what is ordinal variable in research

What Is Ordinal Data?

What is ordinal data, how is it used, and how do you collect and analyze it? Find out in this comprehensive guide.

Whether you’re new to data analytics or simply need a refresher on the fundamentals, a key place to start is with the four types of data. Also known as the four levels of measurement , this data analytics term describes the level of detail and precision with which data is measured. The four types (or scales) of data are:

• nominal data
• ordinal data
• interval data

In this article, I’m going to dive deep into ordinal data.

If the concept of these data types is completely new to you, we’ll start with a quick summary of the four different types, and then explore the various aspects of ordinal data in a bit more detail,

If you’d like to learn more data analytics skills, try our free 5-day data short course .

I’ll cover the following topics:

• An introduction to the four different types of data
• What is ordinal data? A definition

What are some examples of ordinal data?

• How is ordinal data collected and what is it used for?
• How to analyze ordinal data
• Summary and further reading

Ready to get your head around ordinal data? Then let’s get going!

1. An introduction to the four different types of data

To analyze a dataset, you first need to determine what type of data you’re dealing with.

Fortunately, to make this easier, all types of data fit into one of four broad categories: nominal , ordinal , interval, and ratio data. While these are commonly referred to as ‘data types,’ they are really different scales or levels of measurement .

Each level of measurement indicates how precisely a variable has been counted, determining the methods you can use to extract information from it. The four data types are not always clearly distinguishable; rather, they belong to a hierarchy. Each step in the hierarchy builds on the one before it.

The first two types of data, known as categorical data , are nominal and ordinal. These two scales take relatively imprecise measures.

While this makes them easier to analyze, it also means they offer less accurate insights. The next two types of data are interval and ratio. These are both types of numerical data , which makes them more complex. They are more difficult to analyze but have the potential to offer much richer insights.

• Nominal data is the simplest data type. It classifies data purely by labeling or naming values e.g. measuring marital status, hair, or eye color. It has no hierarchy to it.
• Ordinal data classifies data while introducing an order, or ranking. For instance, measuring economic status using the hierarchy: ‘wealthy’, ‘middle income’ or ‘poor.’ However, there is no clearly defined interval between these categories.
• Interval data classifies and ranks data but also introduces measured intervals. A great example is temperature scales, in Celsius or Fahrenheit. However, interval data has no true zero, i.e. a measurement of ‘zero’ can still represent a quantifiable measure (such as zero Celsius, which is simply another measure on a scale that includes negative values).
• Ratio data is the most complex level of measurement. Like interval data, it classifies and ranks data, and uses measured intervals. However, unlike interval data, ratio data also has a true zero. When a variable equals zero, there is none of this variable. A good example of ratio data is the measure of height—you cannot have a negative measure of height.

You’ll find a comprehensive guide to the four levels of data measurement here .

What do the different levels of measurement tell you?

Distinguishing between the different levels of measurement is sometimes a little tricky.

However, it’s important to learn how to distinguish them, because the type of data you’re working with determines the statistical techniques you can use to analyze it. Data analysis involves using descriptive analytics (to summarize the characteristics of a dataset) and inferential statistics (to infer meaning from those data).

These comprise a wide range of analytical techniques, so before collecting any data, you should decide which level of measurement is best for your intended purposes.

2. What is ordinal data? A definition

Ordinal data is a type of qualitative (non-numeric) data that groups variables into descriptive categories.

A distinguishing feature of ordinal data is that the categories it uses are ordered on some kind of hierarchical scale, e.g. high to low. On the levels of measurement, ordinal data comes second in complexity, directly after nominal data.

While ordinal data is more complex than nominal data (which has no inherent order) it is still relatively simplistic.

For instance, the terms ‘wealthy’, ‘middle income’, and ‘poor’ may give you a rough idea of someone’s economic status, but they are an imprecise measure–there is no clear interval between them. Nevertheless, ordinal data is excellent for ‘sticking a finger in the wind’ if you’re taking broad measures from a sample group and fine precision is not a requirement.

While ordinal data is non-numeric, it’s important to understand that it can still contain numerical figures. However, these figures can only be used as categorizing labels, i.e. they should have no inherent mathematical value.

For instance, if you were to measure people’s economic status you could use number 3 as shorthand for ‘wealthy’, number 2 for ‘middle income’, and number 1 for ‘poor.’ At a glance, this might imply numerical value, e.g. 3 = high and 1 = low. However, the numbers are only used to denote sequence. You could just as easily switch 3 with 1, or with ‘A’ and ‘B’ and it would not change the value of what you’re ordering; only the labels used to order it.

Key characteristics of ordinal data

• Ordinal data are categorical (non-numeric) but may use numbers as labels.
• Ordinal data are always placed into some kind of hierarchy or order (hence the name ‘ordinal’—a good tip for remembering what makes it unique!)
• While ordinal data are always ranked, the values do not have an even distribution .
• Using ordinal data, you can calculate the following summary statistics: frequency distribution, mode and median, and the range of variables.

What’s the difference between ordinal data and nominal data?

While nominal and ordinal data are both types of non-numeric measurement, nominal data have no order or sequence.

For instance, nominal data may measure the variable ‘marital status,’ with possible outcomes ‘single’, ‘married’, ‘cohabiting’, ‘divorced’ (and so on). However, none of these categories are ‘less’ or ‘more’ than any other. Another example might be eye color. Meanwhile, ordinal data always has an inherent order.

If a qualitative dataset lacks order, you know you’re dealing with nominal data.

3. What are some examples of ordinal data?

• Economic status (poor, middle income, wealthy)
• Income level in non-equally distributed ranges ($10K-$20K, $20K-$35K, $35K-$100K)
• Course grades (A+, A-, B+, B-, C)
• Education level (Elementary, High School, College, Graduate, Post-graduate)
• Likert scales (Very satisfied, satisfied, neutral, dissatisfied, very dissatisfied)
• Military ranks (Colonel, Brigadier General, Major General, Lieutenant General)
• Age (child, teenager, young adult, middle-aged, retiree)

As is hopefully clear by now, ordinal data is an imprecise but nevertheless useful way of measuring and ordering data based on its characteristics. Next up, let’s see how ordinal data is collected and how it generally tends to be used.

4. How is ordinal data collected and what is it used for?

Ordinal data are usually collected via surveys or questionnaires. Any type of question that ranks answers using an explicit or implicit scale can be used to collect ordinal data. An example might be:

• Question: Which best describes your knowledge of the Python programming language? Possible answers: Beginner, Basic, Intermediate, Advanced, Expert.

This commonly recognized type of ordinal question uses the Likert Scale, which we described briefly in the previous section. Another example might be:

• Question: To what extent do you agree that data analytics is the most important job for the 21st century? Possible answers: Strongly agree, Agree, Neutral, Disagree, Strongly Disagree.

It’s worth noting that the Likert Scale is sometimes used as a form of interval data. However, this is strictly incorrect. That’s because Likert Scales use discrete values , while interval data uses continuous values with a precise interval between them.

The distinctions between values on an ordinal scale, meanwhile, lack clear definition or separation, i.e. they are discrete. Although this means the values are imprecise and do not offer granular detail about a population, they are an excellent way to draw easy comparisons between different values in a sample group.

How is ordinal data used?

Ordinal data are commonly used for collecting demographic information.

This is particularly prevalent in sectors like finance, marketing, and insurance, but it is also used by governments, e.g. the census, and is generally common when conducting customer satisfaction surveys (in any industry).

5. How to analyze ordinal data

As discussed, the level of measurement you use determines the kinds of analysis you can carry out on your data. In general, these fall into two broad categories: descriptive statistics and inferential statistics.

We use descriptive statistics to summarize the characteristics of a dataset. This helps us spot patterns. Meanwhile, inferential statistics allow us to make predictions (or infer future trends) based on existing data. However, depending on the measurement scale, there are limits. You can learn more about the difference between descriptive and inferential statistics here .

For now, though, Let’s see what kinds of descriptive and inferential statistics you can measure using ordinal data.

Descriptive statistics for ordinal data

The descriptive statistics you can obtain using ordinal data are:

Frequency distribution

Measures of central tendency: mode and/or median, measures of variability: range.

Now let’s look at each of these in more depth.

Frequency distribution describes how your ordinal data are distributed.

For instance, let’s say you’ve surveyed students on what grade they’ve received in an examination. Possible grades range from A to C. You can summarize this information using a pivot table or frequency table, with values represented either as a percentage or as a count. To illustrate using a very simple example, one such table might look like this:

As you can see, the values in the sum column show how many students received each possible grade. This allows you to see how the values are distributed. Another option is also to visualize the data , for instance using a bar plot.

Viewing the data visually allows us to easily see the frequency distribution. Note the hierarchical relationship between categories. This is different from the other type of categorical data, nominal data, which lacks any hierarchy.

The mode (the value which is most often repeated) and median (the central value) are two measures of what is known as ‘central tendency.’ There is also a third measure of central tendency: the mean. However, because ordinal data is non-numeric, it cannot be used to obtain the mean. That’s because identifying the mean requires mathematical operations that cannot be meaningfully carried out using ordinal data.

However, it is always possible to identify the mode in an ordinal dataset. Using the barplot or frequency table, we can easily see that the mode of the different grades is B. This is because B is the grade that most students received.

In this case, we can also identify the median value. The median value is the one that separates the top half of the dataset from the bottom half. If you imagined all the respondents’ answers lined up end-to-end, you could then identify the central value in the dataset. With 165 responses (as in our grades example) the central value is the 83rd one. This falls under the grade B.

The range is one measure of what is known as ‘variability.’ Other measures of variability include variance and standard deviation. However, it is not possible to measure these using ordinal data, for the same reasons you cannot measure the mean.

The range describes the difference between the smallest and largest value. To calculate this, you first need to use numeric codes to represent each grade, i.e. A = 1, A- = 2, B = 3, etc. The range would be 5 – 1 = 4. So in this simple example, the range is 4. This is an easy calculation to carry out. The range is useful because it offers a basic understanding of how spread out the values in a dataset are.

Inferential statistics for ordinal data

Descriptive statistics help us summarize data. To infer broader insights, we need inferential statistics. Inferential statistics work by testing hypotheses and drawing conclusions based on what we learn.

There are two broad types of techniques that we can use to do this. Parametric and non-parametric tests. For qualitative (rather than quantitative) data like ordinal and nominal data, we can only use non-parametric techniques.

Non-parametric approaches you might use on ordinal data include:

Mood’s median test

• The Mann-Whitney U test

Wilcoxon signed-rank test

• The Kruskal-Wallis H test:

Spearman’s rank correlation coefficient

Let’s briefly look at these now.

The Mood’s median test lets you compare medians from two or more sample populations in order to determine the difference between them. For example, you may wish to compare the median number of positive reviews of a company on Trustpilot versus the median number of negative reviews. This will help you determine if you’re getting more negative or positive reviews.

The Mann-Whitney U-test

The Mann-Whitney U test lets you compare whether two samples come from the same population.

It can also be used to identify whether or not observations in one sample group tend to be larger than observations in another sample. For example, you could use the test to understand if salaries vary based on age. Your dependent variable would be ‘salary’ while your independent variable would be ‘age’, with two broad groups, e.g. ‘under 30,’ ‘over 60.’

The Wilcoxon signed-rank test explores the distribution of scores in two dependent data samples (or repeated measures of a single sample) to compare how, and to what extent, the mean rank of their populations differs.

We can use this test to determine whether two samples have been selected from populations with an equal distribution or if there is a statistically significant difference.

The Kruskal-Wallis H test

The Kruskal-Wallis H test helps us to compare the mean ranking of scores across three or more independent data samples.

It’s an extension of the Mann-Whitney U test that increases the number of samples to more than two. In the Kruskal-Wallis H test, samples can be of equal or different sizes. We can use it to determine if the samples originate from the same distribution.  

Spearman’s rank correlation coefficient explores possible relationships (or correlations) between two ordinal variables.

Specifically, it measures the statistical dependence between those variable’s rankings. For instance, you might use it to compare how many hours someone spends a week on social media versus their IQ. This would help you to identify if there is a correlation between the two.

Don’t worry if these models are complex to get your head around. At this stage, you just need to know that there are a wide range of statistical methods at your disposal. While this means there is lots to learn, it also offers the potential for obtaining rich insights from your data.

6. Summary and further reading

In this guide, we:

• Introduced the four levels of data measurement: Nominal, ordinal, interval, and ratio.
• Defined ordinal data as a qualitative (non-numeric) data type that groups variables into ranked descriptive categories.
• Explained the difference between ordinal and nominal data: Both are types of categorical data. However, nominal data lacks hierarchy, whereas ordinal data ranks categories using discrete values with a clear order.
• Shared some examples of nominal data: Likert scales, education level, and military rankings.
• Highlighted the descriptive statistics you can obtain using ordinal data: Frequency distribution, measures of central tendency (the mode and median), and variability (the range).
• Introduced some non-parametric statistical tests for analyzing ordinal data, e.g. Mood’s median test and the Kruskal-Wallis H test.

Want to learn more about data analytics or statistics? To further develop your understanding, check out our  free-five day data analytics short course and read the following guides:

• What is quantitative data?
• An introduction to exploratory data analysis
• An introduction to multivariate data analysis

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Ordinal Data: Definition, Examples, Collection, and Analysis

March 24, 2023

by Alex Birkett

In this post

What is ordinal data, 5 examples of ordinal data , how to collect ordinal data, tests to conduct with ordinal data, how to analyze ordinal data.

Companies invest more in data tools to help their marketing teams make better decisions. 

But marketing needs more than just data and analytics tools to implement an effective marketing strategy. They also need to understand the type of data they collect and how to analyze it to gain meaningful insights.

This involves going back to basics and understanding ordinal data, one of the key marketing data types. This article will explore ordinal data and how it informs data-driven marketing decisions.

Ordinal data is quantitative data in which variables are organized in ordered categories, such as a ranking from 1 to 10. However, the variables lack a clear interval between them, and values in ordinal data don’t always have an even distribution.

The level of customer satisfaction is an example of ordinal data. Its variables could be:

• Very Satisfied
• Dissatisfied
• Very dissatisfied 

Using ordinal data, you can calculate the frequency, distribution, mode, median, and range of variables.

Having defined ordinal data, you may wonder about other data types, such as nominal, interval, or ratio data. How do they differ from ordinal data? Here are some quick definitions:

• Nominal data is a classification of data whose variables have a finite set of values and categories that aren't ordered. With nominal data, you measure variables such as type of employment, which has several outcomes, such as freelance, full-time, or hybrid work.
• Interval data is a type of data where the interval between two values isn't constant. Interval data arise in many ways, for example, when measuring time intervals or when the difference between two measurements varies. The most common way to represent interval data is using a table with columns for each range's upper and lower bounds.
• Ratio data is a type of data used for statistical analysis. The ratio data does not provide any information about the values it represents. This information must be obtained from other sources referenced by the ratio data. It is often used in the analysis of financial information but can also be applied to other types of data. 

Ordinal data occurs in different formats. Here are a few examples of ordinal data and how to synchronize it with your business strategy to improve your data management efforts. 

1. Interest level

Whether you've already launched your product into the market or introducing new features to your existing product, you’ll need to conduct market research to ask questions to gauge your target audience's interest. 

Market research involves analyzing both qualitative and quantitative data to understand customer needs, their buying partners, and what motivates them to buy from you. These insights can help improve your marketing campaigns in the future.

For example, if you host conferences regularly, surveys can help you know how well you did and whether your attendees want to attend the conference again. Here's an example of interest-level data:

Source: SurveyMonkey

The questions you ask will reveal potential customers’ interest level in your product or service. Interest levels range from not interested, slightly interested, neutral, to very interested.  

2. Education level

This type of ordinal data provides insights into your target audience's proficiency level. 

Education level may inquire whether your target audience has acquired different levels of formal education, such as high school, college, and graduate school. You may collect this data by assigning numbers to each level, such as 1 for no formal education, 2 for primary schooling, and so on, until 10 for a doctoral university degree.

Education-level data comes in handy when using analytics in your recruitment process to help you evaluate the job applications of potential candidates.

Educational-level data can help you make powerful predictions about who to hire in the future to support company growth, where to focus your recruiting efforts, and find suitable candidates for specific positions.

If you run a sales team, assessing the education level of your team members enables you to know how to support their career development goals. This way, you can build a high-performing sales team and improve retention.

3. Socio-economic status

Understanding the socio-economic status of your target audience helps create and refine your customer segments based on their demographic and psychographic profiles. 

You can then rely on these segments when running personalized marketing campaigns that meet their needs and wants. Ordinal data on socioeconomic status for a B2C target audience includes gender, location, household income, marital status, and age. 

On the other hand, data for a B2B target audience includes gross annual revenue, stage of business growth, number of employees, market position, and type of industry. 

4. Satisfaction level

The satisfaction level reflects how content your customers are with different brand interactions. For example, your customer onboarding process or how well you resolve different customer issues. 

Customer satisfaction may be expressed as extremely satisfied, satisfied, unsatisfied, or extremely dissatisfied. Satisfaction level data helps you gauge customer service and sales handling satisfaction to identify areas for improvement. 

Here’s an example of satisfaction level data from a product-market fit survey that Buffer conducted:

Source: Buffer

With this data, the company could tell how useful Buffer’s Power scheduler is to their customers, meaning that the product was the right fit for their users. 

5. Comparison

This involves asking questions that reveal the similarities or differences between two or more data points. Once you identify the similarities or differences, you can learn what characteristics are similar, which ones are different, and the degree to which they’re different or similar.  

For example, you may want to compare revenue performance from 2021 to 2022. Your comparison will yield significantly less, about the same, more, and significantly more for each year's revenue.

With this, you can gauge macroeconomic and industry trends and adjust your strategy to fit your budgeting process to control spending . You may even decide to take this further and compare industry trends so that you can create reports and write thought leadership content to drive brand awareness. 

If you asked someone to rank their level of satisfaction on a scale from 1-5, their response would be ordinal. You can collect this data ‌through surveys or Likert scales using survey software .

Surveys are one of the oldest methods for collecting ordinal data. You can use surveys to determine your target audience's feelings about products, topics, ‌or specific issues related to your brand, product, or service. You can survey with many methods, including in person, over the phone, or online.

With surveys, however, collecting accurate data from people who don't want to answer questions honestly or understand them is difficult. Surveys also require a lot of time on the researcher's part to create, validate, and analyze them.

A Likert scale is a survey that asks participants to agree or disagree with each statement on the survey, for example, “I strongly disagree.” Participants then assign themselves an answer based on their feelings toward the statement and their level of agreement with it.

Likert scales improve clarity during analysis because respondents rate themselves on an ordered scale with clearly defined intervals, for example, a scale of 1-7.

To collect ordinal data, you must run surveys with questions that rank answers using an implicit or explicit scale. For example, if you have lots of traffic coming to your company’s website, you can use an enterprise website feedback tool to collect feedback from your website. Ask:

“How content are you with the blog post you just read?’’

The possible answers could be:

• Happy 
• Satisfied 
• Unsatisfied

You can conduct several tests on ordinal data to measure the difference between two or more groups. These tests include:

• The Kruskal-Wallis test
• The Mann-Whitney U test
• Wilcoxon rank-sum test
• Mood’s Median test

Ordinal data is a data type that ranks ‌values from least to greatest. In other words, ordinal data is ranked or ordered. 

Kruskal–Wallis H test

The Kruskal-Wallis test is a non-parametric test used to compare the medians of three or more independent groups. It’s used when the data is not normally distributed, and the variance between groups is unequal. The Kruskal-Wallis test can also compare two dependent groups – before and after pictures of a website redesign.

Mann-Whitney U test

The Mann-Whitney test is a non-parametric test used to compare the median of two independent samples. It can be used when there's ordinal data, such as ratings on a scale from 1 to 5, or when there are no clear groups in the data.

Wilcoxon signed-rank test

The Wilcoxon signed-rank test is a non-parametric test that can be used for data sets with or without normal distribution. It's an alternative to the t-test in cases where the data doesn't have a normal distribution. 

When running a t-test, the assumption is that the underlying distribution of the data is normal, but this assumption can be wrong. 

For example, when testing the difference in height between two groups, let's say one group has an average height of 180 cm and the other group has 170 cm. You won't see any significant difference in their heights. 

However, using the Wilcoxon signed rank test, you can see beyond the regular difference in their heights.

Mood’s median test

The test is based on the premise that people's moods cluster around a median point, with some being more positive or negative than others. The Mood's median test often measures how individuals feel about an issue or idea, such as your customer’s opinion about your products or service. It can predict behavior based on their moods, such as whether your customers will buy from you or your competitors. 

There are two ways to analyze ordinal data: inferential and descriptive statistics.

Descriptive statistics summarize the characteristics of a dataset and identify patterns. Here are the descriptive statistics for ordinal data:

• Frequency distribution

Measures of central tendency

• Range (measures of variability)

Inferential statistics , on the other hand, predict what may happen in the future based on the data you have. You can use ordinal data to collect insights, create hypotheses, or even draw conclusions with the four tests described above.

The Kruskal-Wallis, Mann Whitney U, and Wilcoxon signed-rank sum tests all analyze ordinal data. They're all nonparametric tests, meaning they don't rely on any assumptions about data distribution.

Descriptive analytics 

Descriptive analytics collects, analyzes, and reports data about events that have already occurred. This differs from predictive analytics , which predicts future events based on historical data. Descriptive analytics helps businesses identify patterns in the past to improve their future decision-making.

In descriptive analytics, the goal is to find patterns in existing data, not predict what will happen in the future. Descriptive analytics aims to find cause-and-effect relationships between past events and use these relationships to predict future events.

Unlike other analysis methods, descriptive analytics can be used anytime with any data available. This makes it more accessible for smaller businesses with insufficient resources for predictive models or large datasets required by other methods.

Bars and graphs present data in a way that's easy to comprehend. They're beneficial when the data is too large or complicated to be displayed in a table. The type of graph you choose depends on the amount of information you want to convey, the data dimensions, and your audience.

Bar graphs display information as bars with lengths proportional to their values. They're used when the data is categorical, meaning it falls into specific groups. Here’s a bar graph for a call center, showing the time taken to respond each weekday:

Source: Datapine

They're a good choice when you want your audience to be able to compare values easily. Bar graphs are more intuitive and easier to understand as compared to numbers. It's also possible to use bars in combination with lines or other graphics, like scatter plots, histograms, or pie charts.

Line graphs are used when the data has an ordered value. These graphs use lines to connect points on two axes with the same scale on both sides. These lines can be solid or dotted and start at any point on either axis. 

The lines represent change over time, such as how the stock market fluctuates daily or how the cost of energy changes year by year. Here’s an example of monthly inbound leads over 12 months visualized using a line graph :

Central tendency is the average of a set of numbers. It measures how closely the numbers in a data set are clustered around their mean.

Three main types of central tendency are mean, median, and mode. The most common measure of central tendency is the arithmetic mean, calculated by adding up all the values in the data set and dividing this sum by the number of values in that data set. 

The median can also be used as an alternative to calculating central tendency, simply finding the middle value in a data set after arranging all numbers from low to high. The mode is the most frequent value in a set.

Key takeaways

Ordinal data is more complex than nominal data and commonly used to gauge interest. The Likert scale is a popular ordinal data example. 

Use some of the real examples provided here to inspire your own survey data collection. While at it, learn more about polling and how it helps collect data.

Data-driven insights at your fingertips

Collect, analyze, and visualize your data in one place, and get valuable insights to drive business growth and success with analytics platforms.

Alex Birkett is the co-founder of Omniscient Digital , a premium content marketing & SEO agency. He lives in Austin, Texas, with his dog Biscuit and writes at alexbirkett.com. .

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Institute for Digital Research and Education

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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• What is Ordinal Data? Definition, Examples, Variables & Analysis

• Data Collection

Ordinal data classification is an integral step toward the proper collection and analysis of data. Therefore, in order to classify data correctly, we need to first understand what data itself is. 

Data is a collection of facts or information from which conclusions may be drawn. They can exist in various forms – as numbers or text on pieces of paper, as bits and bytes stored in electronic memory, or as facts stored in a person’s mind.

When dealing with data, they are sometimes classified as nominal or ordinal. Data is classified as either nominal or ordinal when dealing with categorical variables – non-numerical data variables, which can be a string of text or date. 

Definition of Ordinal Data  

Ordinal data is a kind of categorical data with a set order or scale to it. For example, ordinal data is said to have been collected when a responder inputs his/her financial happiness level on a scale of 1-10. In ordinal data, there is no standard scale on which the difference in each score is measured.

Considering the example highlighted above, let us assume that 50 people earning between $1000 to $10000 monthly were asked to rate their level of financial happiness. 

An undergraduate earning $2000 monthly may be on an 8/10 scale, while a father of 3 earning $5000 rates 3/10. This is to show that the scale is usually influenced by personal factors and not due to a set rule.

Read Also: What is Nominal Data? Examples, Category Variables & Analysis

Ordinal Data Examples 

Examples of ordinal data include the Likert scale; used by researchers to scale responses in surveys and interval scale; where each response is from an interval of its own. Unlike nominal data, ordinal data examples are useful in giving order to numerical data.

• Likert Scale:

A Likert scale is a point scale used by researchers to take surveys and get people’s opinions on a subject matter. It is usually a 5 or 7-point scale with options that range from one extreme to another. Consider this example:

How satisfied are you with our meal tonight? 

• Very satisfied
• Indifferent
• Dissatisfied
• Very dissatisfied

This is a 5-point Likert scale . Like in this example, each response in a 5-point Likert scale is assigned to a numeric value from 1-5.

Read Also: 7 Types of Data Measurement Scales in Research

• Interval Scale

An interval scale is a type of ordinal scale whereby each response is an interval on its own. Examples of interval scales include; the classification of people into teenagers, youths, middle-aged, etc. done according to their age group.

In which category do you fall? 

• Child – 0 to 12 years
• Teenager – 13 to 19 years
• Youth – 20 to 35 years
• Middle age – 36 to 58 years
• Old – 59 years and above

Example 2: In a school, students are graded as either A, B, C, D, E, or F according to their score. Students that score 70 and above are graded A, 60-69 are graded B, and so on.

• 70 and above
• 34 and below.

Categories of Ordinal Variables  

Ordinal variables can be classified into 2 main categories, namely; the matched and unmatched categories. This ordinal variable classification is based on the concept of matching – pairing up data variables with similar characteristics. 

According to Wikipedia, matching is a statistical technique that is used to evaluate the effect of a treatment by comparing the treated and non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned).

The Matched Category

In the matched category, each member of a data sample is paired with similar members of every other sample with respect to all other variables, aside from the one under consideration. This is done in order to obtain a better estimation of differences. 

By eliminating other variables, we are able to prevent them from influencing the results of our current investigation. For example, when investigating the cause of skin cancer, it is better to match people of the same race together because of melanin deficiency (a condition common to white people) is a known cause. 

There are 2 different types of tests done on the Matched category, depending on the number of sample groups that are being investigated. Namely; the Wilcoxon signed-rank test and Friedman 2-way Anova

• Wilcoxon signed-rank test: This is a qualitative statistical test used to compare the 2 groups of matched samples to assess their differences.  
• Friedman 2-way ANOVA: This is a non-parametric way of finding differences in matched sets of 3 or more groups. Developed by Milton Friedman, this test procedure involves ranking rows together, then considering the values of each rank by columns.

The Unmatched Category

Unmatched samples, also known as independent samples are 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.

For example, suppose examiners want to compare the efficiency of 2 test marking software. They take random samples of 10 students’ answer scripts and send them to the two  (2) software for marking. It doesn’t matter whether the answers ticked by these students are similar or not. 

• Wilcoxon rank-sum test

The Wilcoxon rank-sum test is also known as the Mann-Whitney U test. It is a non-parametric test used to investigate 2 groups of independent samples. This test is usually used to test whether the samples belong to the same population. A similar qualitative test used on matched samples is the Wilcoxon signed-rank test. 

• Kruskal-Wallis 1-way test

This is a non-parametric test for investigating whether 3 or more samples belong to the same population. Named after William Kruskal and W. Allen Wallis, this test concludes whether the median of two or more groups is varied.

Characteristics of Ordinal Data  

• Extension of nominal data

Ordinal data is built on the existing nominal data . Nominal data is known as “named” data, while ordinal data is “named” data with a specific order or rank to it. Let us consider the ordinal data example given below:

Which of the following best describes your current level of financial happiness? 

• Very unhappy

The options in this question are qualitative , with a rank or order to it. The rank, in this case, is a sign of ordinal data. 

• No standardized interval scale

The difference in variation between “Very happy” and “happy” does not necessarily have to be the same as the one between “happy” and “neutral”. There is no standardized interval scale of measurement for each variable.

In fact, the difference in variation can’t be concluded using the ordinal scale. This scale is dependent on factors that are unique for each respondent.

• Establish a relative rank

In the example mentioned above, ”very happy” is definitely better than “unhappy” and “neutral” is worse than “happy”. Unlike the interval scale, there is an established rank of order in this case.

This rank is used to group respondents into different levels of happiness. 

• Measure qualitative traits

The ordinal scale has the ability to measure qualitative traits. The measurement scale, in this case, is not necessarily numbers, but adverbs of degree like very, highly, etc.

In the given example, all the answer options are qualitative with “very” being the adverb of degree used as a scale of measurement. 

• Measure numeric values

Ordinal data can also be quantitative or numeric. When asked to rate your level of financial happiness, for example, the values are numeric.  However, numerical operations (addition, subtraction, multiplication, etc.) cannot be performed on them. 

• Has a median

Unlike nominal data where only the mode can be calculated, ordinal data has a median. The median is the value in the middle but not the middle value of a scale and can be calculated with data that has an innate order. Consider the ordinal variable example below.

Rate your knowledge of Excel according to the following scale. 

• Intermediate

In this example, the middle value is “Basic” while the value in the middle is “intermediate”. 

• Has an order: Ordinal data has a specific rank or order, which may either be ascending or descending. 

Ordinal Data Analysis and Interpretation  

Ordinal data analysis is quite different from nominal data analysis, even though they are both qualitative variables. It incorporates the natural ordering of the variables in order to avoid loss of power. Ordinal variables differ from other qualitative variables because parametric analysis median and mode are used for analysis

This is due to the assumption that equal distance between categories does not hold for ordinal data. Therefore, positional measures like the median and percentiles, in addition to descriptive statistics appropriate for nominal data should be used instead. 

The use of parametric statistics for ordinal data variables may be permissible in some cases, with methods that are a close substitute to mean and standard deviation. Here are some of the parametric statistical methods used for ordinal analysis. 

• Univariate statistics: Used in place of mean and standard deviation, the appropriate univariate statistics for ordinal data include the median, quartiles, percentiles, and quartile deviation. 
• Bivariate statistics: Mann-Whitney, Smirnov, runs and signed-rank tests are used in lieu of testing differences in mean with t-test. 
• Regression applications: Outcomes are predicted using a variant of ordinal regression, such as ordered probit or ordered logit.
• Linear trends: It is used to find similarities between ordinal data and other variables in contingency tables. 
• Classification methods: This method uses matching to categorize data, after which dispersion is measured and minimized in each category to maximize classification results.

Graphical Techniques To Analyse Ordinal Variables

Ordinal data can also be analyzed graphically with the following techniques. 

• Mosaic plots
• Color or grayscale gradation.

Uses of Ordinal Data 

• Surveys/Questionnaires

Ordinal data is used to carry out surveys or questionnaires due to its “ordered” nature. Statistical analysis is applied to collect responses in order to place respondents into different categories, according to their responses.  The result of this analysis is used to draw inferences and conclusions about the respondents with regard to specific variables. Ordinal data is mostly used for this because of its easy categorization and collation process. 

Researchers use ordinal data to gather useful information about the subject of their research. For example, when medical researchers are investigating the side effects of a medication administered to 30 patients, they will need to collect ordinal data.

After using the medication, each patient may be asked to fill out a form, indicating the degree to which they feel some potential side effects. A sample ordinal data collection scale is illustrated below. 

How often do you feel the following? 

Very often not often

Nausea                  ¤ ¤ ¤

Headache              ¤ ¤   ¤

Dizzy                      ¤ ¤ ¤

Hungry                   ¤ ¤ ¤

• Customer service

Companies use ordinal data to improve their overall customer service. After using their service or buying their product, many companies are known to ask customers to fill out an after-service form, describing their experience.

This will help companies improve their customer service. Consider the example below:

Good  Okay Bad

Food                   ¤ ¤ ¤

Waiter                 ¤ ¤ ¤

Waiting time        ¤ ¤ ¤

Environment       ¤ ¤ ¤

• Job applications

During job applications, employers sometimes use a Likert scale to collect information about the level of the applicant’s skill in a field. When an applicant is applying for a social media manager position, for instance, a Likert scale may be used to know how familiar an applicant is with Facebook, Twitter, LinkedIn, etc.

E.g. How familiar are you with the following social networks? 

1  2 3  4 5  

Facebook        ¤ ¤ ¤ ¤ ¤

Instagram        ¤ ¤ ¤ ¤ ¤      

Twitter             ¤ ¤ ¤ ¤ ¤

LinkedIn          ¤ ¤ ¤ ¤ ¤

• Personality tests

This is a common test that is usually administered by employers to their potential employees. This is done so that the employer will know whether the applicant is a good fit for the organization.

Some psychologists also use this to get more information about their patients before treatment. That way, they are able to know which questions to ask, what to say and what not to say. 

Disadvantages of Ordinal Data 

• The options do not have a standardized interval scale. Therefore, respondents are not able to effectively gauge their options before responding.
• The responses are often so narrow in relation to the question that they create or magnify bias that is not factored into the survey. For example, in the customer service example cited above, a customer might be satisfied with the taste of the meal, but the meat was too tough or the water too cold. In the end, the restaurant will have a report on customer experience, but not be able to differentiate the reason why they chose the response they did.
• It does not allow respondents the opportunity to fully express themselves. They are usually restricted to some predefined options.

Why Formplus is the Best Tool For Collecting Ordinal Data 

• 30+ Field Types
• With a wide range of field types, you can easily collect ordinal data.
• Fields like matrices and scales make it easy to collect any set of ordinal data you need from your respondents.
• Do you need your respondents to give you repeatable data where they specify how many times they want to fill a field?
• You can also use tables if you need to collect ordinal data that is repeatable.

• Offline Data Collection 

Collect data in remote locations or places without reliable internet connection with Formplus. Offline forms can also act as a backup to the standard online forms, especially in cases where you have unreliable WiFi, such as large conferences and field surveys. 

When responders fill a form in the offline mode, responses are synced once there is an internet connection. Using conversational SMS, you can also collect data on any mobile device without an internet connection.

• Share & Export Data in Different Formats

You can store collected data in tabular format or even export it as PDF/CSV. Respondents can also submit their responses as PDFs, Doc attachments, or as images. These responses can also be shared as links through other applications like Gmail, WhatsApp, LinkedIn, etc. 

• Get Submission Notifications

You can send notifications to your respondents and your team whenever your form is completed.

The notification could be set such that, you can choose who on your team should receive these emails if you need to route them directly to the responsible people. 

Formplus also allows you to customize the content of the notification message sent to respondents based on what they have filled out in the form.

• Ability to Customise Forms

With Formplus, you can choose how you want your forms to look. You can create an attractive and interactive form that makes your respondents feel encouraged to respond. There are also different choice options for you to choose from. 

• Email Notifications 

You have the ability to choose how and when you receive notifications. There is also a customizable feature on the notifications sent to respondents upon completion of the form. 

In the event that you are working with a team, you can also add team members to your list of notification recipients. 

• Different Storage Options

Formplus allows you to choose how you want to store data. After exporting data in tabular, CSV, or PDF format, you can either save them on your device or upload them to the cloud. 

Although Formplus has a cloud platform, you can also upload your data on Dropbox, Google Drive, or Microsoft OneDrive. There are no limitations to the number of files, images, or videos that can be uploaded. 

Conclusion  

Ordinal data is designed to infer conclusions, while nominal data is used to describe conclusions. Descriptive conclusions organize measurable facts in a way that they can be summarised. 

If a restaurant carries out a customer satisfaction survey by measuring some variables over a scale of 1-5, then the satisfaction level can be stated quantitatively. However, no inference can be drawn about why some customers are satisfied and some are not. 

The only inference that can be made is something like, “Most customers are (dis)satisfied”. This is, however, not the case for descriptive conclusions, where one can get enough information on why customers are (dis)satisfied.

• https://www.slideshare.net/mssridhar/types-of-data-42010881?
• https://www.slideshare.net/Intellspot/nominal-data-vs-ordinal-data-comparison-chart
• https://www.slideshare.net/rosesrred90/inferential-statistics-nominal-data?
• https://www.slideshare.net/SAssignment/graphical-descriptive-techniques-nominal-data-assignment-help
• https://www.slideshare.net/plummer48/scaled-v-ordinal-v-nominal-data3

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What is Ordinal Data? Definition, Analysis, Examples

Appinio Research · 05.02.2024 · 34min read

Have you ever wondered how researchers make sense of data with categories that have a clear order but unequal intervals? In the world of statistics and research, this type of data, known as ordinal data, plays a pivotal role in unraveling complex relationships, making informed decisions, and understanding the preferences and perceptions of individuals. In this guide, we will delve deep into ordinal data, exploring its definition, characteristics, significance, and practical applications. From data collection to advanced analysis techniques, we'll equip you with the knowledge and tools needed to harness the power of ordinal data effectively.

What is Ordinal Data?

Ordinal data represents a categorical or qualitative type of data in which categories possess a meaningful order or ranking but do not have equal intervals between them. Unlike nominal data , where categories are merely labels with no inherent order, ordinal data categorizes information with a clear sequence or hierarchy.

Ordinal Data Characteristics

• Order : The primary feature of ordinal data is that categories are ordered or ranked in a meaningful way. This implies that some categories are "higher" or "lower" than others based on a specific criterion or attribute.
• Unequal Intervals : While there is an order to the categories, the intervals between them are not necessarily equal. In other words, the difference between categories may not be uniform or quantifiable.
• Discrete Categories : Ordinal data consists of discrete categories or levels. Each category represents a distinct and non-overlapping group.
• No Fixed Origin : Ordinal data lacks a fixed origin or zero point. Unlike interval or ratio data, which have meaningful zero points, ordinal data does not possess such a reference point.
• Limited Arithmetic Operations : Mathematical operations like addition, subtraction, multiplication, or division are generally not meaningful for ordinal data. You cannot calculate the average of ordinal categories in a meaningful way.

Understanding these characteristics is essential for appropriate data analysis and interpretation when working with ordinal data.

Importance of Ordinal Data

Ordinal data plays a pivotal role in various fields and research endeavors due to its unique attributes and utility. Here are several reasons why ordinal data holds significant importance:

• Hierarchical Insights : Ordinal data allows researchers to capture hierarchical information, providing insights into the relative order or ranking of categories. This is valuable for understanding preferences, attitudes, or rankings.
• Quantifying Qualitative Information : It bridges the gap between qualitative and quantitative data by providing a structured way to represent subjective or qualitative information. This makes it amenable to statistical analysis .
• Applicability in Surveys : Ordinal data is commonly used in surveys and questionnaires to gauge opinions, perceptions, or levels of agreement. Likert scales, for instance, provide a structured way to collect and analyze ordinal responses.
• Flexibility in Analysis : Researchers can apply various statistical methods tailored to ordinal data, such as ordinal regression, Mann-Whitney U tests, or Kruskal-Wallis tests. This versatility allows for in-depth analysis and hypothesis testing.
• Interdisciplinary Relevance : Ordinal data finds applications in diverse fields, including psychology, social sciences, medicine, marketing, and education. Its ability to capture nuanced relationships and rankings makes it indispensable in these domains.
• Decision-Making Support : In fields like market research and customer satisfaction analysis , ordinal data assists organizations in making informed decisions based on customer preferences and rankings.

Recognizing the importance of ordinal data and its unique characteristics empowers researchers to extract valuable insights and draw meaningful conclusions from this type of data, contributing to the advancement of knowledge across various disciplines.

Ordinal Data Collection and Measurement

In ordinal data, meticulous data collection and measurement are paramount for accurate analysis and meaningful insights. Let's explore this critical aspect, covering various nuances and techniques to enhance your data collection process.

Types of Ordinal Scales

Ordinal scales come in different forms, each suited to specific research questions and scenarios. Here's a closer look at some common types:

• Likert Scale : The Likert scale is perhaps the most familiar ordinal scale. It comprises a series of statements or questions, allowing respondents to express their level of agreement or disagreement. Ranging from "strongly agree" to "strongly disagree," these responses are typically quantified using numerical values, such as 1 to 5 or 0 to 4. Likert scales are widely used in surveys, but variations like the semantic differential scale or the Guttman scale offer additional options.
• Ordinal Rankings : This type of ordinal scale involves ranking items or options based on a specific criterion. For example, you might ask respondents to rank product features from most important to least important or prioritize a list of tasks. Ordinal rankings are valuable when you want to understand preferences or priorities without assigning precise values to the categories.
• Ordinal Categories with Descriptions : In some cases, ordinal data may include categories with descriptions rather than just numerical values. For instance, in a customer feedback survey, respondents might rate their experience on a scale of "excellent," "good," "average," "poor," and "very poor." These descriptive categories can provide richer insights but may require careful handling during analysis.

Remember that the choice of ordinal scale should align with your research objectives and the nature of the data you aim to collect.

Data Collection Methods

Selecting the proper data collection method is pivotal in ensuring the quality and reliability of your ordinal data.

• Surveys and Questionnaires : Surveys and questionnaires are versatile tools for collecting ordinal data. Crafting well-designed questions is crucial. Ensure that your questions are clear, concise, and free from bias . Additionally, pilot testing can help identify and address any ambiguities or issues before launching the survey.
• Observations : When dealing with observable behaviors or phenomena, observational data collection can be invaluable. Researchers systematically record and categorize observations into ordinal scales. For example, in educational research, observers might use ordinal scales to assess classroom behavior or student engagement.
• Interviews : Interviews are an excellent choice when you need to delve deeper into respondents' thoughts and experiences. They allow for open-ended discussions and can be especially beneficial in qualitative research. However, interviews can be resource-intensive and require skilled interviewers to maintain consistency.
• Existing Data : Sometimes, you might have access to existing datasets that contain ordinal data. These datasets can be valuable for secondary analysis . However, it's crucial to understand how the data was collected, coded, and labeled to ensure its suitability for your research.

As you navigate the intricacies of ordinal data collection, consider leveraging cutting-edge solutions like Appinio to streamline your research endeavors. Appinio empowers you with the tools to design user-friendly surveys and questionnaires, ensuring clarity and precision in your data collection process. With its intuitive platform, you can effortlessly gather real-time insights from a global audience, accelerating your research efforts. Ready to see it in action? Book a demo now to discover the power of Appinio and enhance your data collection capabilities!

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Data Coding and Labeling

Once you've gathered your ordinal data, the next step is to code and label it effectively. This process enhances the usability and interpretability of your dataset.

• Numerical Values : Assign numerical values to ordinal categories that reflect their order, but remember that these values do not imply equal intervals. For instance, on a Likert scale ranging from 1 to 5, "strongly agree" might be coded as 5, and "strongly disagree" as 1. Ensure that the chosen numerical scale is logical and meaningful.
• Clear and Consistent Labels : Consistency in labeling is paramount. Use clear and unambiguous labels for each ordinal category. Labels should be intuitive, allowing anyone working with the data to understand the meaning of each category. Ambiguous or confusing labels can lead to misinterpretation.
• Data Validation : Implement data validation procedures to identify and rectify coding or labeling errors. Data validation checks help maintain data accuracy and reliability. They can include range checks, logic checks, and consistency checks to catch inconsistencies or anomalies.
• Documentation : Keep thorough documentation of your coding and labeling process. This documentation should include the rationale behind numerical assignments and any decisions related to category labels. Clear documentation ensures transparency and facilitates collaboration with other researchers.

Properly managed data coding and labeling set the stage for robust analysis and meaningful findings. By paying careful attention to these steps, you ensure that your ordinal data is both accurate and accessible for subsequent research or analysis endeavors.

Descriptive Statistics for Ordinal Data

Now that you've gained a solid understanding of collecting and measuring ordinal data, it's time to explore the tools and techniques used to describe and summarize this type of data. Descriptive statistics provide valuable insights into the distribution, central tendencies, and spread of your ordinal data.

Frequency Distribution

A frequency distribution is a fundamental tool for analyzing ordinal data. It provides a clear overview of how frequently each category or response occurs within your dataset. Let's dive deeper into this crucial aspect:

• Creating a Frequency Table : Start by building a frequency table that lists each ordinal category along with the corresponding counts. This table offers a quick snapshot of your data's distribution.
• Visualizing Frequencies : Transforming your frequency table into a visual representation, such as a bar chart or histogram, can make the distribution patterns even more accessible. These visuals allow you to see the relative frequencies of each category and identify any trends or patterns.
• Interpreting Skewness : Pay attention to the shape of the frequency distribution. Ordinal data distributions can exhibit various patterns, including symmetry, skewness, or multimodality. Understanding these patterns is essential for drawing meaningful conclusions from your data.
• Percentages and Proportions : In addition to counts, consider expressing frequencies as percentages or proportions. This helps you compare the relative importance of different categories within your dataset, particularly in scenarios where sample sizes vary.

Measures of Central Tendency

Measures of central tendency help you identify the "center" or typical value within your ordinal data. While ordinal data lacks precise intervals, these measures provide valuable insights into the data's central tendencies:

• Mode : The mode represents the most frequently occurring category within your ordinal dataset. It is a valuable measure for identifying the most common response or category. For example, in a Likert scale survey, the mode might reveal the most prevalent level of agreement.
• Median : The median is the middle value when your ordinal data is arranged in order. It is less influenced by extreme values or outliers compared to other central tendency measures. For skewed distributions, the median can provide a more robust estimate of the center.
• Mean (Cautionary Note) : While calculating the mean (average) is possible for ordinal data, it's essential to use caution. The mean assumes equal intervals between categories, which may not be valid for ordinal data. If using the mean, be sure to acknowledge its limitations and consider it alongside other measures.

Measures of Dispersion

Measures of dispersion reveal how spread out or variable your ordinal data is. Understanding the spread of data is crucial for assessing the degree of agreement or disagreement among respondents or the variability in rankings:

• Range : The range is the simplest measure of dispersion and indicates the difference between the highest and lowest values in your ordinal dataset. While easy to calculate, the range can be sensitive to outliers.
• Interquartile Range (IQR) : The IQR focuses on the middle 50% of your data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The IQR is robust against outliers and provides insights into the central spread of data.
• Variance and Standard Deviation (Cautionary Note) : Variance and standard deviation are typically used with interval or ratio data. While they can be calculated for ordinal data, their interpretation should be cautious due to the assumption of equal intervals between categories.
• Box Plots : Box plots visually represent the spread of ordinal data by showing quartiles, outliers, and the median. They are especially useful for comparing distributions across different groups or categories.

By exploring these descriptive statistics, you can gain a better understanding of your ordinal data's characteristics, distribution, and central tendencies. These insights pave the way for further analysis and interpretation.

Data Visualization for Ordinal Data

Visualizing ordinal data is a powerful way to extract meaningful insights and communicate your findings effectively. Let's explore various visualization techniques tailored specifically for ordinal data analysis.

Bar charts  are among the most common and intuitive tools for visualizing ordinal data. They are instrumental when working with ordinal data that involves Likert scales or other categorical responses. Here's a closer look at how to effectively use bar charts:

• Category Frequency Display : In a bar chart, each ordinal category is represented as a separate bar. The height or length of the bar corresponds to the frequency or count of responses in that category. This allows you to quickly identify the most and least common responses.
• Comparative Analysis : Bar charts are excellent for comparing different categories or groups. You can easily see which categories have higher or lower frequencies, making it valuable for understanding patterns in your data.
• Grouped Bar Charts : When comparing multiple groups or subcategories, grouped bar charts can be employed. They enable you to display and compare multiple sets of ordinal data side by side, providing insights into variations across groups.
• Stacked Bar Charts : Stacked bar charts are suitable for illustrating the composition of ordinal data within a single category. Each bar is divided into segments, with each segment representing a subcategory or response option. This type of chart is useful when exploring the distribution of ordinal responses within specific contexts.

Pareto Charts

A  Pareto chart  is a specialized form of bar chart that prioritizes ordinal categories based on their frequency or impact. It's handy when you want to focus on the most significant factors within your data:

• Frequency-Ordered Categories : In a Pareto chart, ordinal categories are arranged in descending order of frequency, with the most frequent category on the left. This visual representation helps you identify and prioritize the most prevalent responses or issues.
• Focus on the Vital Few : The Pareto principle, often referred to as the 80/20 rule, suggests that a significant portion of effects comes from a small portion of causes. Pareto charts help you pinpoint the "vital few" categories that contribute the most to your dataset's characteristics.
• Dual-Axis Charts : In some cases, Pareto charts may incorporate a dual-axis approach. This means that you can overlay a line graph on the bar chart to represent cumulative percentages. This provides additional insights into the cumulative impact of ordinal categories as you move from left to right on the chart.
• Actionable Insights : Pareto charts are not only descriptive but also actionable. They guide decision-makers by highlighting areas that require attention or intervention. By focusing efforts on the most significant categories, you can optimize resources and strategies effectively.

Ordered Probit Plots

Ordered probit plots  are specialized graphical tools used primarily in statistical modeling when you want to understand the relationship between ordinal data and other variables, such as time or demographics :

• Probit Transformation : Ordered probit plots are based on the probit transformation, which converts ordinal data into a continuous scale. This transformation is helpful when you want to incorporate ordinal variables into regression models, such as ordinal logistic regression.
• Ordered Categories : In these plots, the ordinal categories are represented on the vertical axis, and the probit-transformed values are plotted on the horizontal axis. This allows you to visualize the relationship between ordinal responses and other continuous variables.
• Slope and Thresholds : By examining the slope and thresholds of ordered probit plots, you can gain insights into how changes in predictor variables impact the likelihood of moving from one ordinal category to another. This is valuable for understanding the drivers of ordinal responses.
• Model Validation : Ordered probit plots are also used in model validation. They help assess the goodness of fit of ordinal regression models by comparing observed and predicted probabilities of category transitions.

By incorporating these advanced visualization techniques into your analysis, you can not only explore the distribution of ordinal data but also uncover relationships and prioritize factors for further investigation. Visualization is a powerful tool for making your ordinal data analysis more insightful and accessible.

Inferential Statistics for Ordinal Data

Once you've explored descriptive statistics and visualized your ordinal data, the next step is to delve into inferential statistics . We'll cover key statistical tests tailored for ordinal data analysis to help you draw meaningful conclusions and make informed decisions based on your findings.

Chi-Square Test

The  Chi-Square Test  is a powerful statistical test for assessing the association or independence between two categorical variables , often involving ordinal data. It's beneficial when you want to determine if there's a significant relationship between the variables. Here's how it works:

• Contingency Tables : To perform a Chi-Square Test with ordinal data, you typically create a contingency table that cross-tabulates the two categorical variables. This table displays the frequency of each combination of responses.
• Expected and Observed Frequencies : The test calculates expected frequencies under the assumption of independence between the variables. It then compares these expected frequencies to the observed frequencies in your dataset. Deviations from expected values indicate a significant association.
• Degrees of Freedom : The Chi-Square Test is associated with degrees of freedom, which depend on the dimensions of the contingency table. Degrees of freedom affect the critical value used for hypothesis testing.
• Hypothesis Testing : The Chi-Square Test involves setting up null and alternative hypotheses. The test statistic is compared to a critical value (usually from a Chi-Square distribution table) to determine whether to reject the null hypothesis, indicating a significant relationship.
• Interpretation : A significant Chi-Square result suggests that the two categorical variables are not independent. The strength and direction of the relationship can be further explored through measures like Cramér's V or phi coefficient.

Mann-Whitney U Test

The  Mann-Whitney U Test  is a non-parametric statistical test used to compare two independent groups when the dependent variable is ordinal. It's used when you want to assess whether there are significant differences in ordinal data between two groups. Here's how it operates:

• Ranking Data : In the Mann-Whitney U Test, data from both groups are combined and ranked. Each observation receives a rank based on its position in the combined dataset, from lowest to highest.
• Test Statistic : The test statistic U is calculated, representing the sum of ranks for one group relative to the other. It measures the likelihood that a randomly selected observation from one group will have a higher value than a randomly selected observation from the other group.
• Hypothesis Testing : Similar to other statistical tests, the Mann-Whitney U Test involves setting up null and alternative hypotheses. The test statistic U is compared to critical values to determine statistical significance.
• Effect Size : Effect size measures like the common language effect size (CL) or the rank-biserial correlation (r) can be calculated to assess the practical significance of the differences between the groups.
• Assumptions : Unlike parametric tests, the Mann-Whitney U Test does not assume normality of data or equal variances. It is robust against outliers and skewed distributions.

Kruskal-Wallis Test

The  Kruskal-Wallis Test  is an extension of the Mann-Whitney U Test and is used to compare ordinal data among three or more independent groups. It's a non-parametric alternative to one-way analysis of variance (ANOVA) when dealing with ordinal data. Here's how it works:

• Ranking Data : Similar to the Mann-Whitney U Test, the Kruskal-Wallis Test ranks data from all groups together. It assigns ranks based on the combined dataset's values.
• Test Statistic : The Kruskal-Wallis test statistic H is calculated to assess whether there are significant differences among the groups. It considers the dispersion and distribution of ordinal data across multiple groups.
• Hypothesis Testing : The Kruskal-Wallis Test involves formulating null and alternative hypotheses. The test statistic H is compared to critical values from the Kruskal-Wallis distribution to determine if there are significant differences among the groups.
• Post-Hoc Tests : If the Kruskal-Wallis Test indicates significant differences among groups, post-hoc tests like Dunn's test or Conover's test can be conducted to identify which specific groups differ from each other.
• Assumptions : Like the Mann-Whitney U Test, the Kruskal-Wallis Test does not assume normality of data or equal variances. It is robust against skewed distributions and outliers.

These inferential statistical tests provide valuable insights into relationships and differences within ordinal data, allowing you to draw conclusions about the significance of your findings. Choosing the appropriate test depends on the nature of your research question and the number of groups you're comparing.

Regression Analysis with Ordinal Data

Regression analysis is a powerful statistical tool that allows you to explore relationships between variables. When working with ordinal data, it's essential to use specialized regression techniques tailored to the unique characteristics of this data type.

Ordinal Logistic Regression

Ordinal Logistic Regression  is a regression model designed to analyze the relationship between ordinal dependent variables and one or more independent variables. It's a versatile tool when you want to predict the odds of an outcome falling into a specific ordinal category. Here's a detailed look at this regression method:

• Dependent Variable : In ordinal logistic regression, the dependent variable is ordinal, meaning it consists of categories with a natural order but unequal intervals. Examples include Likert scale ratings, educational attainment levels, or socioeconomic status.
• Cumulative Logit Model : Ordinal logistic regression employs the cumulative logit model, which estimates the cumulative odds of an observation falling into a specific category or a lower category on the ordinal scale. These cumulative odds are then used to make predictions.
• Independent Variables : You can include one or more independent variables in the model to assess their impact on the ordinal dependent variable. Independent variables can be categorical or continuous, making this regression method flexible for a variety of research questions.
• Proportional Odds Assumption : Ordinal logistic regression assumes the proportional odds assumption. This means that the odds of an observation falling into a specific category are proportional across all levels of the independent variables. Violation of this assumption may necessitate alternative regression models.
• Interpretation : Interpretation of ordinal logistic regression results involves examining odds ratios. These ratios provide insights into the likelihood of an outcome occurring in a particular category compared to the reference category based on changes in the independent variables.
• Model Fit and Validation : Assessing the goodness of fit of the model and validating its predictive performance are essential steps in ordinal logistic regression. Techniques like likelihood ratio tests and cross-validation can be employed for this purpose.

Proportional Odds Model

The  Proportional Odds Model , also known as the parallel regression model, is a specific form of ordinal logistic regression. It assumes that the relationship between independent variables and the ordinal dependent variable is consistent across all levels of the ordinal categories. Here's a closer examination of this model:

• Cumulative Log-Odds : Like ordinal logistic regression, the Proportional Odds Model estimates cumulative log-odds of an observation falling into a specific category or a lower category on the ordinal scale.
• Simplified Assumption : The key assumption of this model is that the coefficients for independent variables remain constant across the ordinal categories. In other words, the odds ratios associated with the independent variables do not vary as you move up or down the ordinal scale.
• Advantages : The Proportional Odds Model simplifies interpretation by assuming a consistent relationship. This can be advantageous when this assumption holds true in your data.
• Likelihood Ratio Test : Researchers often use the likelihood ratio test to assess whether the proportional odds assumption is met. If the assumption is violated, alternative models like the partial proportional odds model or adjacent-category logit model may be considered.
• Practical Application : This model is widely applied in various fields, such as psychology, epidemiology, and social sciences, to analyze ordinal data when the proportional odds assumption is deemed reasonable.

Selecting the appropriate regression method for your ordinal data analysis depends on the nature of your research question, the assumptions of the models, and the characteristics of your data. Careful consideration and model validation are crucial in conducting meaningful regression analyses with ordinal data.

Ordinal Data Examples

To gain a deeper understanding of ordinal data and its real-world applications, let's explore some concrete examples across various domains. These examples illustrate how ordinal data is collected, represented, and utilized in different contexts.

Education Levels

One common application of ordinal data is the representation of educational attainment levels. In this scenario, individuals' highest education achieved is categorized into ordinal categories, typically ranging from lower to higher levels of education. Examples of such categories include:

• High School Diploma : This category represents individuals who have completed their high school education.
• Associate's Degree : This level indicates individuals who have earned an associate's degree typically obtained from a community college.
• Bachelor's Degree : Individuals who have completed a bachelor's degree at a college or university fall into this category.
• Master's Degree : Those who have pursued further education and obtained a master's degree occupy this ordinal category.
• Doctorate : The highest level of educational achievement is often represented by this category, including individuals with doctoral degrees such as Ph.D. or Ed.D.

Ordinal data on education levels is frequently used in studies related to employment, income, and socioeconomic status. Researchers can analyze this data to understand the impact of education on various outcomes, such as job opportunities, earnings potential, and career advancement.

Rating Scales in Customer Surveys

Ordinal data is extensively utilized in customer satisfaction surveys and product evaluations. Researchers often employ rating scales to gather customer opinions, preferences, or feedback. A prime example is the Likert scale, which offers respondents a range of options to express their level of agreement or satisfaction, such as:

• Strongly Disagree
• Strongly Agree

Each response category in the Likert scale represents an ordinal level of agreement, and respondents select the option that best aligns with their sentiment. The data collected using such scales are then analyzed to assess customer satisfaction, identify areas for improvement, or make marketing decisions.

Pain Severity Assessment

In healthcare and medical research, ordinal data is frequently encountered when assessing the severity of pain or discomfort experienced by patients. Medical professionals often use ordinal pain scales to gauge the intensity of pain, with categories that may include:

• Moderate Pain
• Severe Pain
• Excruciating Pain

Patients are asked to describe their pain levels based on these ordinal categories, allowing healthcare providers to make informed decisions regarding pain management and treatment options.

Socioeconomic Status

Socioeconomic status (SES) is another area where ordinal data plays a crucial role. Researchers and sociologists often classify individuals or households into ordinal categories based on factors such as income, education, and occupation. Ordinal categories for SES may include:

• Lower-Middle SES
• Upper-Middle SES

Analyzing ordinal SES data helps researchers understand disparities in access to resources, opportunities, and quality of life, contributing to studies on social inequality and policy development.

These examples illustrate how ordinal data is encountered in diverse fields and how it effectively captures information with inherent order or ranking. By recognizing and appropriately analyzing ordinal data, researchers can extract valuable insights and inform decision-making processes in numerous areas of study.

Assumptions of Ordinal Data Analysis

When working with ordinal data, several assumptions should guide your analysis. Here are the key assumptions:

• Proportional Odds Assumption : Many ordinal data analysis techniques, such as ordinal logistic regression and the proportional odds model, rely on the assumption that the relationship between independent variables and the ordinal dependent variable remains constant across all levels of the ordinal categories. Violating this assumption can lead to inaccurate results.
• Independence of Observations : It is assumed that the observations in your dataset are independent of each other. In other words, the response of one individual or unit should not be influenced by or related to the response of another individual.
• Ordinality of the Data : It's crucial to recognize that your data truly represents ordinal categories with a meaningful order but unequal intervals. Treating ordinal data as if it were interval or ratio data can lead to erroneous conclusions.
• Proper Scaling : When assigning numerical values to ordinal categories for analysis, ensure that the scaling is logical and meaningful. Avoid arbitrary numerical assignments that might misrepresent the data.

Ordinal Data Limitations

While ordinal data is valuable in various research contexts, it comes with inherent limitations that researchers must consider:

• Loss of Information : Ordinal data, by nature, does not capture the full range of nuances in underlying attitudes, preferences, or perceptions. It simplifies complex information into ordered categories, potentially leading to a loss of detailed insights.
• Equal Spacing Assumption : Analyzing ordinal data often involves treating the intervals between categories as equal, even though they may not be. This assumption can introduce errors in statistical analyses, mainly when working with models that assume equal intervals.
• Limited Arithmetic Operations : Arithmetic operations like addition and subtraction are not meaningful with ordinal data. You cannot accurately calculate the average of ordinal categories or perform other mathematical operations without violating the data's characteristics.
• Statistical Power : Ordinal data analysis may have lower statistical power compared to analyses of continuous data . This can make detecting statistically significant effects or relationships more challenging, especially with small sample sizes.
• Subjectivity in Coding : Assigning numerical values to ordinal categories can be subjective and may vary across researchers. This subjectivity can introduce inconsistencies or bias into the analysis.
• Interpretation Complexity : Interpreting results from ordinal data analyses can be more complex than working with continuous data. Researchers need to be cautious in explaining the practical significance of findings.

Understanding these assumptions and limitations is crucial for making informed decisions throughout the research process. While ordinal data analysis offers valuable insights, acknowledging its constraints helps researchers avoid pitfalls and draw robust conclusions.

Conclusion for Ordinal Data

Ordinal data is a valuable asset in the world of research and analysis. Its ordered categories help us understand preferences, make informed decisions, and uncover patterns in various fields, from education to healthcare. By recognizing the characteristics and nuances of ordinal data, you can confidently collect, analyze, and interpret this type of information to gain valuable insights. Remember, ordinal data may have its limitations, but when handled with care and using appropriate statistical techniques, it can unlock a wealth of knowledge and contribute to meaningful discoveries. So, whether you're conducting surveys, evaluating customer feedback, or exploring socioeconomic trends, ordinal data is a reliable companion on your journey to better understand the world around you.

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Interval Scale: Definition, Characteristics, Examples

What is ordinal data? A simple explanation with examples

Last updated

16 April 2023

Reviewed by

Cathy Heath

By leveraging ordinal data, you can gain valuable insights into customer behavior and introduce a hierarchic order to the collected information for further analytics.

Let's take a closer look at what ordinal data is and how it applies to your business.

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• What is ordinal data?

Ordinal data is classified data with an order or a ranking. It's a type of qualitative data that groups information into ordered categories.

Businesses often work with ordinal data when they analyze customer survey responses. An example of this type of data is the level of education. You can group customers by their level of education, from high school diploma to doctorate.

Ordinal data categories always have a pre-set natural order. You can't get a doctorate before getting a bachelor's degree or earn a bachelor's degree before finishing high school.  

One of the most recognizable features of ordinal data is the lack of value in the intervals between data. The differences between data points can't be determined or have no meaning.

For example, the time interval between getting a high school diploma and a bachelor's degree can drastically differ from the interval between bachelor's and master's degrees. Meanwhile, this information doesn't provide any value to a marketing specialist grouping the target audience by its level of education.

Ordinal data can't be analyzed using mathematical operators. That's why you can't find an "average" value, but determining a "median" is possible.

Overall, the key elements of ordinal data are:

Ordinal data is non-numeric

There is always a hierarchy or order (that's why the data is called ordinal)

Ordinal data values don't have an even distribution

The results of ordinal data analytics are frequency distribution, median, and range of variables.

It's an excellent tool for studying and analyzing information when precision isn't a necessity.

• Ordinal data: examples

The easiest way to understand ordinal data is by studying common examples, such as: 

Income level

Middle level

Upper level

Level of education

Post-secondary

One of the most common examples of ordinal data is the Likert scale . This points scale is designed to rate a person's opinion about a subject.

An example of a Likert scale looks like this:

How satisfied are you with our customer service?

Very satisfied

Unsatisfied

Extremely unsatisfied

While ordinal data is more complex than nominal data, it still doesn't provide extensive information about the subject. However, it can provide valuable insight into human behavior.

• Ordinal data and other data types

Ordinal data is one of the four common data types. Let's see how it compares with the rest of them.

Ordinal data vs. nominal data

Nominal data is the simplest form of a scale of measure. You can use this data type to label variables without adding any quantitative value or order. 

Examples of nominal data are:

Male/female

Animal/fish

Blond hair/brown hair

To analyze nominal data, you can group it into categories and determine the frequency. Meanwhile, ordinal data takes nominal data to the next level by giving these valuables an order or a hierarchy. In short, it categorizes and labels data points.

Ordinal data vs. interval data

Interval data takes another step towards providing a more precise measurement. Besides categorizing and ordering data as nominal and ordinal data does, it also implements equal intervals between neighboring data points. 

Examples of interval data include:

Temperature

Income ranges

While interval data has pre-set intervals, intervals between data points in ordinal data can be random. They provide no value for data analysis.

Ordinal data vs. ratio data

Similar to ordinal data, ratio data can be categorized and ranked. There are also equal intervals between data points (as in interval data). In addition, ratio data has a true zero. True zero is an absolute absence of a variable. For example, if you are analyzing income, market share, weight, or height, there is always a zero.

• How to collect ordinal data

The easiest way to collect ordinal data is by using questionnaires and surveys . Businesses use this type of data collection to gain more information about their customers.  

Being classified into categories is psychologically easier than providing precise answers. Customers are often willing to answer questions that collect ordinal data because they don't feel invasive. For example, a customer may be more willing to say that their income is between $20,000 and $40,000 than to mention an exact number.

• Uses of ordinal data

Ordinal data is extremely useful in the financial, marketing, and insurance sectors. Common applications include:

Marketers use ordinal data for many purposes, including:

Building a buyer's persona

Evaluating customer satisfaction

Monitoring customer behavior

Gaining insights into market trends

Regularly arranging ordinal data surveys and analyzing them correctly, you can streamline marketing strategies, improve customer satisfaction, increase retention , and more.

Medical research

Ordinal data can be instrumental in medical studies and clinical trials. Researchers may arrange a survey to determine how people feel after taking a certain medication. 

For example, they can ask, "Did your mood improve after taking this drug?"

Stayed the same

Slightly improved

Significantly improved

While it's impossible to measure mood improvements precisely, such responses can provide data for analytics.

Schools and universities use ordinal data to evaluate student experience and make adjustments to improve how students are educated.

An example is a survey with questions like "How comfortable do you feel asking questions in class?"

Very comfortable

Comfortable

Uncomfortable

Very uncomfortable

Like customer experience surveys, student experience surveys provide valuable insight into how schools, colleges, and universities operate from a user’s point of view.

• How to analyze ordinal data

The best way to analyze ordinal data is to visually represent the variables. For example, bar graphs can help you understand how many people from your target audience belong to the same category.

You can find out that most of your customers are between ages 25 and 35 or learn that more than a thousand have doctorate degrees.

Statistical tests that can help you analyze ordinal data include:

Mood's median test: This test allows you to compare medians (middle values) from two or several samples of populations, so you can see the difference between them.

Mann-Whitney U test : This test allows you to compare two independent samples and see whether they belong to the same population.

Wilcoxon signed-rank test: This test allows you to compare the scores' distribution in two dependent data samples to see if populations' means differ.

Kruskal-Wallis H test : This test allows you to compare the mean across three or more independent data samples.

These methods seem complicated and hard to grasp at first. With the right tools, it's possible to analyze ordinal data without getting deep into the methodology. Depending on the goal of data analysis, you can determine the need for in-depth data testing. In most cases, a simple bar graph can provide all the information you need.  

However, if you want to use this data to predict trends, you may need to go deeper into inferential statistics and implement the tests mentioned above.

• Taking advantage of ordinal data

Ordinal data can provide extra insight when evaluating different segments of your target audience. While it's not precise, this data provides valuable insights into customer behavior. You can also use it to predict behavioral trends, possible new customer segments, product development possibilities, and much more.

Continuous analytics can help streamline customer relationships and improve your marketing strategies. Creating the right survey questions and answer variants is critical to uncover the data you want. You can gather this data throughout the customer's lifecycle with the company through regular surveys.

What are examples of ordinal data variables?

Examples of ordinal data variables are education (high school, bachelor's, doctorate), age ranges (0–18, 18–25, 25–45), and income levels ($10,000–$20,000, $20,000–$30,000, $30,000–$40,000).

Is age an ordinal variable?

Depending on the question, age can be a nominal or ordinal variable. If the question is "How old are you?" it's a nominal variable. If the question is "What age range are you in?" it's an ordinal variable.

Is gender an example of an ordinal variable?

No. Gender is an example of a nominal variable. Ordinal variables can be put in an order. For example, income level can be described in ranges and put into a certain order ($10K–$20K, $20K–$30K, $30K–$40K). You can't do the same with gender.

Is height nominal or ordinal?

Height is neither nominal nor ordinal. It's a ratio variable. It can be categorized and ordered with equal intervals and a true zero.

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• What Is Ordinal Data? | Examples & Definition

What Is Ordinal Data? | Examples & Definition

Published on 18 September 2022 by Pritha Bhandari .

Ordinal data is classified into categories within a variable that have a natural rank order. However, the distances between the categories are uneven or unknown.

For example, the variable ‘frequency of physical exercise’ can be categorised into the following:

There is a clear order to these categories, but we cannot say that the difference between ‘never’ and ‘rarely’ is exactly the same as that between ‘sometimes’ and ‘often’. Therefore, this scale is ordinal.

Table of contents

Levels of measurement, examples of ordinal scales, how to collect ordinal data, how to analyse ordinal data, frequently asked questions.

Ordinal is the second of 4 hierarchical levels of measurement : nominal, ordinal, interval, and ratio. The levels of measurement indicate how precisely data is recorded.

While nominal and ordinal variables are categorical , interval and ratio variables are quantitative.

Nominal data differs from ordinal data because it cannot be ranked in an order. Interval data differs from ordinal data because the differences between adjacent scores are equal.

In social scientific research, ordinal variables often include ratings about opinions or perceptions, or demographic factors that are categorised into levels or brackets (such as social status or income).

Ordinal variables are usually assessed using closed-ended survey questions that give participants several possible answers to choose from. These are user-friendly and let you easily compare data between participants.

Choosing the level of measurement

Some types of data can be recorded at more than one level. For example, for the variable of age:

• You could collect ordinal data by asking participants to select from four age brackets, as in the question above.
• You could collect ratio data by asking participants for their exact age.

The more precise level is always preferable for collecting data because it allows you to perform more mathematical operations and statistical analyses.

Likert scale data

In the social sciences, ordinal data is often collected using Likert scales . Likert scales are made up of 4 or more Likert-type questions with continuums of response items for participants to choose from.

Since these values have a natural order, they are sometimes coded into numerical values. For example, 1 = Never, 2 = Rarely, 3 = Sometimes, 4 = Often, and 5 = Always.

But it’s important to note that not all mathematical operations can be performed on these numbers. Although you can say that two values in your data set are equal or unequal (= or ≠) or that one value is greater or less than another (< or >), you cannot meaningfully add or subtract the values from each other.

This becomes relevant when gathering descriptive statistics about your data.

Ordinal data can be analysed with both descriptive and inferential statistics.

Descriptive statistics

You can use these descriptive statistics with ordinal data:

• the frequency distribution in numbers or percentages,
• the mode or the median to find the central tendency ,
• the range to indicate the variability.

To get an overview of your data, you can create a frequency distribution table that tells you how many times each response was selected.

To visualise your data, you can present it on a bar graph. Plot your categories on the x-axis and the frequencies on the y-axis.

Unlike with nominal data, the order of categories matters when displaying ordinal data.

Central tendency

The central tendency of your data set is where most of your values lie. The mode, mean, and median are three most commonly used measures of central tendency.

While the mode can almost always be found for ordinal data, the median can only be found in some cases.

The mean cannot be computed with ordinal data. Finding the mean requires you to perform arithmetic operations like addition and division on the values in the data set. Since the differences between adjacent scores are unknown with ordinal data, these operations cannot be performed for meaningful results.

The medians for odd- and even-numbered data sets are found in different ways.

• In an odd-numbered data set, the median is the value at the middle of your data set when it is ranked.
• In an even-numbered data set, the median is the mean of the two values at the middle of your data set.

Now, suppose the two values in the middle were Agree and Strongly agree instead. How would you find the mean of these two values?

Since addition or division isn’t possible, the mean can’t be found for these two values even if you coded them numerically. There is no median in this case.

Variability

To assess the variability of your data set, you can find the minimum, maximum and range. You will need to numerically code your data for these.

• 1 = Strongly disagree
• 2 = Disagree
• 3 = Neither disagree nor agree
• 5 = Strongly agree

To find the minimum and maximum, look for the lowest and highest values that appear in your data set. The minimum is 1, and the maximum is 5.

For the range, subtract the minimum from the maximum:

Range = 5 – 1 = 4

The range gives you a general idea of how widely your scores differ from each other. From this information, you can conclude there was at least one answer on either end of the scale.

Statistical tests

Inferential statistics help you test scientific hypotheses about your data. The most appropriate statistical tests for ordinal data focus on the rankings of your measurements. These are non-parametric tests.

Parametric tests are used when your data fulfils certain criteria, like a normal distribution . While parametric tests assess means, non-parametric tests often assess medians or ranks.

There are many possible statistical tests that you can use for ordinal data. Which one you choose depends on your aims and the number and type of samples.

Ordinal data has two characteristics:

• The data can be classified into different categories within a variable.
• The categories have a natural ranked order.

However, unlike with interval data, the distances between the categories are uneven or unknown.

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.

Nominal and ordinal are two of the four levels of measurement . Nominal level data can only be classified, while ordinal level data can be classified and ordered.

In statistics, ordinal and nominal variables are both considered categorical variables .

Even though ordinal data can sometimes be numerical, not all mathematical operations can be performed on them.

Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.

Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.

The type of data determines what statistical tests you should use to analyse your data.

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• How it works

Ordinal Data-Definition, Examples, and Interpretation

Published by Owen Ingram at August 31st, 2021 , Revised On February 8, 2023

Ordinal data is crucial in data collection and analysis. And, if you want to classify data accurately, you must first understand what ordinal data itself is. That is precisely what we are here for. This blog will take you along the ordinal data journey, discussing its uses, examples, collection, and analysis. But before that, here is a brief description of what data is:

Data is a set or collection of information and facts from which conclusions can be deduced. Data can exist in the different forms-as text, numbers, and figures on either a piece of paper, bytes, and bits stored on electronic devices, or stored in a person’s mind.

Data can be classified as ordinal or nominal. Nominal is a type of data used to label variables without offering any quantitative value. This means there is no specific order. On the other hand, ordinal data, as the name itself suggests, has its variables in a specific hierarchy or order.

Ordinal data is, thus, categorical data with a set scale or order to it.

Examples of Ordinal Data

Have you ever heard of Likert scales? Well, that is one example of ordinal data. Another would be the interval scale.

Let’s discuss what these are for those who are new to these terms.

Likert Scale

Likert scale is a five, sometimes a seven-point scale used by researchers to see how much an individual disagrees or agrees with a particular opinion or statement. For example,

“I believe a complete lockdown should be active immediately to stop the COVID cases from rising.”

Now, this is a statement of opinion, whatever you call it,  will have these possible responses;

A Likert scale suggests that an attitude’s strength/intensity is linear, i.e., on a scale extending from strongly agree to strongly disagree, and that attitudes can be quantified.

Each of the five (or seven) responses, for example, would be assigned a numerical value that would be used to assess the attitude under examination.

Apart from calculating and assessing statements of agreement, this scale also measures other variations, such as quality, frequency, importance, and so on.

Interval Scale

Another type of ordinal scale is the interval scale , where every response in the survey is an interval on its own. Classifying employment levels into the professional, mid-career level, intermediate, and entry-level is an example of an interval scale.

In which category do you fall?

• a) Professional/senior level
• b) Mid-level
• c) Intermediate
• d) Entry level

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Categories of Ordinal Variables

The ordinal variables are classified into two main groups, namely: the matched and the unmatched group. This classification is based on pairing up data variables with the same properties and characteristics.

Matching is defined as a technique to check and assess the effect of a treatment. The treatment is done by comparing the non-treated and treated units in a quasi-experiment or an observational study.

The Matched Group

In this category, every member in the data sample is grouped with similar members of another sample with respect to all other variables. This is done to find a better estimation of differences. Two types of tests on the matched category depend on the number of samples under study. These are Friedman 2-way ANOVA and Wilcoxon signed-rank test .

Friedman 2-way ANOVA:

Friedman 2-way ANOVA is a non-parametric method for detecting differences in matched groups of three or more groups. This test was created by Milton Friedman and involves ranking rows together and then considering the values of each rank by columns.

Wilcoxon signed-rank test:

Wilcoxon signed-rank test is a qualitative statistical test used to assess the differences between two sets of matched samples.

The Un-matched Group

The unmatched samples are the independent samples that are selected randomly. The variables here do not depend on the values of all other ordinal variables. Though there are a few exceptional cases where the samples are dependent, most researchers base their analysis on the assumption that they are independent samples.

Following are the tests for the unmatched category:

Wilcoxon rank-sum test:

The Mann-Whitney U test is another name for the Wilcoxon rank-sum test. It is a non-parametric test that is used to compare two sets of independent samples. This test is commonly used to see if two samples are from the same population. The Wilcoxon signed-rank test is a comparable qualitative test that is used on matched samples.

Kruskal-Wallis 1-way test:

This is a non-parametric test that decides whether three or more samples are from the same population. This test, named after William Kruskal and W. Allen Wallis, determines if the median of two or more groups is different.

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Ordinal Data Analysis and Interpretation

Although both ordinal and nominal data are qualitative variables, their data analysis process is completely different. When it comes to ordinal data analysis, it incorporates the natural ordering of variables so that loss of power can be avoided.

The fact that the parametric analysis median and mode are utilized for data analysis, ordinal variables are completely different from other types of qualitative variables. This is related to the assumption that ordinal data does not have equal distance between categories. As a result, descriptive statistics appropriate for nominal data , as well as positional measurements like the median and percentiles, should be employed instead.

In some circumstances, using parametric statistics for ordinal data variables with methods that are close substitutes for mean and standard deviation may be permitted.

Descriptive Statistics

These are some of the descriptive statistics you can use with ordinal data:

• The frequency distribution in percentages or numbers. To have a better understanding of your data, make a frequency distribution table that shows how many times each response was chosen
• The mode or median to determine the central tendency . The majority of your values are found in the central tendency of your data collection . The three most widely used metrics of central tendency are the mode, mean, and median
• The range to show variability. You can use the lowest, maximum, and range to examine the variability of your data collection. For this, you will need to numerically code your data.

Inferential Statistics

These tests help you test scientific hypotheses about your data. These statistical tests for ordinal data emphasize the rankings of your measurements and are called non-parametric tests. The parametric tests, however, are used when the data at hand fulfil certain criteria, like a normal distribution .

Note: Non-parametric tests evaluate ranks or medians while parametric tests assess means.

Some of the statistical tests you can use for ordinal data depending on the number and type of samples are:

• Mann-Whitney U test (Wilcoxon rank-sum test)- compares the addition of rankings of scores
• Mood’s median test- makes a comparison between medians
• Kruskal–Wallis H test -compares mean rankings of the scores

What is ordinal data?

Ordinal data, as the name itself suggests, has its variables in a specific hierarchy or order. It is, thus, categorical data with a set scale or order to it.

What is the difference between ordinal data?

Nominal data is used to name variables but does not provide a quantitative value. On the other hand, ordinal data, as the name itself suggests, has its variables in a specific hierarchy or order.

How is ordinal data analysed?

Ordinal data is assessed with inferential and descriptive statistics : 1) Inferential Statistics Some of the statistical tests you can use for ordinal data depending on the number and type of samples are: • Mann-Whitney U test (Wilcoxon rank-sum test) • Mood’s median test • Kruskal–Wallis H test

2) Descriptive Statistics These are some of the descriptive statistics you can use with ordinal data: • The frequency distribution in percentages or numbers • The mode or median to determine the central tendency • The range to show variability

What is a central tendency?

It is the data set where most of the values lie. The three most widely used metrics of central tendency are the mode, mean, and median

Name and explain different ordinal data categories

The ordinal variables are classified into two main groups, namely: the matched and the unmatched group. This classification is based on pairing up data variables with the same properties and characteristics. The Matched Group In this category, every member in the data sample is grouped with similar members of another sample with respect to all other variables. This is done to find a better estimation of differences. The Un-matched Group The unmatched samples are the independent samples that are selected randomly. The variables here do not depend on the values of all other ordinal variables. Though there are a few exceptional cases where the samples are dependent, most researchers base their analysis on the assumption that they are independent samples.

What are examples of ordinary scales?

The two most common ordinary scales examples are: Likert Scale Likert scale is a five, sometimes a seven-point scale used by researchers to see how much an individual agrees or disagrees with a particular opinion or statement. Interval Scale Another type of ordinal scale is the interval scale, where every response in the survey is an interval on its own.

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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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Table of Contents

What is ordinal data, ordinal data characteristics, ordinal variables, ordinal data examples, how to analyze ordinal data, inferential statistics, nominal vs. ordinal data, frequently asked questions, what is ordinal data definition, examples, variables & analysis.

If your profession involves working with data in any capacity, you must know the four main data types – nominal, ordinal, interval, and ratio. In this guide, we’ll focus on ordinal data. We’ll define what ordinal data is, look at its characteristics, and provide ordinal data examples. Read on to learn everything you need to know about analyzing ordinal data, its use, and nominal vs. ordinal data. 

Ordinal data is a kind of qualitative data that groups variables into ordered categories, which have a natural order or rank based on some hierarchal scale, like from high to low. But there is a lack of distinctly defined intervals between the categories. In terms of levels of measurement, ordinal data ranks second in complexity after nominal data. 

We use ordinal data to observe customer feedback, satisfaction, economic status, education level, etc. Such data only shows the sequences and cannot be used for statistical analysis . We cannot perform arithmetical tasks on ordinal data.   

• Ordinal data are non-numeric or categorical but may use numerical figures as categorizing labels. 
• Ordinal data are always ranked in some natural order or hierarchy. So, they are termed ordinal.
• Ordinal data is labeled data in a specific order. So, it can be described as an add-on to nominal data. 
• Ordinal data is always ordered, but the values are not evenly distributed. The differences between the intervals are uneven or unknown. 
• Ordinal data can be used to calculate summary statistics, e.g., frequency distribution, median, and mode, range of variables. 
• Ordinal data has a median . 

Ordinal variables are categorical variables with ordered possible values. They can be considered as “in-between” categorical and quantitative variables.  

Ordinal variables can be classified as:

Matched Category 

In this category, each member of a data sample is matched with similar members of all other samples in terms of all other variables apart from the one considered. This helps get a better estimation of differences. Elimination of other variables prevents their influence on the results of the investigation being done. 

There are two types of tests done on the matched category of variables –

• Wilcoxon signed-rank test
• Friedman 2-way ANOVA

Unmatched Category

In this category, unmatched or independent samples are randomly selected with variables independent of the values of other variables. 

The tests done on the unmatched category of variables are – 

• Wilcoxon rank-sum test or Mann-Whitney U test
• Kruskal-Wallis 1-way test

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Ordinal data often include ratings about opinions or feelings or demographic factors like social status or income that are categorized into levels.

Interval Scale

An Interval Scale is a kind of ordinal scale where each response is in the form of an interval on its own. 

1. Rank economic status according non-equally distributed to Income level range:

• Poor or Low Income ($10K-$20K) 
• Middle income ($20K-$35K)
• Wealthy ($35K-$100K)

2. Rate education level according to:

• High School
• Post-graduate

Likert Scale

A Likert Scale refers to a point scale that researchers use to take surveys and get people’s opinions on a subject.  

1. 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 

2. Company asking customers for Feedback, experience, or satisfaction on the scale

• Very satisfied
• Dissatisfied
• Very dissatisfied

The level of measurement you use on ordinal data decides the kind of analysis you can perform on the data. Ordinal data can be analyzed using Descriptive Statistics and Inferential Statistics.

Descriptive Statistics allows you to summarize a dataset's characteristics, while Inferential Statistics helps make predictions based on current data. 

The following Descriptive Statistics can be obtained using ordinal data:

• Frequency Distribution – Describes, in numbers or percentages, how your ordinal data are distributed. For example, you can summarize grades received by students using a pivot table or frequency table, where values are represented as a percentage or count. The table enables you to see how the values are distributed. 
• Another way of overviewing frequency distribution is by visualizing the data through a bar graph. The order of categories is important while displaying ordinal data. 
• Measures of central tendency: Mode and/or median – the central tendency of a dataset is where most of the values lie. The mean, median (the central value) and mode (the value that is most often repeated) are the most common measures of central tendency. However, since ordinal data is not numeric, identifying the mean through mathematical operations cannot be performed with ordinal data.     

The mode can be easily identified from the frequency table or bar graph. 

The median value is: 

The value in the middle of the dataset for an odd-numbered set

The mean of the two values in the middle of an even-numbered dataset

Measures of variability: Range – variability can be assessed by finding a dataset's minimum, maximum, and range. Numeric codes need to be used to calculate this. The range is useful as it indicates how spread out the values in a dataset is. 

Inferential Statistics help infer broader insights about your data. Statistical tests work by testing hypotheses and drawing conclusions based on knowledge. These tests can be parametric or non-parametric. Only Non- Parametric tests can be used with ordinal data since the data is qualitative. 

Some Non-parametric tests that can be used for ordinal data are:

• Mood’s median test – to compare the medians of two or more samples and determine their differences.
• The Mann-Whitney U test – compares whether two independent samples belong to the same population or if observations in one sample group tend to be larger than in another. 
• Wilcoxon signed-rank test – to compare how and by how much the distribution of scores differ in two dependent samples of data or repeated measures of the same sample.
• The Kruskal-Wallis H test – compares mean rankings of scores in three or more independent data samples. The test helps determine if the samples originate from a single distribution.  
• Spearman’s rank correlation coefficient – to explore correlations between two ordinal variables. This test measures the statistical dependence between the rankings of the variables.

Nominal data is another qualitative data type used to label variables without a specific order or quantitative value. 

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 ordinal data?

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, like from high to low. But there is no clearly defined interval between the categories.

2. What are the four levels of measurement?

Levels of measurement indicate how precisely variables have been recorded. The four levels of measurement are:

• Nominal: the simplest data type where data can only be categorized.
• Ordinal: the data can be categorized while introducing an order or ranking.
• Interval: the data can be categorized and ranked, in addition to being spaced at even intervals.
• Ratio: the most complex level of measurement. Here data can be categorized, ranked, and evenly spaced. It also has a true zero.

3. What’s the difference between nominal and ordinal data?

Nominal and ordinal are two levels of measurement. While Nominal Data can only be classified without any intrinsic ordering or rank, Ordinal Data can be classified and has some kind of predetermined or natural order. 

4. Are ordinal variables categorical or quantitative?

Ordinal variables are categorical variables that contain categorical or non-numeric data representing groupings. 

5. Are Likert scales ordinal or interval scales?

A Likert Scale refers to a point scale that researchers use to take surveys and get people’s opinions on a specific subject. Individual Likert scale score is generally considered ordinal data since the values have clear rank or order but do not have an evenly spaced distribution. 

However, overall Likert scale scores are often considered interval data possessing directionality and even spacing. 

What we discussed here scratches the tip of the iceberg with ordinal data, examples, variables, and analysis. If you’re interested in diving deep into these topics or looking to build a career in the lucrative data science field, we recommend exploring our top-ranked courses, like Caltech Post Graduate Program In Data Science .

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COMMON MISTEAKS MISTAKES IN USING STATISTICS: Spotting and Avoiding Them

Introduction        types of mistakes         suggestions         resources         table of contents         about      glossary, ordinal variables.

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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Home Market Research

Ordinal Scale: Definition, Level of Measurement and Examples

Ordinal Scale Definition

Ordinal scale is the 2nd  level of measurement that reports the ranking and ordering of the data without actually establishing the degree of variation between them. Ordinal level of measurement is the second of the four measurement scales.

“Ordinal” indicates “order”. Ordinal data is quantitative data which have naturally occurring orders and the difference between is unknown. It can be named, grouped and also ranked.

For example:

Survey respondents will choose between these options of satisfaction but the answer to “how much?” will remain unanswered. The understanding of various scales helps statisticians and researchers so that the use of data analysis techniques can be applied accordingly.

LEARN ABOUT: Level of Analysis

Thus, an ordinal scale is used as a comparison parameter to understand whether the variables are greater or lesser than one another using sorting. The central tendency of the ordinal scale is Median.

Likert Scale is an example of why the interval difference between ordinal variables cannot be concluded. In this scale the answer options usually polar such as, “Totally satisfied” to “Totally dissatisfied”.

The intensity of difference between these options can’t be related to specific values as the difference value between totally satisfied and totally dissatisfied will be much larger than the difference between satisfied and neutral. If someone loves Mercedes Benz cars and is asked “How likely are you to recommend Mercedes Benz to your friends and family?” will be troubled to choose between Extremely likely and Likely. Thus, an ordinal scale is used when the order of options is to be deduced and not when the interval difference is also to be established.

Ordinal Characteristics

• Along with identifying and describing the magnitude, the ordinal scale shows the relative rank of variables.
• The properties of the interval are not known.
• Measurement of non-numeric attributes such as frequency, satisfaction, happiness etc.
• In addition to the information provided by nominal scale , ordinal scale identifies the rank of variables.
• Using this scale, survey makers can analyze the degree of agreement among respondents with respect to the identified order of the variables.

Advantages of Ordinal Scale

• The primary advantage of using ordinal scale is the ease of comparison between variables.
• Extremely convenient to group the variables after ordering them.
• Effectively used in surveys , polls , and questionnaires due to the simplicity of analysis and categorization. Collected responses are easily compared to draw impactful conclusions about the target audience.
• As the values are indicated in a relative manner using a linear rating scale , the results are more informative than the nominal data .

Learn about:  Interval Scale and Ratio Scale

Ordinal Examples

• Ranking of high school students – 1st, 3rd, 4th, 10th… Nth. A student scoring 99/100 would be the 1st rank, another student scoring 92/100 would be 3rd and so on and so forth.
• Rating surveys in restaurants –  When a waiter gets a paper or online survey with a question: “How satisfied are you with the dining experience?” having 0-10 option, 0 being extremely dissatisfied and 10 being extremely satisfied.
• Likert Scale – The Likert scale is a variant of the ordinal scale that is used to calculate customer or employee satisfaction .

• Understanding the socio-economic background of the target audience – Rich, middle class, poor etc. fall under the ordinal data category.
• Totally agree
• Totally disagree

LEARN ABOUT: Average Order Value

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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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