Ordinal data is probably the level of measurement you will encounter most often in social science, psychology, education, and health research, particularly in surveys. It sits above nominal in the hierarchy (you can rank categories) but below interval (the gaps between ranks are not guaranteed to be equal).
Getting comfortable with ordinal data, what it is, how to describe it, and which tests to use, will directly improve the quality of your analysis and your methodology chapter.
What Is Ordinal Data
Ordinal measurement assigns observations to ordered categories. You know which observations rank higher or lower than others, but you do not know by how much.
The three defining features of ordinal data includes:
- Categories can be meaningfully ranked from lowest to highest (or vice versa).
- The direction of the ordering is meaningful.
- The size of the differences between ranks is unknown, ranks are not equally spaced.
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Common Examples Of Ordinal Data
| Variable | Scale / Categories | Why Ordinal |
|---|---|---|
| UK degree classification | First / 2:1 / 2:2 / Third / Pass | Ordered, but a First is not a fixed ‘amount’ better than a 2:1 |
| A-level grades | A* / A / B / C / D / E / U | Ordered, but grade gaps are not guaranteed equal |
| Likert satisfaction item | Very dissatisfied → Very satisfied | Ordered, but psychological gaps may vary |
| Pain scale (NHS) | 0 (no pain) → 10 (worst imaginable) | Ordered, but a 6 is not twice as painful as a 3 |
| NS-SEC classification | Managerial → Routine occupations (8 categories) | Ordered by social status, gaps not equal |
| Ofsted rating | Outstanding / Good / Requires Improvement / Inadequate | Clearly ordered, but distances between ratings are unclear |
Statistics Appropriate For Ordinal Data
Because equal intervals cannot be assumed, statistics that rely on interval-level properties (like the mean or standard deviation) are technically not appropriate for ordinal data.
Measures of Central Tendency
- Median – the preferred measure. It identifies the middle rank without requiring equal gaps.
- Mode – also appropriate; shows the most common response.
- Mean – technically not appropriate, though widely used in practice for composite Likert scales (see below).
Non-Parametric Tests
| Research Question | Parametric Equivalent | Appropriate Ordinal Test |
|---|---|---|
| Compare two independent groups | Independent t-test | Mann-Whitney U test |
| Compare two related groups / time points | Paired t-test | Wilcoxon signed-rank test |
| Compare three or more groups | One-way ANOVA | Kruskal-Wallis test |
| Measure association between two variables | Pearson’s r | Spearman’s rank correlation (rho) |
| Compare distributions across groups | ANOVA | Kruskal-Wallis + post-hoc Dunn test |
The Parametric Vs Non-Parametric Debate For Likert Scales
This is one of the most contested topics in applied statistics education. Here is where most researchers actually land:
- Single Likert item (e.g., ‘How satisfied are you? 1–5’): treat as ordinal. Use the median and non-parametric tests.
- Composite Likert scale (e.g., 20 items summed into a total score): commonly treated as interval in practice. Use the mean and parametric tests.
- The justification: summing multiple items tends to produce an approximately normal, continuous distribution, even if individual items are ordinal.
Example: A psychology student measures student well-being using the Warwick-Edinburgh Mental Well-being Scale (WEMWBS), a 14-item Likert-type questionnaire widely used in UK health research. Total scores range from 14 to 70. Most published studies using WEMWBS treat the total score as interval and use t-tests or regression. The student follows this convention and cites it in their methodology chapter.
Visualising Ordinal Data
- Ordered bar chart – categories on the x-axis in rank order (not alphabetical). This is non-negotiable; scrambling the order destroys the meaning.
- Stacked bar chart – useful for comparing ordinal distributions across groups (e.g., satisfaction breakdown by age group or hospital site).
- Box plot – shows median, IQR, and outliers. Excellent for comparing ordinal distributions between groups without implying equal intervals.
- Avoid histograms – these imply continuous, equally-spaced values.
Student Tip: When reporting ordinal data in your results section, state the median and IQR (interquartile range), and present a frequency table showing percentages in each category. Do not just report a mean for a single Likert item and call it a day, examiners will notice
Frequently Asked Questions
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.
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.
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
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
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.
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.
Strictly no, and methodologists are generally firm on this for single items. However, in practice, means are routinely reported for composite Likert scales in many disciplines. If you do this, acknowledge in your methodology that you are treating the scale as approximately interval and explain why (e.g., precedent in the literature, large number of items, approximately normal distribution of scores).
Spearman’s rank correlation coefficient measures the strength and direction of association between two ordinal variables. It works by ranking all scores and correlating the ranks rather than the raw values. Use it when at least one variable is ordinal, or when Pearson’s assumptions are not met.
