Levels of Measurement: Definition, Examples and How to Tell

Two questionnaires want the same thing. The first asks “How old are you?” and leaves an empty box for the number. The second offers four age brackets to check. Once the responses are in, one of them gives you a mean age to the year, the other only a rough estimate.

The difference is the level of measurement. A level of measurement tells you how much information the values of a variable carry, and it therefore decides which calculations and which analyses are open to you later. Four levels are distinguished: nominal, ordinal, interval and ratio, from the least information to the most. We show you how to place any question in three steps, before the survey goes out.

📌 The key points at a glance

• Four levels: nominal, ordinal, interval and ratio.
• In practice they collapse into two groups, categorical and quantitative.
• The level is set by the question, not by the analysis.
• Nominal data allows frequencies and the mode, never a mean.
• The median needs a ranking and so starts at ordinal.
• Letter grades are ordinal, despite the GPA math.
• Likert scales are strictly ordinal data.

What is a level of measurement?

A level of measurement is the property of a variable that decides which statements its values support: only equal and unequal, additionally a rank order, additionally equal distances, or additionally a natural zero point.

Measurement scale and scale level are used for the same idea. The four-level classification comes from the psychologist Stanley Smith Stevens, who set it out in 1946 in the journal Science. Public health training still teaches it that way: the CDC course Principles of Epidemiology in Public Health Practice states that nominal and ordinal variables count as categorical, while interval and ratio variables count as quantitative.

People often ask about the scale alone, without the level. A scale in statistics is the set of all values a variable can take, together with the rules that hold between those values. How strict those rules are is what the level of measurement tells you: whether the values can only be told apart, or whether they also carry an order, equal distances and a zero point.

Two terms get mixed up in day-to-day questionnaire work. A rating scale is the visible answer format, for example the five steps from “very satisfied” to “very dissatisfied”. The level of measurement is a property of the data those steps produce.

Categorical means the answer options carry no usable numeric value, which covers nominal and ordinal. Quantitative means the values are real numbers you can calculate with, which covers interval and ratio.

A level of measurement describes not the question, but what ends up in the data table.

The four levels of measurement

The four levels build on one another. Each level does everything the level below it does, plus one thing more. That is why a higher level can always be treated as a lower one, while the reverse is impossible.

For a questionnaire this means the higher the level, the more analysis you have available later. Where it costs nothing, collect at the highest level you can. Where a question would become unanswerable or intrusive as a result, the lower level is the better decision.

Nominal data: categories without an order

Nominal data sorts values into categories that carry no ranking. Single, married and divorced sit side by side as equals, and their order on the questionnaire can be swapped at will. Numbers you assign to such categories in the dataset are pure labels: whether single becomes a 1 or a 7 changes nothing. More in the article on the nominal scale.

Ordinal data: a ranking without fixed distances

Ordinal data adds a rank order but says nothing about the gaps. The CDC uses stage of cancer as its example and spells out the consequence: the values can be ranked, but you cannot claim that the difference between stages 1 and 3 equals the difference between stages 2 and 4. The same logic covers education levels and satisfaction steps. More in the article on the ordinal scale.

Interval data: equal distances, arbitrary zero

Interval data has equal distances but no natural zero point. With temperature in degrees Fahrenheit, the difference between 50 and 55 degrees is the same as the one between 75 and 80 degrees. Because zero degrees Fahrenheit is not an absence of heat, 80 degrees is still not twice as warm as 40. Details in the article on the interval scale.

Ratio data: a true zero and real ratios

Ratio data has equal distances and a natural zero point at which the property genuinely is absent. Zero dollars of income means no income, zero years means no age. Only then does the phrase “twice as much” make sense: $3,000 really is double $1,500. Further cases appear in the article on the ratio scale.

Two further names come up regularly. The cardinal scale is not a fifth level but the umbrella term for interval and ratio, in other words for everything quantitative. The absolute scale sits above the ratio scale in some textbooks, because the unit of measurement is fixed as well, as with a count of credit hours.

Categorical and quantitative: the two groups used in practice

Lectures, methods chapters and statistics packages rarely work with four levels. They work with two groups, categorical and quantitative, and often with three labels, because ordinal sits in a class of its own. That is no contradiction of Stevens, only a summary: interval and ratio land in one group, since the same rules govern the analysis of both.

SPSS is the clearest example. It offers exactly three measurement levels per variable, Nominal, Ordinal and Scale, with Scale covering interval and ratio together. For everyday questionnaire work that grouping answers the question that actually comes up: may I calculate here, or only count?

What makes a variable quantitative

A variable is quantitative when its values are real numbers and the distances between neighboring values are the same everywhere. Typical survey examples are age in years, income in dollars, duration in minutes, height in inches and a headcount of employees.

A common short circuit is to read quantitative as “there is a number in the dataset”. A ZIP code is written with digits and is still nominal, a grade point is a number and still rests on an ordinal scale. What makes a variable quantitative is the equal distances, never the digits on their own.

Quantitative or ordinal: how to tell them apart

The border between ordinal and quantitative is where most methods chapters start to slide. Both carry an order, and both look identical in the dataset. The difference lies entirely in the distances.

The test is a single question: is the step from one value to the next the same size everywhere? For “18 years, 19 years, 20 years” the answer is yes, every step is one year. For “high school, bachelor, master” the answer is no, because nobody can say how much education sits between two degrees.

Binary variables are a special case

A binary or dichotomous variable has exactly two values, such as yes and no, or took part and did not take part. It belongs to nominal data, because two categories do not establish a ranking. It does have one peculiarity: code the two values as zero and one and the mean is exactly the share of yes answers. That is why binary variables turn up in methods that otherwise require quantitative data.

How to determine the level of measurement in three questions

The level of measurement of a variable follows from three yes-or-no questions asked in this order. As soon as one of them gets a no, the level is settled and you can stop.

The test works for any variable, whether it comes from your own questionnaire or from somebody else’s dataset. The only condition is that you keep the exact wording of the question in view rather than the topic in general.

1. Do the values carry an order? If no, the data is nominal. If yes, move to question 2.
2. Are the distances between neighboring values equal? If no, the data is ordinal. If yes, move to question 3.
3. Is there a zero point at which the property genuinely is absent? If no, the data is interval. If yes, it is ratio.

Question 1 is where most mistakes start. It does not ask whether the values can be sorted somehow, because car brands can be sorted alphabetically too. It asks whether the order means something, whether one value is more, higher or better than the one before it.

Question 3 has a useful cross-check: does the phrase “twice as much” make sense? Twice as much income is a clear statement, twice as much calendar year is not.

The test stops at four levels. Where a variable counts whole units whose size is not freely chosen, such as credit hours or children, some textbooks add an absolute scale on top. For analysis, the same rules apply there as for ratio data.

Which level of measurement does each variable have?

The table below places the variables that questionnaires ask about most often. Each row assumes the obvious answer format, which the third column keeps in mind.

One warning applies to the whole table: the level of measurement follows the answer format, not the topic. Age is ratio data as long as you collect the years as a number. Ask for age brackets instead and the data is ordinal, even though the subject is still age.

For the standard questions about the respondent, the article on demographic questions in a questionnaire is worth a look. It also covers which of them you actually need.

The borderline cases: house number, shoe size, clothing size

Three variables keep showing up in homework problems, and for two of them the answer is not clear cut. The house number is the easy one: it is a label and therefore nominal, even though the numbers rise along the street.

Shoe size and clothing size are where it gets contested. In favor of quantitative: US shoe sizes rise in fixed steps of a third of an inch. Against it: the same size means a different length depending on the manufacturer and the country, and with clothing sizes the spread between brands is wider still.

For a thesis the answer is procedural. Decide, write the decision into the methods section and give it one sentence of reasoning. Either choice is defensible with the reasoning in place, and neither is defensible without it.

The level of measurement is set by the question, not by the analysis

The level of measurement of your data is fixed the moment you choose the answer format, not later at the computer. Offer age brackets to check and you have ordinal data, and no analysis software in the world will change that afterward.

The reason lies in the direction information can travel. A year of birth can be turned into an age bracket at any point, while an age bracket never yields a year of birth again. Because the levels build on one another and the information content rises with each step, you can only move down afterward, never up.

What the open number field gives you

• Mean, median and spread are all available.
• Brackets can be redrawn afterward as you like.
• Relationships with other numbers can be calculated.

What age brackets cost you

• The mean can only be estimated roughly.
• The bracket boundaries are locked in for good.
• Studies with different boundaries barely compare.

A second reason for brackets is comparability with official figures. If you plan to set your results alongside U.S. Census Bureau data later, adopt their bracket boundaries while you are still building the questionnaire. The article how to create a questionnaire walks through the order of steps. And if you would rather see it than read it, put the open number field and the answer list side by side in a free online survey tool and the preview shows right away which analysis each format produces.

Is a Likert scale ordinal or interval?

A Likert scale strictly produces ordinal data, because nobody can demonstrate that respondents perceive the gap between “agree” and “strongly agree” as being the same width as the gap between “neither” and “agree”.

In research practice such items are very often treated as quantitative data anyway, means included. That is not sloppiness but a deliberate assumption, and it needs stating. It holds up better the more carefully the scale has been put together.

The GESIS Survey Guidelines by Natalja Menold and Kathrin Bogner (2015) set out clear requirements: a rating scale should be balanced, with the same number of positive and negative categories, and the distances between categories should be equal, in other words equidistant. That equidistance is the condition under which quantitative treatment becomes defensible at all.

The ordinal character has a practical consequence beyond the math. Pew Research Center notes that questions with ordinal response categories, such as excellent, good, only fair and poor, are generally not randomized, because the order of the categories itself conveys important information. Nominal answer lists are a different matter and are often rotated.

How to put such a scale together in detail is covered in the article on the Likert scale.

Which analysis does each level of measurement allow?

The level of measurement decides which summary statistics make sense. With nominal data you can count, with ordinal data you can additionally take the median, and with quantitative data the full range is open to you.

Permissibility accumulates upwards: whatever is allowed at a lower level stays allowed at every level above it. The mode therefore fits at every level, the median from ordinal upwards, and the mean only from interval upwards.

Measures of central tendency by level: mode, median, mean

All three measures of central tendency describe the middle of a distribution, but they assume different amounts of information. That is why they arrive one after another, in exactly the order of the levels of measurement.

• Mode: the most frequent value. It needs nothing but countable categories and fits from nominal upwards.
• Median: the value in the middle once you sort every answer. It needs a ranking and fits from ordinal upwards.
• Mean: the sum divided by the count. It needs equal distances and fits from interval upwards.

Why a mean of nominal data means nothing. The numbers in the dataset are freely chosen labels there. Code single as 1, married as 2 and divorced as 3 and you get some value between 1 and 3. Swap the codes and you get a different value, although not one person answered differently. A statistic that changes with the coding measures nothing.

Why the median starts at ordinal data. The median is the value with the same number of answers to its left and to its right. For that, “left” and “right” have to be defined at all, and only a ranking does that. College majors have no middle, satisfaction steps do.

And the difference between mode and median. The mode counts, the median sorts. On a satisfaction question, “very satisfied” can be the single most frequent step and therefore the mode, while the median sits in the middle of the scale because the remaining answers spread across the weaker steps. Both figures are correct and answer different questions.

Which test and which measure of association fits

The same split runs through significance testing. Parametric procedures assume quantitative data, while nominal and ordinal variables call for non-parametric alternatives. For associations the pattern repeats.

• Two nominal variables: a cross tabulation and a chi-square test.
• Two ordinal variables: Spearman rank correlation.
• Two quantitative variables: Pearson correlation.

Statistical software will not check this for you. In SPSS the measurement level is set by hand in the variable view, and nothing stops anyone from averaging nominal codes. The check stays your job.

How to get from raw responses to these figures is covered step by step in the guide on how to analyze a questionnaire.

Common mistakes with levels of measurement

Most mistakes happen while reading the data rather than while calculating. Four patterns show up especially often, and all four come from the same source: a number in a dataset always looks the same, whatever it stands for.

All four are avoidable if you note the level of measurement once, while the questionnaire is still in front of you. Later on, the error usually surfaces only when the results have already been written up.

Treating labels as measurements

ZIP codes, phone numbers, bus routes and student ID numbers are made of digits but measure nothing. They are labels and therefore nominal. A mean ZIP code produces a number, but no information about where your respondents live. Frequencies are the only thing that fits here.

Reading a GPA as a measurement

Letter grades are ordinal, and grade point average turns them into numbers by convention: an A counts as four points, a B as three, an F as zero. That conversion assumes the steps are evenly spaced, which nobody has measured. Using GPA as interval data is standard practice and usually fine, but in a thesis it belongs in the methods section as an assumption rather than a fact.

Mixing grading scales from different countries

A GPA of 4.0 is the top of the American scale, while in Germany and Austria the best mark is a 1 and in Switzerland it is a 6 out of 6. Put answers from several systems in one column and you invert the ranking for part of your sample. In international surveys, collect the grade per country or convert it to a shared sequence first.

Collecting age in brackets from the start

Age brackets are quick to check and look privacy-friendly. The price only shows up later: a mean age can then only be estimated, and anyone hoping to compare the results with another study runs into mismatched boundaries. Unless something speaks against it, ask for the year of birth or the number of years.

Conclusion

The level of measurement is not a formality for the methods section. It is the decision that fixes your analysis weeks in advance. Writing next to every question which level it will produce saves you from asking later why the one comparison you cared about is no longer possible.

Where to go next

• Looking for the right question format? Question types in a questionnaire
• Want to know which methods build on which level? Evaluation methods in empirical research
• Curious about the level above ratio? The absolute scale with examples

Want to try the answer formats right away?

empirio.ai, an online survey tool from Germany, comes with 35+ question types, all free, from the open number field to the matrix. For students and dissertations that helps, because the analysis tools and the charts are part of the free plan as well.

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