Types of Measurement Variables

Nominal variable.

A nominal variable is a type of variable that is used to name, label or categorize particular attributes that are being measured. It takes qualitative values representing different categories, and there is no intrinsic ordering of these categories.

You can code nominal variables with numbers, but the order is arbitrary and arithmetic operations cannot be performed on the numbers. This is the case when a person’s phone number, National Identification Number postal code, etc. are being collected.

A nominal variable is one of the 2 types of categorical variables and is the simplest among all the measurement variables. Some examples of nominal variables include gender, Name, phone, etc.

Types of Nominal Variable

In statistics, there is no standard classification of nominal variables into types. However, we can classify them into different types based on some factors. We will be considering 2 factors in this case, namely; collection technique and numeric property.

Nominal Variable Classification Based on Collection Technique

There are different methods of collecting nominal variables, which may vary according to the purpose of collecting nominal data in the first place. Some of these methods include surveys, questionnaires, interviews, etc.

It doesn’t matter which method is used for data collection, one thing is however common to these methods—they are implemented using questions. The respondents are either asked, open-ended or closed-ended.

The open-ended technique gives respondents the freedom to respond the way they like. They are allowed to freely express their emotions.

This technique is used to collect detailed and descriptive information. For example, an organization who wants to receive feedback from its customers may ask, “How do you think we can improve our service?”—where the question asked is the nominal variable.

• Closed-ended

This technique restricts the kind of response a respondent can give to the questions asked. Questionnaires give predefined options for the respondent to choose from.

Unlike open-ended , this technique collects data from the questionnaire’s point of view, thereby limiting the respondent’s freedom. A closed-ended approach to the question asked above will be

How do you think we can improve our service?

• Better design
• Train chefs
• More attractive plating

Nominal Variable Classification Based on Numeric Property

Nominal variables are sometimes numeric but do not possess numerical characteristics. Some of thee numeric nominal variables are; phone numbers, student numbers, etc.

Therefore, a nominal variable can be classified as either numeric or not.

Characteristics of Nominal Variable

• The responses to a nominal variable can be divided into two or more categories. For example, gender is a nominal variable that can take responses male/female, which are the categories the nominal variable is divided into.
• A nominal variable is qualitative, which means numbers are used here only to categorize or identify objects. For example, the number at the back of a player’s jersey is used to identify the position he/she is playing.
• They can also take quantitative values. However, these quantitative values do not have numeric properties. That is, arithmetic operations cannot be performed on them.

Examples of Nominal Variable

• Personal Biodata: The variables included in a personal biodata is a nominal variable. This includes the name, date of birth, gender, etc. E.g
• Full Name _____
• Email address_____
• Customer Feedback: Organizations use this to get feedback about their product or service from customers. E.g.

How long have you been using our product?

• Less than 6 months
• What do you think about our mobile app?_____

Categories of Nominal Variable

There are 2 main categories of nominal variables, namely; the matched and unmatched categories.

• The Matched Category: In this category, all the values of the nominal variable are paired up or grouped so that each member of a group has similar characteristics except for the variable under investigation.
• The Unmatched Category: This is an independent sample of unrelated groups of data. Unlike in the matched category, the values in a group do not necessarily have similar characteristics.

Ordinal Variable

An ordinal variable is a type of measurement variable that takes values with an order or rank. It is the 2nd level of measurement and is an extension of the nominal variable.

They are built upon nominal scales by assigning numbers to objects to reflect a rank or ordering on an attribute. Also, there is no standard ordering in the ordinal variable scale . 

In another sense, we could say the difference in the rank of an ordinal variable is not equal. It is mostly classified as one of the 2 types of categorical variables, while in some cases it is said to be a midpoint between categorical and numerical variables .

Types of Ordinal Variable

Similar to the nominal variable, there is no standard classification of ordinal variables into types. However, we will be classifying them according to the value assignment. I.e. Ordinal Variable type based on numerical and non numerical values.

What do we mean by value assignment?

The possible values of ordinal variables do have a rank or order, and a numeric value may be assigned to each rank for respondents to better understand them. In other cases, numeric values are not assigned to the ranks. 

Below are examples of ordinal variable with and without numeric value.

Ordinal Variable With Numeric Value

How satisfied are you with our service tonight?

• Very satisfied
• Indifferent
• Dissatisfied
• Very dissatisfied

Ordinal Variable Without Numeric value

Characteristics of ordinal variable.

• It is an extension of nominal data.
• It has no standardized interval scale.
• It establishes a relative rank.
• It measures qualitative traits.
• The median and mode can be analyzed.
• It has a rank or order.

Examples of Ordinal Variable

Likert Scale: A Likert scale is a psychometric scale used by researchers to prepare questionnaires and get people’s opinions.

How satisfied are you with our service? 

Interval Scale: each response in an interval scale is an interval on its own.

How old are you?

• 13-19 years
• 20-30 years
• 31-50 years

Categories of Ordinal Variable

There are also 2 main categories of ordinal variables, namely; the matched and unmatched category.

• The Matched Category: In the matched category, each member of a data sample is paired with similar members of every other sample concerning all other variables, aside from the one under consideration. This is done to obtain a better estimation of differences.
• The Unmatched Category: Unmatched category, also known as the independent category contains randomly selected samples with variables that do not depend on the values of other ordinal variables. Most researchers base their analysis on the assumption that the samples are independent, except in a few cases.

Differences Between Nominal and Ordinal Variable

• The ordinal variable has an intrinsic order while nominal variables do not have an order.
• It is only the mode of a nominal variable that can be analyzed while analysis like the median, mode, quantile, percentile, etc. can be performed on ordinal variables.
• The tests carried on nominal and ordinal variables are different.

Similarities Between Nominal and Ordinal Variable

• They are both types of categorical variables.
• They both have an inconclusive mean and a mode.
• They are both visualized using bar charts and pie charts.

Read Also: Nominal Vs Ordinal Data: 13 Key Differences & Similarities

Interval Variable

The interval variable is a measurement variable that is used to define values measured along a scale, with each point placed at an equal distance from one another. It is one of the 2 types of numerical variables and is an extension of the ordinal variable.

Unlike ordinal variables that take values with no standardized scale, every point in the interval scale is equidistant. Arithmetic operations can also be performed on the numerical values of the interval variable.

These arithmetic operations are, however, just limited to addition and subtraction. Examples of interval variables include; temperature measured in Celsius or Fahrenheit, time, generation age range, etc.

Characteristics of Interval Variable

• It is one of the 2 types of quantitative variables. It takes numeric values and may be classified as a continuous variable type.
• Arithmetic operations can be performed on interval variables. However, these operations are restricted to only addition and subtraction.
• The interval variable is an extension of the ordinal variable. In other words, we could say interval variables are built upon ordinary variables.
• The intervals on the scale are equal in an interval variable. The scale is equidistant.
• The variables are measured using an interval scale, which not only shows the order but also shows the exact difference in the value.
• It has no zero value.

Examples of Interval Variable

• Temperature: Temperature, when measured in Celsius or Fahrenheit is considered as an interval variable.
• Mark Grading: When grading test scores like the SAT, for example, we use numbers as a reference point.
• Time: Time, if measured using a 12-hour clock, or it is measured during the day is an example of interval data .
• IQ Test: An individual cannot have a zero IQ, therefore satisfying the no zero property of an interval variable. The level of an individual’s IQ will be determined, depending on which interval the score falls in.
• CGPA : This is an acronym for Cumulative Grade Point Average. It is used to determine a student’s class of degree, which depends on the interval a student’s point falls in.
• Test: When grading test scores like the SAT, for example, the numbers from 0 to 200 are not used when scaling the raw score to the section score. In this case, absolute zero is not used as a reference point. Therefore, it is an interval the score is an interval variable.

Categories of Interval Variable

There are 2 main categories of interval variables, namely; normal distribution and non-normal distributions.

• Normal Distribution: It is also called Gaussian distribution and is used to represent real-valued random variables with unknown distribution. This can be further divided into matched and unmatched samples
• Non-Normal Distribution: It can also be called the Non-Gaussian distribution, and is used to represent real-valued random variables with known distribution. It can also be further divided into matched and unmatched samples.

Ratio Variable

The ratio variable is one of the 2 types of continuous variables, where the interval variable is the 2nd. It is an extension of the interval variable and is also the peak of the measurement variable types.

The only difference between the ratio variable and interval variable is that the ratio variable already has a zero value. For example, temperature, when measured in Kelvin is an example of ratio variables.

The presence of a zero-point accommodates the measurement in Kelvin. Also, unlike the interval variable multiplication and division operations can be performed on the values of a ratio variable.

Characteristics of Ratio Variable

• Ratio variables have absolute zero characteristics. The zero point makes is what makes it possible to measure multiple values and perform multiplication and division operations. Therefore, we can say that an object is twice as big or as long as another.
• It has an intrinsic order with an equidistant scale. That is, all the levels in the ratio scale has an equal distance.
• Due to the absolute point characteristics of a ratio variable, it doesn’t have a negative number like an interval variable. Therefore, before measuring any object on a ratio scale, researchers need to first study if it satisfies all the properties of an interval variable and also the zero point characteristic.
• Ratio variable is the peak type of measurement variable in statistical analysis. It allows for the addition, interaction, multiplication, and division of variables.

Also, all statistical analysis including mean, mode, median, etc. can be calculated on the ratio scale.

Examples of Ratio Variable

Here are some examples of ratio variables according to their uses:

• Multiple Choice Questions

Multiple choice questions are mostly used for academic testing and ratio variables are sometimes used in this case. Especially for mathematics tests, or word problems we see many examples of ratio variables.  

E.g. If Frank is 20 years old and Paul is twice as old as Frank. How old will Paul be in the next 10 years?

• Surveys/Questionnaires

Organizations use this tool whenever they want to get feedback about their product or service, perform market research, and competitive analysis. They use ratio variables to collect relevant data from respondents.

How much time do you spend on the internet daily?

• Less than 2 hours
• More than 6 hours
• Measurement

When registering for National passport, National ID Card, etc. there is always a need to profile applicants. As part of this profiling, a record of the applicant’s height, weight, etc. is usually taken.

What is your height in feet and inches?

• Less than 5ft
• 5ft 1inch – 5ft 4Inches
• 5ft 5Inches – 5ft 9Inches
• 6ft and above

E.g.2.  What is your weight in kgs?

• Less than 50 kgs
• More than 110 kgs

Categories of Ratio Variable

The categories of ratio variables are the same as that of interval variables. Ratio variables are also classified into Gaussian and Non-Gaussian distributions. 

They are both further divided into matched and unmatched samples.

The classification of variables according to their measurement type is very useful for researchers in concluding which analytical procedure should be used. It helps to determine the kind of data to be collected, how to collect it and which method of analysis should be used.

For a nominal variable, it is quite easy to collect data through open-ended or closed-ended questions . However, there is also a lot of downsides to this, as nominal data is the simplest data type and as such has limited capabilities.

Ratio variable, on the other hand, is the most complex of the measurement variables and as such can be used to perform the most complex analysis. Even at that, it may be unnecessarily complex times and one of the other variable types will be a better option.

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Home » Variables in Research – Definition, Types and Examples

Variables in Research – Definition, Types and Examples

Table of Contents

Variables in Research

Definition:

In Research, Variables refer to characteristics or attributes that can be measured, manipulated, or controlled. They are the factors that researchers observe or manipulate to understand the relationship between them and the outcomes of interest.

Types of Variables in Research

Types of Variables in Research are as follows:

Independent Variable

This is the variable that is manipulated by the researcher. It is also known as the predictor variable, as it is used to predict changes in the dependent variable. Examples of independent variables include age, gender, dosage, and treatment type.

Dependent Variable

This is the variable that is measured or observed to determine the effects of the independent variable. It is also known as the outcome variable, as it is the variable that is affected by the independent variable. Examples of dependent variables include blood pressure, test scores, and reaction time.

Confounding Variable

This is a variable that can affect the relationship between the independent variable and the dependent variable. It is a variable that is not being studied but could impact the results of the study. For example, in a study on the effects of a new drug on a disease, a confounding variable could be the patient’s age, as older patients may have more severe symptoms.

Mediating Variable

This is a variable that explains the relationship between the independent variable and the dependent variable. It is a variable that comes in between the independent and dependent variables and is affected by the independent variable, which then affects the dependent variable. For example, in a study on the relationship between exercise and weight loss, the mediating variable could be metabolism, as exercise can increase metabolism, which can then lead to weight loss.

Moderator Variable

This is a variable that affects the strength or direction of the relationship between the independent variable and the dependent variable. It is a variable that influences the effect of the independent variable on the dependent variable. For example, in a study on the effects of caffeine on cognitive performance, the moderator variable could be age, as older adults may be more sensitive to the effects of caffeine than younger adults.

Control Variable

This is a variable that is held constant or controlled by the researcher to ensure that it does not affect the relationship between the independent variable and the dependent variable. Control variables are important to ensure that any observed effects are due to the independent variable and not to other factors. For example, in a study on the effects of a new teaching method on student performance, the control variables could include class size, teacher experience, and student demographics.

Continuous Variable

This is a variable that can take on any value within a certain range. Continuous variables can be measured on a scale and are often used in statistical analyses. Examples of continuous variables include height, weight, and temperature.

Categorical Variable

This is a variable that can take on a limited number of values or categories. Categorical variables can be nominal or ordinal. Nominal variables have no inherent order, while ordinal variables have a natural order. Examples of categorical variables include gender, race, and educational level.

Discrete Variable

This is a variable that can only take on specific values. Discrete variables are often used in counting or frequency analyses. Examples of discrete variables include the number of siblings a person has, the number of times a person exercises in a week, and the number of students in a classroom.

Dummy Variable

This is a variable that takes on only two values, typically 0 and 1, and is used to represent categorical variables in statistical analyses. Dummy variables are often used when a categorical variable cannot be used directly in an analysis. For example, in a study on the effects of gender on income, a dummy variable could be created, with 0 representing female and 1 representing male.

Extraneous Variable

This is a variable that has no relationship with the independent or dependent variable but can affect the outcome of the study. Extraneous variables can lead to erroneous conclusions and can be controlled through random assignment or statistical techniques.

Latent Variable

This is a variable that cannot be directly observed or measured, but is inferred from other variables. Latent variables are often used in psychological or social research to represent constructs such as personality traits, attitudes, or beliefs.

Moderator-mediator Variable

This is a variable that acts both as a moderator and a mediator. It can moderate the relationship between the independent and dependent variables and also mediate the relationship between the independent and dependent variables. Moderator-mediator variables are often used in complex statistical analyses.

Variables Analysis Methods

There are different methods to analyze variables in research, including:

• Descriptive statistics: This involves analyzing and summarizing data using measures such as mean, median, mode, range, standard deviation, and frequency distribution. Descriptive statistics are useful for understanding the basic characteristics of a data set.
• Inferential statistics : This involves making inferences about a population based on sample data. Inferential statistics use techniques such as hypothesis testing, confidence intervals, and regression analysis to draw conclusions from data.
• Correlation analysis: This involves examining the relationship between two or more variables. Correlation analysis can determine the strength and direction of the relationship between variables, and can be used to make predictions about future outcomes.
• Regression analysis: This involves examining the relationship between an independent variable and a dependent variable. Regression analysis can be used to predict the value of the dependent variable based on the value of the independent variable, and can also determine the significance of the relationship between the two variables.
• Factor analysis: This involves identifying patterns and relationships among a large number of variables. Factor analysis can be used to reduce the complexity of a data set and identify underlying factors or dimensions.
• Cluster analysis: This involves grouping data into clusters based on similarities between variables. Cluster analysis can be used to identify patterns or segments within a data set, and can be useful for market segmentation or customer profiling.
• Multivariate analysis : This involves analyzing multiple variables simultaneously. Multivariate analysis can be used to understand complex relationships between variables, and can be useful in fields such as social science, finance, and marketing.

Examples of Variables

• Age : This is a continuous variable that represents the age of an individual in years.
• Gender : This is a categorical variable that represents the biological sex of an individual and can take on values such as male and female.
• Education level: This is a categorical variable that represents the level of education completed by an individual and can take on values such as high school, college, and graduate school.
• Income : This is a continuous variable that represents the amount of money earned by an individual in a year.
• Weight : This is a continuous variable that represents the weight of an individual in kilograms or pounds.
• Ethnicity : This is a categorical variable that represents the ethnic background of an individual and can take on values such as Hispanic, African American, and Asian.
• Time spent on social media : This is a continuous variable that represents the amount of time an individual spends on social media in minutes or hours per day.
• Marital status: This is a categorical variable that represents the marital status of an individual and can take on values such as married, divorced, and single.
• Blood pressure : This is a continuous variable that represents the force of blood against the walls of arteries in millimeters of mercury.
• Job satisfaction : This is a continuous variable that represents an individual’s level of satisfaction with their job and can be measured using a Likert scale.

Applications of Variables

Variables are used in many different applications across various fields. Here are some examples:

• Scientific research: Variables are used in scientific research to understand the relationships between different factors and to make predictions about future outcomes. For example, scientists may study the effects of different variables on plant growth or the impact of environmental factors on animal behavior.
• Business and marketing: Variables are used in business and marketing to understand customer behavior and to make decisions about product development and marketing strategies. For example, businesses may study variables such as consumer preferences, spending habits, and market trends to identify opportunities for growth.
• Healthcare : Variables are used in healthcare to monitor patient health and to make treatment decisions. For example, doctors may use variables such as blood pressure, heart rate, and cholesterol levels to diagnose and treat cardiovascular disease.
• Education : Variables are used in education to measure student performance and to evaluate the effectiveness of teaching strategies. For example, teachers may use variables such as test scores, attendance, and class participation to assess student learning.
• Social sciences : Variables are used in social sciences to study human behavior and to understand the factors that influence social interactions. For example, sociologists may study variables such as income, education level, and family structure to examine patterns of social inequality.

Purpose of Variables

Variables serve several purposes in research, including:

• To provide a way of measuring and quantifying concepts: Variables help researchers measure and quantify abstract concepts such as attitudes, behaviors, and perceptions. By assigning numerical values to these concepts, researchers can analyze and compare data to draw meaningful conclusions.
• To help explain relationships between different factors: Variables help researchers identify and explain relationships between different factors. By analyzing how changes in one variable affect another variable, researchers can gain insight into the complex interplay between different factors.
• To make predictions about future outcomes : Variables help researchers make predictions about future outcomes based on past observations. By analyzing patterns and relationships between different variables, researchers can make informed predictions about how different factors may affect future outcomes.
• To test hypotheses: Variables help researchers test hypotheses and theories. By collecting and analyzing data on different variables, researchers can test whether their predictions are accurate and whether their hypotheses are supported by the evidence.

Characteristics of Variables

Characteristics of Variables are as follows:

• Measurement : Variables can be measured using different scales, such as nominal, ordinal, interval, or ratio scales. The scale used to measure a variable can affect the type of statistical analysis that can be applied.
• Range : Variables have a range of values that they can take on. The range can be finite, such as the number of students in a class, or infinite, such as the range of possible values for a continuous variable like temperature.
• Variability : Variables can have different levels of variability, which refers to the degree to which the values of the variable differ from each other. Highly variable variables have a wide range of values, while low variability variables have values that are more similar to each other.
• Validity and reliability : Variables should be both valid and reliable to ensure accurate and consistent measurement. Validity refers to the extent to which a variable measures what it is intended to measure, while reliability refers to the consistency of the measurement over time.
• Directionality: Some variables have directionality, meaning that the relationship between the variables is not symmetrical. For example, in a study of the relationship between smoking and lung cancer, smoking is the independent variable and lung cancer is the dependent variable.

Advantages of Variables

Here are some of the advantages of using variables in research:

• Control : Variables allow researchers to control the effects of external factors that could influence the outcome of the study. By manipulating and controlling variables, researchers can isolate the effects of specific factors and measure their impact on the outcome.
• Replicability : Variables make it possible for other researchers to replicate the study and test its findings. By defining and measuring variables consistently, other researchers can conduct similar studies to validate the original findings.
• Accuracy : Variables make it possible to measure phenomena accurately and objectively. By defining and measuring variables precisely, researchers can reduce bias and increase the accuracy of their findings.
• Generalizability : Variables allow researchers to generalize their findings to larger populations. By selecting variables that are representative of the population, researchers can draw conclusions that are applicable to a broader range of individuals.
• Clarity : Variables help researchers to communicate their findings more clearly and effectively. By defining and categorizing variables, researchers can organize and present their findings in a way that is easily understandable to others.

Disadvantages of Variables

Here are some of the main disadvantages of using variables in research:

• Simplification : Variables may oversimplify the complexity of real-world phenomena. By breaking down a phenomenon into variables, researchers may lose important information and context, which can affect the accuracy and generalizability of their findings.
• Measurement error : Variables rely on accurate and precise measurement, and measurement error can affect the reliability and validity of research findings. The use of subjective or poorly defined variables can also introduce measurement error into the study.
• Confounding variables : Confounding variables are factors that are not measured but that affect the relationship between the variables of interest. If confounding variables are not accounted for, they can distort or obscure the relationship between the variables of interest.
• Limited scope: Variables are defined by the researcher, and the scope of the study is therefore limited by the researcher’s choice of variables. This can lead to a narrow focus that overlooks important aspects of the phenomenon being studied.
• Ethical concerns: The selection and measurement of variables may raise ethical concerns, especially in studies involving human subjects. For example, using variables that are related to sensitive topics, such as race or sexuality, may raise concerns about privacy and discrimination.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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Types of Variable

All experiments examine some kind of variable(s). A variable is not only something that we measure, but also something that we can manipulate and something we can control for. To understand the characteristics of variables and how we use them in research, this guide is divided into three main sections. First, we illustrate the role of dependent and independent variables. Second, we discuss the difference between experimental and non-experimental research. Finally, we explain how variables can be characterised as either categorical or continuous.

Dependent and Independent Variables

An independent variable, sometimes called an experimental or predictor variable, is a variable that is being manipulated in an experiment in order to observe the effect on a dependent variable, sometimes called an outcome variable.

Imagine that a tutor asks 100 students to complete a maths test. The tutor wants to know why some students perform better than others. Whilst the tutor does not know the answer to this, she thinks that it might be because of two reasons: (1) some students spend more time revising for their test; and (2) some students are naturally more intelligent than others. As such, the tutor decides to investigate the effect of revision time and intelligence on the test performance of the 100 students. The dependent and independent variables for the study are:

Dependent Variable: Test Mark (measured from 0 to 100)

Independent Variables: Revision time (measured in hours) Intelligence (measured using IQ score)

The dependent variable is simply that, a variable that is dependent on an independent variable(s). For example, in our case the test mark that a student achieves is dependent on revision time and intelligence. Whilst revision time and intelligence (the independent variables) may (or may not) cause a change in the test mark (the dependent variable), the reverse is implausible; in other words, whilst the number of hours a student spends revising and the higher a student's IQ score may (or may not) change the test mark that a student achieves, a change in a student's test mark has no bearing on whether a student revises more or is more intelligent (this simply doesn't make sense).

Therefore, the aim of the tutor's investigation is to examine whether these independent variables - revision time and IQ - result in a change in the dependent variable, the students' test scores. However, it is also worth noting that whilst this is the main aim of the experiment, the tutor may also be interested to know if the independent variables - revision time and IQ - are also connected in some way.

In the section on experimental and non-experimental research that follows, we find out a little more about the nature of independent and dependent variables.

Experimental and Non-Experimental Research

• Experimental research : In experimental research, the aim is to manipulate an independent variable(s) and then examine the effect that this change has on a dependent variable(s). Since it is possible to manipulate the independent variable(s), experimental research has the advantage of enabling a researcher to identify a cause and effect between variables. For example, take our example of 100 students completing a maths exam where the dependent variable was the exam mark (measured from 0 to 100), and the independent variables were revision time (measured in hours) and intelligence (measured using IQ score). Here, it would be possible to use an experimental design and manipulate the revision time of the students. The tutor could divide the students into two groups, each made up of 50 students. In "group one", the tutor could ask the students not to do any revision. Alternately, "group two" could be asked to do 20 hours of revision in the two weeks prior to the test. The tutor could then compare the marks that the students achieved.
• Non-experimental research : In non-experimental research, the researcher does not manipulate the independent variable(s). This is not to say that it is impossible to do so, but it will either be impractical or unethical to do so. For example, a researcher may be interested in the effect of illegal, recreational drug use (the independent variable(s)) on certain types of behaviour (the dependent variable(s)). However, whilst possible, it would be unethical to ask individuals to take illegal drugs in order to study what effect this had on certain behaviours. As such, a researcher could ask both drug and non-drug users to complete a questionnaire that had been constructed to indicate the extent to which they exhibited certain behaviours. Whilst it is not possible to identify the cause and effect between the variables, we can still examine the association or relationship between them. In addition to understanding the difference between dependent and independent variables, and experimental and non-experimental research, it is also important to understand the different characteristics amongst variables. This is discussed next.

Categorical and Continuous Variables

Categorical variables are also known as discrete or qualitative variables. Categorical variables can be further categorized as either nominal , ordinal or dichotomous .

• Nominal variables are variables that have two or more categories, but which do not have an intrinsic order. For example, a real estate agent could classify their types of property into distinct categories such as houses, condos, co-ops or bungalows. So "type of property" is a nominal variable with 4 categories called houses, condos, co-ops and bungalows. Of note, the different categories of a nominal variable can also be referred to as groups or levels of the nominal variable. Another example of a nominal variable would be classifying where people live in the USA by state. In this case there will be many more levels of the nominal variable (50 in fact).
• Dichotomous variables are nominal variables which have only two categories or levels. For example, if we were looking at gender, we would most probably categorize somebody as either "male" or "female". This is an example of a dichotomous variable (and also a nominal variable). Another example might be if we asked a person if they owned a mobile phone. Here, we may categorise mobile phone ownership as either "Yes" or "No". In the real estate agent example, if type of property had been classified as either residential or commercial then "type of property" would be a dichotomous variable.
• Ordinal variables are variables that have two or more categories just like nominal variables only the categories can also be ordered or ranked. So if you asked someone if they liked the policies of the Democratic Party and they could answer either "Not very much", "They are OK" or "Yes, a lot" then you have an ordinal variable. Why? Because you have 3 categories, namely "Not very much", "They are OK" and "Yes, a lot" and you can rank them from the most positive (Yes, a lot), to the middle response (They are OK), to the least positive (Not very much). However, whilst we can rank the levels, we cannot place a "value" to them; we cannot say that "They are OK" is twice as positive as "Not very much" for example.

Continuous variables are also known as quantitative variables. Continuous variables can be further categorized as either interval or ratio variables.

• Interval variables are variables for which their central characteristic is that they can be measured along a continuum and they have a numerical value (for example, temperature measured in degrees Celsius or Fahrenheit). So the difference between 20°C and 30°C is the same as 30°C to 40°C. However, temperature measured in degrees Celsius or Fahrenheit is NOT a ratio variable.
• Ratio variables are interval variables, but with the added condition that 0 (zero) of the measurement indicates that there is none of that variable. So, temperature measured in degrees Celsius or Fahrenheit is not a ratio variable because 0°C does not mean there is no temperature. However, temperature measured in Kelvin is a ratio variable as 0 Kelvin (often called absolute zero) indicates that there is no temperature whatsoever. Other examples of ratio variables include height, mass, distance and many more. The name "ratio" reflects the fact that you can use the ratio of measurements. So, for example, a distance of ten metres is twice the distance of 5 metres.

Ambiguities in classifying a type of variable

In some cases, the measurement scale for data is ordinal, but the variable is treated as continuous. For example, a Likert scale that contains five values - strongly agree, agree, neither agree nor disagree, disagree, and strongly disagree - is ordinal. However, where a Likert scale contains seven or more value - strongly agree, moderately agree, agree, neither agree nor disagree, disagree, moderately disagree, and strongly disagree - the underlying scale is sometimes treated as continuous (although where you should do this is a cause of great dispute).

It is worth noting that how we categorise variables is somewhat of a choice. Whilst we categorised gender as a dichotomous variable (you are either male or female), social scientists may disagree with this, arguing that gender is a more complex variable involving more than two distinctions, but also including measurement levels like genderqueer, intersex and transgender. At the same time, some researchers would argue that a Likert scale, even with seven values, should never be treated as a continuous variable.

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Levels of measurement: Nominal, ordinal, interval, ratio

Published on 12 September 2022 by Pritha Bhandari . Revised on 5 December 2022.

Levels of measurement, also called scales of measurement, tell you how precisely variables are recorded. In scientific research, a variable is anything that can take on different values across your data set (e.g., height or test scores).

There are 4 levels of measurement:

• Nominal : the data can only be categorised
• Ordinal : the data can be categorised and ranked
• Interval : the data can be categorised, ranked, and evenly spaced
• Ratio : the data can be categorised, ranked, evenly spaced, and has a natural zero.

Depending on the level of measurement of the variable, what you can do to analyse your data may be limited. There is a hierarchy in the complexity and precision of the level of measurement, from low (nominal) to high (ratio).

Table of contents

Nominal, ordinal, interval, and ratio data, why are levels of measurement important, which descriptive statistics can i apply on my data, quiz: nominal, ordinal, interval, or ratio, frequently asked questions about levels of measurement.

Going from lowest to highest, the 4 levels of measurement are cumulative. This means that they each take on the properties of lower levels and add new properties.

The level at which you measure a variable determines how you can analyse your data.

The different levels limit which descriptive statistics you can use to get an overall summary of your data, and which type of inferential statistics you can perform on your data to support or refute your hypothesis .

In many cases, your variables can be measured at different levels, so you have to choose the level of measurement you will use before data collection begins.

• Ordinal level: You create brackets of income ranges: $0–$19,999, $20,000–$39,999, and $40,000–$59,999. You ask participants to select the bracket that represents their annual income. The brackets are coded with numbers from 1–3.
• Ratio level: You collect data on the exact annual incomes of your participants.

At a ratio level, you can see that the difference between A and B’s incomes is far greater than the difference between B and C’s incomes.

Descriptive statistics help you get an idea of the “middle” and “spread” of your data through measures of central tendency and variability .

When measuring the central tendency or variability of your data set, your level of measurement decides which methods you can use based on the mathematical operations that are appropriate for each level.

The methods you can apply are cumulative; at higher levels, you can apply all mathematical operations and measures used at lower levels.

Some variables have fixed levels. For example, gender and ethnicity are always nominal level data because they cannot be ranked.

However, for other variables, you can choose the level of measurement . For example, income is a variable that can be recorded on an ordinal or a ratio scale:

• At an ordinal level , you could create 5 income groupings and code the incomes that fall within them from 1–5.
• At a ratio level , you would record exact numbers for income.

If you have a choice, the ratio level is always preferable because you can analyse data in more ways. The higher the level of measurement, the more precise your data is.

Depending on the level of measurement , you can perform different descriptive statistics to get an overall summary of your data and inferential statistics to see if your results support or refute your hypothesis .

Levels of measurement tell you how precisely variables are recorded. There are 4 levels of measurement, which can be ranked from low to high:

• Nominal : the data can only be categorised.
• Ordinal : the data can be categorised and ranked.
• Interval : the data can be categorised and ranked, and evenly spaced.
• Ratio : the data can be categorised, ranked, evenly spaced and has a natural zero.

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Explaining the Department of Labor’s new overtime rule that will benefit 4.3 million workers

The U.S. Department of Labor issued a final rule today making changes to the regulations about who is eligible for overtime pay. Here’s why this matters:

How the overtime threshold works

Overtime pay protections are included in the Fair Labor Standards Act (FLSA) to ensure that most workers who put in more than 40 hours a week get paid 1.5 times their regular pay for the extra hours they work. Almost all hourly workers are automatically eligible for overtime pay. But workers who are paid on a salary basis are only automatically eligible for overtime pay if they earn below a certain salary. Above that level, employers can claim that workers are “exempt” from overtime pay protection if their job duties are considered executive, administrative, or professional (EAP) —essentially managers or highly credentialed professionals.

The current overtime salary threshold is too low to protect many workers

The pay threshold determining which salaried workers are automatically eligible for overtime pay has been eroded both by not being updated using a proper methodology, and by inflation. Currently, workers earning $684 per week (the equivalent of $35,568 per year for a full-time, full-year employee) can be forced to work 60-70 hours a week for no more pay than if they worked 40 hours. The extra 20-30 hours are completely free to the employer, allowing employers to exploit workers with no consequences.

The Department of Labor’s new final rule will phase in the updated salary threshold in two steps over the next eight months, and automatically update it every three years thereafter.

• This is the equivalent of $43,888 per year for a full-time, full-year worker.
• In 2019, the Department updated the salary threshold to a level that was inappropriately low. Further, that threshold has eroded substantially in the last 4+ years as wages and prices have risen over that period, leaving roughly one million workers without overtime protections who would have received those protections under the methodology of even that inappropriately weak rule. This first step essentially adjusts the salary threshold set in the 2019 rule for inflation.
• This is the equivalent of $58,656 per year for a full-time, full-year worker.
• This level appropriately sets the threshold at the 35th percentile of weekly wages for full-time, salaried workers in the lowest-wage Census region, currently the South.
• The salary threshold will automatically update every three years thereafter, based on the methodology laid out in the rule, to ensure that the strength of the rule does not erode over time as prices and wages rise.

The final rule will benefit 4.3 million workers

• 2.4 million of these workers (56%) are women
• 1.0 million of these workers (24%) are workers of color
• The largest numbers of impacted workers are in professional and business services, health care and social services, and financial activities.
• The 4.3 million represents 3.0% of workers subject to the FLSA.

Expanding overtime protections is good for workers and manageable for employers

• The final rule will result in a transfer of $1.5 billion annually from employers to workers in increased pay.
• While that increase in wages will be enormously impactful to affected workers, it represents well under one-tenth of one-percent of total wages and salaries in the U.S. economy. Employers will be more than able to adjust to the rule without negatively impacting the overall economy.
• In addition to increasing pay for many workers, the overtime rule will also reduce excessive hours of unpaid work. Before this update to the salary threshold, the cost to employers of overworking salaried EAP workers who make more than $684 weekly was effectively zero. The concept of overtime pay is designed to protect workers’ most valuable asset—their time—and to push employers to value it too.
• Automatic updating is a smart and easy way to  simply maintain the labor standard established in the proposal. If the threshold is not updated automatically over time, it will steadily weaken as a labor standard until the next rulemaking, covering fewer and fewer workers as the salary distribution naturally rises over time with inflation and productivity growth.
• With automatic updating, employers will know exactly what to expect and when to expect it. They will also be able to get a reasonable sense well in advance of what the next threshold will be, because they will be able to track on a dedicated Bureau of Labor Statistics website how the 35th percentile of full-time salaried worker earnings in the lowest-wage Census region is evolving over time.

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