What Kind of Data Is This? (Levels of Measurement)

Info sheet · Statistics for Psychology & Neuroscience

Author

Andrew Bell

Published

August 13, 2026

Info sheet 0.2 (draft) · Prerequisites: none · Give feedback ↗

✎ Editing notes — to do / to check

Working notes for the author — not shown to students once collapsed; remove before publishing.

What you’ll get from this sheet

Not all numbers are created equal. By the end you should be able to:

Tell the four levels of measurement apart.
Say which summaries and tests each one permits.

Four levels, in increasing richness: nominal (labels, no order) → ordinal (ordered, uneven spacing) → interval (equal spacing, no true zero) → ratio (equal spacing and a true zero). The level decides what’s meaningful: mode for nominal, median for ordinal, mean/SD for interval and ratio.

The four levels

Categorical (nominal) — labels with no order: diagnosis (depressed / anxious / control), stimulus type, handedness. You can count them, but “average diagnosis” is meaningless.
Ordinal — an order, but unequal or unknown spacing: Likert ratings (1–5), education level, disease stage. The categories rank, but the gap from “agree” to “strongly agree” needn’t equal the gap from “neutral” to “agree.”
Interval — equal spacing, no true zero: temperature in °C, many standardised test scores. Differences are meaningful; ratios aren’t (20 °C isn’t “twice as hot” as 10 °C).
Ratio — equal spacing and a meaningful zero: reaction time, firing rate, error counts. Ratios finally make sense — a 400 ms response really is twice as slow as a 200 ms one.

The practical payoff: the level constrains your options. A mean and SD suit interval and ratio data; a median suits ordinal data; a mode or a count is all that’s meaningful for categorical data.

Quiz: what level is it?

Pick a variable, make your call, and see the reasoning — and which “centre” is legitimate.

md`**Variable**`

viewof v = html`<select style="font-size:15px;padding:4px 8px">
  <option value="0">Diagnosis: depressed / anxious / control</option>
  <option value="1">Agreement on a 1–5 Likert scale</option>
  <option value="2">Temperature in degrees Celsius</option>
  <option value="3">Reaction time in milliseconds</option>
  <option value="4">Handedness: left / right / mixed</option>
  <option value="5">Highest education: GCSE / A-level / degree</option>
  <option value="6">Number of errors on a task</option>
</select>`
md`**Your call**`

viewof guess = html`<select style="font-size:15px;padding:4px 8px"><option value="">— choose —</option><option>Nominal</option><option>Ordinal</option><option>Interval</option><option>Ratio</option></select>`

lomWidget = {
  const items=[
    ["Nominal","Just labels with no inherent order — you can count how many fall in each category (and take a mode), but they can't be ranked or averaged."],
    ["Ordinal","Ordered categories, but the spacing isn't guaranteed equal — the median is the natural centre; treating it as fully numeric (a mean) is a common shortcut but strictly a stretch."],
    ["Interval","Equal spacing, but no true zero (0 °C isn't 'no temperature'). Differences are meaningful and you can take a mean/SD, but ratios aren't valid."],
    ["Ratio","Equal spacing and a meaningful zero (0 ms = no time). Everything is fair game — mean, SD, and ratios ('twice as slow')."],
    ["Nominal","Unordered labels — mode only. 'Average handedness' means nothing."],
    ["Ordinal","A clear rank, but the gaps between qualifications aren't equal 'units' — median, not mean."],
    ["Ratio","A count with a true zero (0 errors = none) and equal units — mean, SD and ratios all valid."]
  ];
  const [ans,why]=items[+v];
  let verdict,col;
  if(guess===""){verdict="Make your call above…";col="#94a3b8";}
  else if(guess===ans){verdict="✓ Correct — "+ans+".";col="#1E7A34";}
  else {verdict="✗ Not quite — it's "+ans+".";col="#c0392b";}
  const box=document.createElement("div");
  box.style.cssText="background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;padding:12px 14px";
  box.innerHTML=`<div style="font-weight:600;color:${col};margin-bottom:.3rem">${verdict}</div>`+
    (guess!==""?`<div style="color:#334;font-size:14px">${why}</div>`:`<div style="color:#94a3b8;font-size:14px">Ask: are they ordered? Is the spacing equal? Is there a true zero?</div>`);
  return box;
}

See it in code

R encodes the level with the variable’s type — an unordered factor, an ordered factor, or plain numeric:

Check your understanding

Why is it wrong to report the mean of a 1–5 Likert item, strictly speaking?

Because a Likert scale is ordinal: the responses are ordered, but the psychological distance between “disagree” and “neutral” isn’t guaranteed to equal the distance between “agree” and “strongly agree.” A mean assumes equal‑sized units (interval data), so averaging ranks can mislead. The strictly‑correct centre is the median. (In practice people often average Likert items anyway — especially when several are summed into a scale — but it’s a shortcut worth knowing you’re taking.)

Don’t let a variable’s appearance fool you: numbers can be nominal (participant ID, jersey number) and words can be ordinal (disease stage). The classic trap is treating ordinal data as interval and averaging it. And watch the true‑zero test for interval vs ratio — Celsius and IQ have no meaningful zero, so “twice as hot” or “twice as smart” are nonsense, whereas reaction time and counts do.

Where this shows up next

The level of measurement decides which descriptive statistics and which tests are legitimate — the very next sheet, Describing Data, puts them to work. See Chapter (Foundations).

What you’ll get from this sheet

The four levels

Quiz: what level is it?

See it in code

Where this shows up next

Related topics