Ordinal data is a type of categorical data whose categories follow a meaningful order or rank, but where the gaps between those categories are not necessarily equal. You can say one value is higher or lower than another (for example, ‘satisfied’ is more positive than ‘dissatisfied’), but you cannot say exactly how much higher, because the distances between the ranks are unknown. This makes ordinal data the second of the four levels of measurement, sitting above nominal but below interval and ratio.
It is probably the level of measurement you will encounter most often in social science, psychology, education and health research, particularly in surveys. It ranks above nominal in the hierarchy (you can order the 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 statistical tests to use — will directly improve the quality of your analysis and your methodology chapter. This guide walks through the definition, real-world examples, how ordinal compares with nominal and interval data, the statistics that are valid for it, and how to present it correctly.
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 word ‘ordinal’ comes from ‘order’ — the defining property is the rank.
The three defining features of ordinal data are:
- Categories can be meaningfully ranked from lowest to highest (or vice versa).
- The direction of the ordering is meaningful — moving up the scale always means ‘more’ (or always ‘less’).
- The size of the differences between ranks is unknown — the categories are ordered but not equally spaced.
A simple test: if you can sort the categories into a sensible ‘league table’ but cannot do arithmetic on the labels (you cannot say rank 4 minus rank 2 equals rank 2), you are almost certainly looking at ordinal data.
“In the ordinal scale, the numbers assigned to objects represent the rank order (1st, 2nd, 3rd, etc.) of the entities measured. The ordinal scale conveys no information about the magnitude of the differences between ranks.” — Adapted from S. S. Stevens, ‘On the Theory of Scales of Measurement’, Science, 1946
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Common Examples Of Ordinal Data
Ordinal data is everywhere once you start looking. The most familiar examples are Likert scales (the agree-to-disagree response options in almost every questionnaire), grades and classifications, and ranked positions such as finishing 1st, 2nd or 3rd in a race. In every case the categories are ordered, but the spacing between them is not guaranteed to be the same.
| Variable | Scale / Categories | Why Ordinal |
|---|---|---|
| Likert satisfaction item | Very dissatisfied → Dissatisfied → Neutral → Satisfied → Very satisfied | Ordered, but the psychological gaps between points may vary |
| 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 to be equal |
| Race / competition finish | 1st / 2nd / 3rd / 4th … | Ranks only — 1st may beat 2nd by a second or an hour |
| Pain scale (NHS) | 0 (no pain) → 10 (worst imaginable) | Ordered, but a 6 is not twice as painful as a 3 |
| NS-SEC classification (ONS) | Managerial → Routine occupations (8 classes) | Ordered by socio-economic position, gaps not equal |
| Ofsted rating | Outstanding / Good / Requires Improvement / Inadequate | Clearly ordered, but distances between ratings are unclear |
Notice that some of these use numbers (the 0–10 pain scale) and some use words (degree classes). Numbers in an ordinal scale are just labels for rank order — the arithmetic distance between them carries no guaranteed meaning. This is the single most important idea to remember about ordinal data.
Statistics Appropriate For Ordinal Data
Because equal intervals cannot be assumed, statistics that rely on interval-level properties (such as the mean or standard deviation) are technically not appropriate for ordinal data. Instead, you use rank-based statistics and non-parametric tests.
Measures of Central Tendency
- Median — the preferred measure. It identifies the middle rank without requiring equal gaps.
- Mode — also appropriate; it shows the most common response category.
- Mean — technically not appropriate, because it requires equal intervals. It is, however, widely used in practice for composite Likert scales (see below).
For spread, report the range and the interquartile range (IQR) rather than the standard deviation, since the IQR is also rank-based.
Non-Parametric Tests
Non-parametric tests work on ranks rather than raw values, which is exactly what ordinal data provides. Use this table to map your research question to the correct test. For a fuller walk-through, see our guide on which statistical test you should use.
| 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 three or more groups, then locate the difference | ANOVA + post-hoc | Kruskal-Wallis + post-hoc Dunn test |
Step 1 — rank all 10 scores together from lowest to highest, sharing tied ranks. The two 2s take ranks 1 and 2 (mean = 1.5 each); the three 3s take ranks 3, 4, 5 (mean = 4 each); the three 4s take ranks 6, 7, 8 (mean = 7 each); the two 5s take ranks 9, 10 (mean = 9.5 each).
Step 2 — sum the ranks for each group. Online (5, 4, 5, 4, 3) = 9.5 + 7 + 9.5 + 7 + 4 = 37. In-person (2, 3, 2, 4, 3) = 1.5 + 4 + 1.5 + 7 + 4 = 18.
Step 3 — calculate U with U = n₁n₂ + n₁(n₁+1)/2 − R₁. For the online group: U = (5×5) + (5×6/2) − 37 = 25 + 15 − 37 = 3. The smaller U is then compared with the critical value (for n₁=n₂=5, α=0.05 two-tailed, the critical value is 2). Here U = 3 > 2, so the difference is not statistically significant at the 5% level — the online group ranks higher, but not significantly so in this tiny sample.
The Parametric Vs Non-Parametric Debate For Likert Scales
This is one of the most contested topics in applied statistics. Here is where most researchers actually land:
- Single Likert item (e.g. ‘How satisfied are you? 1–5’): treat as ordinal. Report the median and use non-parametric tests.
- Composite Likert scale (e.g. 20 items summed into a total score): commonly treated as interval in practice. Researchers report the mean and use parametric tests.
- The justification: summing many items tends to produce an approximately continuous, roughly normal distribution, even when each individual item is ordinal.
Whichever route you take, state your decision explicitly in your methodology and justify it — examiners care far more about a clearly reasoned choice than about which side of the debate you choose.
Ordinal vs Nominal vs Interval Data
Ordinal data sits between nominal data and interval data in the levels of measurement. The quickest way to place a variable is to ask two questions: Are the categories ordered? and Are the gaps between them equal?
- Nominal — categories are named but not ordered (e.g. eye colour, country of birth, blood type). No category is ‘higher’ than another.
- Ordinal — categories are ordered, but the gaps are not equal (e.g. satisfaction ratings, grades, ranks).
- Interval — categories are ordered and the gaps are equal, but there is no true zero (e.g. temperature in °C, calendar years).
Nominal vs ordinal vs interval
- Labels, no order
- Mode, chi-square
- Ordered, unequal gaps
- Median, Spearman
- Equal gaps, no true zero
- Mean, SD, t-test
| Property | Nominal | Ordinal | Interval |
|---|---|---|---|
| Categories are labelled | Yes | Yes | Yes |
| Categories have a rank order | No | Yes | Yes |
| Equal gaps between values | No | No | Yes |
| Differences can be calculated | No | No | Yes |
| Central tendency to use | Mode | Median, mode | Mean, median, mode |
| Example | Blood type (A, B, O) | Degree class (First, 2:1…) | Temperature in °C |
The key boundary to watch is between ordinal and interval. Mistaking ordinal data for interval data is the most common error in student dissertations, because it leads to using the mean and parametric tests when they may not be justified.
Visualising Ordinal Data
Good charts respect the rank order and never imply equal spacing. Choose from:
- Ordered bar chart — categories on the x-axis in rank order (not alphabetical). This is non-negotiable; scrambling the order destroys the meaning.
- Stacked / diverging bar chart — useful for comparing ordinal distributions across groups (e.g. satisfaction broken down by age group or hospital site).
- Box plot — shows the median, IQR and outliers. Excellent for comparing ordinal distributions between groups without implying equal intervals.
- Frequency / percentage table — the simplest honest summary; show the count and percentage falling in each category.
- Avoid histograms — they imply continuous, equally-spaced values, which ordinal data does not have.
