What is a Nominal Scale? Definition and Example

Two entries from the same dataset: the ZIP code 10001 and the age 27. The difference between them is called the nominal scale.

Both are numbers and both can be added up, but the sum of all the ZIP codes means nothing while the sum of all the ages means something. The nominal scale is the lowest level of measurement: it sorts every answer into exactly one category, and between those categories there is neither an order nor a measurable distance. All you may report are frequencies and the most common category, never the mean or the median. By the end of this article you will be able to tell, for every question in your questionnaire, whether it produces nominal data and which analysis still holds.

📌 Key points at a glance

• The nominal scale separates categories without ranking them.
• Gender, college major, blood type and ZIP code are nominal.
• Frequencies, the mode, cross-tabulation and chi-square are allowed.
• Mean, median and standard deviation make no sense here.
• Numbers on a nominal scale are labels, not quantities.

What is a nominal scale?

A nominal scale is a level of measurement on which values can only be told apart and named. There is no ranking and no distance between the categories, which is why only one statement about two answers is possible: they are either the same or different.

The name comes from the Latin nomen, meaning name, and that is exactly what this level does. It hands out names for classes. Penn State’s online statistics program defines nominal variables as qualitative variables that do not have a natural order and gives hair color, religion and the residence ZIP code of a student as its examples (Penn State, STAT 508).

The four levels of measurement go back to the psychologist S. S. Stevens, who set them out in the journal Science in 1946. On the nominal scale he writes that the numerals serve only as labels and that words or letters would do the same job (Stevens 1946). His rule for assigning them is as short as it gets: no class gets two different numerals and no numeral stands for two different classes.

On a nominal scale a number stands for a name, not for an amount.

Two conditions every nominal question has to meet

Two requirements for the answer categories follow from that rule, and questionnaires break both of them regularly. The categories have to be mutually exclusive, so that every person fits into exactly one box. And they have to be exhaustive, so that every person finds a box at all.

Exclusivity fails fastest with numeric ranges. Offering age brackets of “18 to 25” and “25 to 35” lets a 25-year-old fit into two boxes and the count then depends on chance. Exhaustiveness fails with lists written from your own surroundings: a question about the highest degree completed that offers only a bachelor’s and a master’s leaves out the associate degree, the professional degree and everyone who finished high school and stopped there.

For where the nominal scale sits among the other levels and how to work out the level of a variable, see our article on the level of measurement.

Examples of nominal variables

Nominal variables are those whose values can only be named: gender, college major, blood type, state of residence, marital status, citizenship, first language or the make of someone’s phone. The table gives the values for each example and the sentence that does not follow from them.

The highway number is the most instructive of the three, because it is a number and still counts for nothing. There are no 25 units of anything between I-70 and I-95, and the numbers could just as well be letters. With blood types this is easier to spot, because letters are used there anyway.

The special case with only two categories

A nominal variable with exactly two values is called dichotomous or binary. Examples are “took part” against “did not take part”, or “member” against “not a member”. Such variables are a borderline case: with only one step between the two values, an order can neither be claimed nor ruled out, and the distinction between nominal and ordinal loses its purpose.

Dichotomous variables are usually coded as 0 and 1, and in that form they can be used even in procedures that normally require a higher level of measurement. The mean is then the proportion of ones and has a clear meaning as a relative frequency. That is a special case of the coding and not a promotion of the nominal scale.

Nominal or ordinal: how to tell the difference

Nominal and ordinal scales differ in exactly one respect, namely the order. An ordinal scale puts the categories into a natural ranking, a nominal scale does not. Everything else they share, above all the division into categories that exclude one another.

The test is a single question: is there a value that is in itself more, higher or better than another? For letter grades the answer is yes, a B is better than a D, so the variable is ordinal. For college major the answer is no, because Psychology does not sit above Engineering. The full distinction with all the arithmetic rules is in our article on the ordinal scale.

Educational attainment is ordinal, college major is nominal

Educational attainment and college major look the same at first glance, because both are lists of names. Attainment, however, carries a recognized progression from high school through an associate degree to a bachelor’s and beyond, and that progression is part of the thing itself. Penn State uses exactly this example for the boundary case: the steps are ordered, but the gaps between them are not equal, so the variable stays categorical rather than becoming quantitative.

The order on screen decides nothing

You often read that a question is ordinal because its answer options sit in an order. That only holds if the order comes from the variable itself rather than from the display. Listing the fifty states alphabetically does not make them ordinal, and sorting them by population does not either: the ordered variable would then be the population, not the state.

When numbers are only labels

Numbers on a nominal scale are names, not quantities. This includes the ZIP code, the student ID number, the jersey number, the area code and the codes 1, 2 and 3 that a statistics package uses to store answer categories. Every one of these numbers could be swapped for another without any loss of information.

Stevens distinguished two uses in 1946, and the distinction is still useful. In the first, every single object gets its own number, and his example is the jersey numbers of football players. There the only sensible figure is the number of cases. In the second, one number stands for a whole class with several members, and only here can you determine the most frequent class and test for association.

For your questionnaire this produces a simple rule: a student ID number is an identifier, not a variable. It belongs in the data file so that answers can be matched up, but in no analysis.

⚠️ Careful

Spreadsheets and statistics packages will happily calculate the mean of a nominal variable. No warning appears, the result looks like a number and travels straight into the write-up. Set the level of measurement when you create the variable and record it in your codebook.

What you can calculate with nominal data

With nominal data every procedure that only counts is allowed, and every procedure that assumes an order or a distance is ruled out. Stevens set this out in a table in 1946 and gave the nominal scale exactly three entries: the number of cases, the mode and measures of association from a contingency table. The overview below translates that into the calculations you actually meet in an analysis.

The direction of that table only runs one way, and Penn State states the rule plainly: procedures developed for interval or ratio data cannot be applied to nominal or ordinal data, while the reverse is possible but wasteful, because it ignores the information the higher level carries. The chi-square test is therefore the standard procedure for nominal variables, and it needs independent observations plus an expected count of at least five in every cell. For two groups you can check significance directly.

Bar and pie charts suit nominal data

Nominal frequencies belong in a bar chart or a pie chart, because both show shares only and claim no order. A histogram does not fit, because it assumes adjoining, ordered classes. A boxplot does not fit either, because it rests on the median and the quartiles. You choose the order of the bars yourself, and descending by frequency is the usual choice.

In regression, nominal variables become 0/1 variables

Nominal variables can perfectly well be used in a regression, just not in their raw form. The variable is split into dummy variables that take only 0 or 1. Four categories produce three dummies, and the fourth serves as the reference against which the others are compared. Any statistics package does this at the press of a button once the variable is marked as nominal. For the wider picture of analysis stages, see our article on descriptive and inferential statistics.

Nominal scale in a questionnaire: five things to settle first

Whether you end up with nominal data is decided by the wording of the question, not by the analysis. Afterwards a variable can only be made coarser, never finer. Settle the following five points before the survey goes out.

1. List the categories in full. Write down every value that can occur in your target group, not only the obvious ones.
2. Rule out overlaps. Check every category against every other one, especially with numeric ranges and lists containing umbrella terms.
3. Give the residual category a text field. An “other” without an input box collects exactly the answers you will not be able to reconstruct later.
4. Separate single choice from multiple choice. Decide deliberately whether exactly one answer should be possible and word the question accordingly.
5. Collect fine rather than coarse. Ask for the college major in plain text if you can group majors yourself afterwards.

Point three is the one most often underestimated. A residual category that ends up attracting a fifth of all answers makes the whole question useless, because the largest block stays nameless. With empirio.ai, an online survey tool from Germany, you can attach a text field to an answer option and change the list after a pilot run without setting the questionnaire up again.

A multiple choice question gives you several variables, not one

A multiple choice question does not produce a single nominal variable. Every answer option becomes a dichotomous variable of its own, with the values checked and not checked. Eight options therefore give you eight variables and the percentages do not add up to 100. Miss this and you will later report shares that total 180 percent and have to redo the table. For which question type yields which data, see our overview of question types in a questionnaire.

💡 Tip

Have three people from your target group read the list of categories before you send it out, with one question only: can you find yourself in here? Anyone who cannot will later check “other” or drop out.

Common mistakes with the nominal scale

Most mistakes around the nominal scale happen not in the arithmetic but in the classification. A variable is recorded at the wrong level and everything that follows inherits that decision. Three cases turn up particularly often.

Averaging numeric codes

If single is stored as 1, married as 2 and divorced as 3, every package will dutifully report a mean of 1.9. That number describes nothing, because the codes could just as well have been 7, 3 and 12 and the mean would have been completely different. Report the frequency per category and the mode instead.

Recording an ordered variable as nominal

Educational attainment, satisfaction and frequency answers such as never, rarely and often carry an order within them. Treating them as plain categories gives away the median and every rank-based procedure. The check takes a moment: if one value can sensibly be described as more or less than another, the variable is at least ordinal.

Letting the residual category grow

“Other” is a fallback, not a category. Once it ranks among the three most common answers, the list was incomplete and the analysis cannot name its largest part. With a text field the block can still be broken down afterwards; without one, nobody reaches that information again.

Conclusion

The nominal scale is the simplest level of measurement and still the one that goes wrong most often in questionnaires. The reason is rarely the statistics, it is the answer categories: get them complete and free of overlap and the hard part is behind you, because counting is quick. Remember the one question that settles it: is one value worth more than another? If the answer is no, you are looking at a nominal scale.

Where to go next

• Want to see how the four levels fit together? Determining the level of measurement
• Need the next level up? Ordinal scale
• Working with distances? Interval scale
• Putting your questionnaire together? Creating a questionnaire

Want to try your answer categories out right away?

With empirio.ai you can set up a question with fixed categories in a few minutes, send it to three test readers and change the list before the real survey starts.

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