The measurement ladder
Levels of measurement (Stevens' classic scheme) rank data by how much arithmetic their values support. Each level keeps the properties of the ones below and adds one: nominal has identity, ordinal adds order, interval adds equal spacing, ratio adds a true zero. Knowing a variable's level tells you which statistics are meaningful for it: not permitted by software, but meaningful.
| Level | What values mean | Examples | Statistics that fit |
|---|---|---|---|
| Nominal | Names only | Blood group, city, gender | Counts, proportions, mode |
| Ordinal | Names with order | Ratings, ranks, education level | Median, percentiles, rank correlation |
| Interval | Ordered, equal gaps, no true zero | Temperature in C or F, calendar year, IQ score | Mean, SD, Pearson correlation |
| Ratio | Equal gaps and a real zero | Height, weight, income, counts | Everything, plus ratios and CV |
The two judgement calls
Interval vs ratio turns on zero: 0 °C is not "no temperature", so 20 °C is not "twice" 10 °C (in Fahrenheit the same pair is 68 and 50, ratio 1.36: the ratio changed with the ruler, so ratios are meaningless there). Kelvin has a true zero, making it ratio. Income's zero is real: 60k is twice 30k in any currency. Ordinal vs interval turns on spacing: a satisfaction scale earns interval treatment only if the steps behave as equal, which is an assumption to argue, not a fact to assert.
Race results carry two variables from one event. Finishing position (1st, 2nd, 3rd) is ordinal: the gap between 1st and 2nd is not the gap between 2nd and 3rd in any unit. Finishing time is ratio: 10.40 s is exactly twice 5.20 s of elapsed time, and zero means no time elapsed. Same race, different levels, different legal statistics: median position, mean time.
Treating the scheme as a police force. Real analysis is pragmatic: means of multi-item rating scales are routine and often behave well; the levels tell you where the burden of justification sits. The error is not computing a mean of ordinal data; it is computing one without noticing a choice was made.
Where this page pays off
Test selection: nominal data route to chi-square and proportion methods; ordinal data to rank tests and Spearman; interval and ratio data unlock means, t tests, Pearson and regression. The which-test guide builds on exactly this ladder.
Frequently asked questions
Is age nominal, ordinal, interval or ratio?
Ratio: it has equal spacing (a year is a year) and a true zero (birth). Grouped into bands (18-24, 25-34) it becomes ordinal, which is why raw ages are more valuable than banded ones.
Why can I not average nominal data?
The values are names. Assigning numbers to categories (1 = red, 2 = blue) makes an average computable and meaningless: relabel the codes and the average changes while the data do not. Mode and proportions are the summaries that survive relabelling.
Is money interval or ratio?
Ratio. Zero money is a real absence, and ratios hold across currencies: 60k is twice 30k in dollars, pounds or rupees after conversion. Debts (negative balances) do not break this: the zero stays meaningful.