Levels of Measurement

Nominal Level

• Definition: Categories with no intrinsic order.
• Key properties: no ranked order; arithmetic beyond counting not meaningful.
• Allowed statistics: mode, frequency.
• Examples: gender, color.

Ordinal Level

• Definition: Ordered categories; ranks exist.
• Key properties: unequal rank differences.
• Allowed statistics: median, percentiles.
• Examples: letter grades, Likert scales.

Interval Level

• Definition: Ordinal with meaningful differences; arbitrary zero.
• Key properties: equal intervals; zero doesn't indicate absence.
• Allowed operations: addition/subtraction.
• Examples: Celsius, Fahrenheit, calendar years.
• Mathematical note: if you have two values a and b, the difference b-a is meaningful, but the ratio \frac{b}{a} is not.

Ratio Level

• Definition: Interval with absolute zero; zero indicates absence.
• Key properties: all arithmetic is meaningful.
• Examples: height, weight, age, Kelvin.
• Notes: ratios like \frac{b}{a} are meaningful when zero indicates none.

Quick Summary

• Nominal: categories → mode/frequency.
• Ordinal: ordered → median, rank comparisons.
• Interval: equal intervals; arbitrary zero → addition/subtraction; mean is meaningful.
• Ratio: true zero → meaningful ratios.