What is an Ordinal Scale? Definition and Example

Three students finish a course with an A, a B and a C. You know right away who did best. What you do not know is whether the step from an A to a B means as much as the step from a B to a C.

That gap is what the ordinal scale describes. An ordinal scale is a level of measurement that puts the values of a variable into a genuine rank order without saying anything about the distance between the ranks. Order, the median and the quartiles therefore hold up, while the mean and the standard deviation rest on an assumption you have to justify. By the end of this article you will recognize every ordinal variable in your questionnaire.

📌 Key points at a glance

• An ordinal scale ranks categories without fixing the gaps.
• Letter grades, highest degree and satisfaction levels are ordinal.
• The median and quartiles hold, the mean only under an assumption.
• Ordinal data fits Mann-Whitney, Kruskal-Wallis and rank correlation.
• A “don’t know” option does not belong in the rank order.

What is an ordinal scale?

An ordinal scale is a level of measurement on which the values of a variable can not only be told apart but also placed in order. Two answers therefore allow three statements: greater, smaller or equal. How far apart they sit is left open.

The name comes from the Latin ordo, meaning order or series. That is exactly what separates this level from the nominal scale, because both sort responses into categories and only the ordinal scale claims an order on top of that. The statistical consulting group at UCLA builds its whole test selection guide on that difference and lists a separate row for ordinal variables wherever a parametric test assumes interval data (UCLA OARC, Choosing the Correct Statistical Test).

The four levels of measurement go back to the psychologist S. S. Stevens, who set them out in the journal Science in 1946. He describes the ordinal scale as arising from the operation of rank ordering and gives the hardness scale of minerals as the classic example (Stevens 1946). That talc is softer than quartz can be checked. By how much, the scale does not say.

An ordinal scale tells you who comes first. It does not tell you by how far.

Trichotomy and transitivity: the two conditions behind a rank order

A rank order only holds if two conditions are met. The first is trichotomy: for any two values, either a is greater than b, or b is greater than a, or a equals b, and exactly one of those three applies. The second is transitivity: if a is greater than b and b is greater than c, then a must also be greater than c.

Both conditions sound obvious and questionnaires break them all the time. A satisfaction scale that runs from very satisfied to very dissatisfied and then adds “does not apply to me” breaks trichotomy, because that answer stands in no greater-or-smaller relation to the rest. Where the ordinal scale sits among the other levels is set out in our overview of the levels of measurement.

Examples of ordinal variables

Ordinal variables are those whose values carry a recognized order without fixed distances between them: letter grades, highest degree earned, satisfaction measured in steps, a finishing position, an income bracket, a credit rating or the Saffir-Simpson hurricane category.

The table shows three of them with their values and the sentence that does not follow. That is the quickest check in practice, because the sentence you are not allowed to say is usually easier to spot than the correct classification.

Two forms: ranks you award and categories you order

Ordinal data arrives by two routes and telling them apart saves work later. Ranks you award directly come from a ranking question, for instance when respondents put five options into an order of preference. Each rank then appears once per person and the analysis works with rank positions.

Ordered categories, by contrast, are the ones you set out yourself, such as the steps from very satisfied to very dissatisfied. Many people choose the same step, frequencies build up per category and that is what the median and the quartiles rest on. A ranking question with eight positions produces not eight answers but a single ordered series per person, which looks different in the data file from what most people expect.

When a continuous variable turns ordinal

Age and income are continuous by nature, as long as you record the exact figure. Ask for age brackets or income brackets instead and you hold ordinal data, even though the subject has not changed. The answer format is what does it: “37 years” becomes “30 to 39” and where exactly inside the bracket someone sits can no longer be recovered. The route runs one way only, because brackets never turn back into individual values.

Ordinal, nominal or continuous: the distinction in two questions

The level of measurement of a variable comes out of two questions asked in a fixed order, and the first separates nominal from ordinal. It runs: is one value in itself more, higher or better than another? If the answer is no, you have a nominal scale.

The second question separates ordinal from continuous: are the gaps between neighboring values demonstrably equal? If the answer is no again, the variable stays ordinal. Everything hangs on the word demonstrably, because a scale numbered 1 to 5 looks like equal gaps without proving them. Where the classification stays in doubt, take the lower level and justify it in your methods section.

The check applied to three variables

• Major: no order, so a nominal scale.
• Highest degree: order yes, equal gaps no, so ordinal.
• Temperature in degrees Fahrenheit: equal gaps demonstrable, so an interval scale.

Degree is ordinal, major is nominal

Both variables consist of a list of names and look alike for that reason. Degree, however, carries a recognized progression from an associate degree through a bachelor’s to a doctorate, and that progression belongs to the thing itself rather than to the order of options on screen. Treating it as nominal throws the information away and leaves you unable to report a median that the data would have supported. Major is different, because psychology sits neither above nor below mechanical engineering and any ranking there would be invented.

What you can calculate with ordinal data

Ordinal data allows every procedure that counts or sorts and rules out every procedure that needs fixed distances. Stevens set this out in a table in 1946 and assigned the ordinal scale exactly two summaries: the median and percentiles.

Any transformation that preserves the order is allowed as well. Stevens calls this the isotonic group: every strictly increasing monotonic function may be applied to the values without the scale losing its meaning. In practice that means you can replace the steps 1 to 5 with 10, 20, 40, 80 and 160, or with the letters A to E. As long as the order stands, the information stays the same, and that is how you can tell the numbers here are not quantities.

The median with an even number of cases: the interpolation trap

With an even number of answers two values sit in the middle and spreadsheets quietly average the pair. The steps “neither agree nor disagree” and “agree” then produce a median of 3.5, a step that does not exist in your questionnaire. Stevens warned about precisely this: assigning a value by linear interpolation within a class interval is, on rank ordered data, strictly out of bounds, because the equal spacing of the scale is the very thing in question.

With an even number of cases, report the lower of the two middle categories and name the other one alongside it. A sentence such as “the median falls on ‘neither agree nor disagree’, with ‘agree’ as the neighboring category above” is more honest than any decimal place and easier to defend in front of a committee.

The quartile range instead of the standard deviation

Spread on ordinal data is best given as the range between the lower and the upper quartile, because both quartiles are permissible as percentiles at this level. It shows the band the middle 50 percent of your answers fall into. Report it from category to category: “the middle 50 percent lie between ‘neither agree nor disagree’ and ‘agree’.”

Working out the difference between the two quartiles as a single number goes one step further than the scale strictly allows, since subtraction assumes equally sized gaps. The standard deviation is out in any case, because it builds on the mean. More on the stages of analysis is in our article on descriptive and inferential statistics.

Can you take a mean of ordinal data?

The mean assumes equally sized gaps between values and an ordinal scale does not supply them. It is therefore not the right summary here, and in a thesis the median is the figure nobody can challenge.

A common claim is that Stevens banned means on ordinal data. His 1946 paper says something different and considerably more precise. He notes that, in the strictest propriety, the mean and standard deviation ought not to be used at this level, but invokes what he calls a kind of pragmatic sanction, because in many instances the practice leads to fruitful results. Outlawing it, he says, would serve no good purpose. In the same paragraph he states the condition that matters: the error grows exactly to the extent that successive intervals on the scale are unequal in size.

That leaves you with a workable rule. Always report frequencies and the median, because they need no extra assumption. A mean may sit alongside them if your response steps are evenly worded and you state the assumption in your methods section. On a single item it stays open to challenge; on a scale built from several items it is accepted practice. The full weighing up is in our article on the Likert scale.

⚠️ Watch out

A grade point average is the same case and nobody notices. Letter grades are ordinal, yet averaging them into a GPA is routine on every transcript. In your own research that is no free pass: if you average, add the sentence saying you are treating the steps as equally far apart.

Which tests fit ordinal data

Ordinal data calls for non-parametric procedures, which work with rank positions rather than measured values. They assume no normal distribution and therefore cope with the small or skewed samples that student projects usually produce.

Which procedure fits depends on two things: how many groups you are comparing and whether those groups are independent or the same people measured more than once. The UCLA statistical consulting group lists exactly this pairing, giving a separate ordinal row next to each parametric test (UCLA OARC, Choosing the Correct Statistical Test).

When the outcome itself is ordinal

If the variable you want to explain is ordinal rather than the one doing the explaining, a regression is still available to you. The model for that case is ordered logistic regression, which predicts the probability of landing at or below each step instead of predicting a number. UCLA lists it in the ordinal row wherever the parametric route would call for a factorial ANOVA or a linear regression. Ordinal outcomes are therefore not a dead end, they simply need a different model.

Why rank correlation sits in the wrong row in Stevens

Spearman’s rank correlation counts today as the standard procedure for ordinal associations and almost every introduction lists it in the ordinal row. In Stevens’s own 1946 table it sits in the interval row, and he gives his reason in a bracket: the coefficient assumes equal intervals between successive ranks and therefore calls for an interval scale. That strict reading never caught on and current practice is what applies to your work. Knowing the passage, though, makes it easier to see that matching procedures to levels of measurement is a convention rather than a law of nature.

Ordinal scales in a questionnaire: the response steps decide

Whether you end up with ordinal data is settled by the response options, not by the analysis. A question yields exactly the level of measurement its answer format supports, and afterward a variable can only be made coarser, never finer.

Five points are worth settling before the survey goes out. Together they take ten minutes and save you half the analysis later on.

1. Let the order follow the subject. The steps run in the order the variable dictates, not the order they occurred to you in.
2. Space the wording evenly. From “never” through “rarely” to “sometimes” is more even than jumping from “never” straight to “almost always”.
3. Keep escape options out of the series. “Don’t know” and “prefer not to answer” belong visually apart and are treated as missing values in the analysis.
4. Set bracket boundaries without overlap. For age that means 18 to 24 and 25 to 34, not 18 to 25 and 25 to 35.
5. Test before you send. Three people from your target group sort the steps themselves before the question goes live.

Point three is the one most often skipped and it does the most damage. As soon as “don’t know” counts as another step, a category sits inside the series that is neither above nor below the rest, and the median alone already moves to the wrong place. With empirio.ai, an online survey tool from Germany, you set such an option as an escape answer so that it is reported separately in the analysis. Which question type yields which data is set out in our overview of question types in a questionnaire.

💡 Tip

Read your response steps aloud from the bottom up. If one step stands out as not belonging in the series, you either have an escape option inside the scale or two variables mixed into one question.

Common mistakes with ordinal scales

Most mistakes around ordinal scales happen one step before the arithmetic, at the point where the variable is classified. Once that decision is made everything else follows it and nobody spots the problem in the analysis.

What is striking is that the three most common cases pull in different directions. In one the scale is classified too high and treated as though measured values were available. In another it is classified too low and information is thrown away. In the third the classification is right, but the scale itself does not carry the order the analysis assumes.

Adding up rank positions

Adding the placings from several rounds and dividing treats ranks as if they were points. The result then depends on how far apart the participants happened to be in each round, and that is precisely the information rank positions do not hold. Report the median of the placings instead, or analyze the underlying measurements directly if you have them.

Treating ordinal data as nominal

Satisfaction levels, frequency wordings such as never, rarely and often, and highest degree all carry an order. Merely counting them throws away the median, the quartiles and every rank based procedure, and leaves you unable to say anything about direction. The check takes a moment: if one value can sensibly be called more or less than another, the variable is at least ordinal.

Breaking the scale in the middle

A five point agreement scale can take a neutral midpoint, but not a step that belongs to a different question. Replace “neither agree nor disagree” with “cannot judge” and the rank order breaks at its most sensitive point, leaving the two halves of the scale no longer comparable. If you need an escape option, hang it outside the scale.

Conclusion

The ordinal scale is the level most questionnaire data actually sits on and at the same time the level whose limits are crossed most often. Report frequencies, the median and the quartile range and you are on safe ground while still saying everything the data supports. Anything beyond that is not a calculation but an assumption, and assumptions belong in the methods section.

Remember the one question: do I know the order but not the distances? Then you are looking at an ordinal scale.

Where to go next

• Want to see how the four levels fit together? Determining the level of measurement
• Missing the level below? Nominal scale
• Need equal distances? Interval scale
• Putting your response steps together right now? Creating a questionnaire

Want to try your response steps out first?

With empirio.ai you set up a question with ordered steps in minutes, send it to three test participants and change the order before the real survey starts.

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