Levels of measurement: nominal, ordinal, interval, ratio

Levels of measurement describe what the numbers or labels in a variable can tell you: only categories (nominal), an order (ordinal), equal distances between values (interval), or a true zero that makes ratios meaningful (ratio). The level of each survey question decides which averages, charts and statistical tests are valid for its answers.

The four-level classification comes from the psychologist S. S. Stevens, who described it in "On the theory of scales of measurement" (Science, 1946). It is still the standard starting point in research methods courses.

The four levels at a glance

Each level keeps the properties of the one before it. Ratio data can be treated as ordinal (you can rank incomes), but ordinal data cannot be treated as ratio (a rating of 4 is not twice a rating of 2).

Each level in more detail

Nominal

Labels without order. You can count how many people chose each option and report shares. If you code "North = 1, South = 2, West = 3", the average code of 1.8 means nothing. Use the mode and a chi-square test (try the chi-square calculator) to compare groups.

Ordinal

Ordered categories with unknown distances. The gap between "satisfied" and "very satisfied" is not guaranteed to equal the gap between "neutral" and "satisfied". The median and percentiles are safe; see mean, median and mode for the difference. A single item on a rating scale is ordinal in the strict sense.

Interval

Equal distances, but zero does not mean "none". 20 °C is not twice as warm as 10 °C. Means, standard deviations and the t-test are allowed; ratios are not.

Ratio

A true zero, so ratios make sense. A customer with 10 orders placed twice as many as one with 5. Ask these as an open number whenever you can; grouping age or income into brackets turns ratio data into ordinal data and loses detail you cannot recover later.

Likert items and the "ordinal or interval" debate

The most common practical question is whether you may average answers on a Likert scale. Strictly, one Likert item is ordinal. Jamieson (Medical Education, 2004) argued that means and parametric tests are therefore inappropriate for such data. Norman (Advances in Health Sciences Education, 2010) showed that parametric tests such as the t-test and Pearson correlation still give reliable results on Likert data, even with small samples and skewed distributions.

A workable rule many textbooks follow:

• For a single item, report the distribution, the median and the top-box share. A mean is fine as an extra summary if you state the scale.
• For a summed or averaged scale of several items that measure one construct (check with Cronbach's alpha), treating the score as interval is common practice.
• Whatever you choose, say so in the methods section so readers can judge.

Worked example: one survey, four levels

A customer survey has four questions:

1. "Which region are you in?" (North, South, West) is nominal. Report shares: 52%, 30%, 18%.
2. "How satisfied are you?" on five labeled points is ordinal. Report the median (4, "satisfied") and the share of 4–5 answers.
3. A 10-item satisfaction index, averaged per person, is usually treated as interval. Compare two segments with a t-test.
4. "How many times did you contact support last month?" is ratio. A mean of 2.4 contacts against 1.2 means twice as many, a statement you cannot make about question 2.

Common mistakes

• Averaging codes of categories. Region codes, department numbers and product IDs are labels.
• Putting "Don't know" inside the scale. If "Don't know" is coded 6 on a 1–5 scale, every mean is wrong. Code it as missing or as a separate category.
• Making ratio claims about ratings. "Satisfaction doubled from 2 to 4" is not a valid reading of an ordinal scale.
• Bracketing numbers you could have asked directly. You can always group exact ages later; you cannot ungroup "25–34".
• Picking the test before checking the level. The level of the dependent variable narrows the list of valid tests, so check it first.

Choosing the level when you write a survey

The question type you pick fixes the level of the data. Single choice and dropdown give nominal data, or ordinal data if the options form an order. Rating, opinion scale and ranking questions give ordinal data. A numerical answer gives ratio data when the quantity has a true zero. In SurveyNinja, the Numerical response question is available from the Basic plan, and exports to CSV, XLSX and SPSS work on every plan.

Free calculators help once the level is clear: the Likert scale calculator for ordinal items, the median and percentile calculator, the Spearman correlation calculator for ranks and the t-test calculator for interval and ratio data.