Chapter 1 · §1.4

Nominal, Ordinal, Interval, Ratio — sort 'em!

Learn what math each measurement scale allows, then defend your answer in the Stevens debate.

Sorting arena

Which Scale Is It?

Tap the right bin for the item — or drag the card onto it.

0 / 12Score 0🔥 ×0

Read the item below, then choose its measurement scale. A wrong answer resets your combo.

Cumulative hierarchy

The Measurement Skyscraper

Each floor keeps every operation from the floors below and unlocks two more. Tap a floor.

▲ more structure, more allowed math ▲

The great debate

Stevens vs. the Pragmatists

Does the measurement scale dictate which statistics you may use?

🧑‍🏫

S. S. Stevens · The Purist

On the theory of scales of measurement (1946)

The scale you measured on decides your statistics. Ranks? Use rank methods, not means.
  • ✔ Match the statistic to the scale's admissible transformations
  • ✔ Ordinal data → medians, ranks, nonparametrics
  • ✔ Nonparametric tests are the safe, principled choice
VS
🧑‍🔬

Lord · Boneau · The Pragmatists

Lord (1953) · Boneau (1961)

The numbers don't remember how they were measured. What matters is whether the test's assumptions hold.
  • ✔ Validity depends on the data's distribution, not on the scale label
  • ✔ Parametric tests are often robust in practice
  • ✔ Check assumptions and consider the research question

🤝 Middle ground: know your scale, know your test's assumptions — and when in doubt, nonparametric methods make fewer of them.

Up next

§1.5 Nonparametric Statistics →