What it shows
Stevens’s four levels of measurement and the property each one adds. Each level keeps the properties of the level before it: nominal data have categories, ordinal adds order, interval adds equal intervals, and ratio adds a true zero.
Each level has an everyday example, and under each property the diagram gives the operations it makes meaningful, from = and ≠ for categories to × and ÷ for ratios.
How to read it
Read down a column to see which levels have a property. A filled circle means yes; an open circle means no.
Read along a row to see what a level supports. For temperature in degrees Celsius, differences between temperatures are meaningful, but ratios are not, because zero degrees is not an absence of temperature.
Length in centimeters has a true zero, so “twice as long” is a meaningful statement.
The four levels
- Nominal: categories (= and ≠). Example: cat, dog, rabbit.
- Ordinal: adds order (< and >). Example: mostly agree, completely agree.
- Interval: adds equal intervals (+ and −). Example: temperature in degrees Celsius.
- Ratio: adds a true zero (× and ÷). Example: length in centimeters.
- The four properties follow the basic empirical operations in Stevens (1946), Table 1: determining equality, greater or less, equality of intervals, and equality of ratios. The operation symbols are a common teaching convention.
Ways to use it in teaching
A quick exercise: place the variables from students’ own projects on the diagram.
The ordinal example leads into the question of whether Likert responses can be averaged.
Return to it when students choose a statistical test and need to state the level of their data.
Our guide to nominal, ordinal, interval and ratio data covers each level with further examples.
Sources
Stevens, S. S. (1946), "On the theory of scales of measurement", Science 103(2684): 677–680, Table 1, doi:10.1126/science.103.2684.677. Examples follow Wikipedia's Level of measurement article.
