Definition

Nominal, ordinal, interval and ratio scales

Statistics • Data Classification

Statement

A nominal scale carries bare labels with no order (blood group, brand). An ordinal scale carries ordered labels whose gaps have no fixed size (star ratings, rank in a race, grades). An interval scale has equal gaps but an arbitrary zero, so differences are meaningful but ratios are not (temperature in degrees Celsius). A ratio scale has equal gaps and a true zero, so ratios are meaningful (length, mass, income). Each level permits everything the one before it does, and more.

How to use it

1Ask what the data permit, in order: can the values be ordered? are the gaps equal? is there a genuine zero meaning 'none'?
2If values can be ranked but not sensibly averaged, the scale is ordinal — this is where ratings, grades and ranks sit.
3A number standing for a category, such as $1$ for male and $2$ for female, is nominal despite looking numerical.
4If 'twice as much' is a meaningful statement about the data, the scale is ratio.

Worked example

Name the scale for each: (i) jersey numbers of players, (ii) finishing positions in a race, (iii) temperature in degrees Celsius, (iv) the mass of a parcel.

Step-by-step

1
$(i) jersey numbers are labels with no order$
Why: Nominal.
2
$(ii) positions are ordered, but first-to-second need not match second-to-third$
Why: Ordinal.
3
$(iii) equal gaps, but 0^{\circ} C is not ’no temperature’$
Why: Interval: $2 0^{\circ}$ C is not twice as hot as $1 0^{\circ}$ C.
4
$(iv) equal gaps and 0 kg means no mass$
Why: Ratio: $4$ kg really is twice $2$ kg.

Answer

(i) nominal, (ii) ordinal, (iii) interval, (iv) ratio

Watch out

The test for the ratio scale is the zero, not the presence of decimals; and an ordinal scale may be written with numbers without those numbers being addable. Averaging ordinal data is the standard error — the median is the right summary there.

Builds on

Qualitative, discrete and continuous data

Also known as

levels of measurement, nominal scale, ordinal scale, interval scale, ratio scale, measurement scale, Stevens scales

Appears in past papers

2018 (II)

Q55