# Definition Level of measurement

In statistics, depending on the kind of data we ascertained, we use different kinds of scales. Not every attribute or variable can be translated to numerical values in the same way. While body size can easily be depicted in centimeters or in feet and inches, this is not possible for variables such as gender and possible but difficult for levels of personal satisfaction.

The level of measurement expresses, how quantifiable a value actually is, i.e. to what extend we can apply mathematical operations. We differ four levels of measurement:

The nominal scale offers the least statistical information content, the ratio scale the highest. Nominal and ordinal are non-metric or categorical scales, that is, their response values are not directly usable as a numerical value. Interval and ration scales are metric scales that allow for various arithmetic operations. Examples:

Nominal scale:

• gender (male, female)
• color (blue, yellow, red, green, etc.)

Ordinal scale

• type of residence (single house, village, town, city)
• category of vehicle (compact car, medium-sized vehicle, luxury car, etc.)

Interval scale

• temperature in Celsius
• IQ scale

Ratio scale

• body height
• monthly income

A summary:

 Nominal scale qualitative categorical not numerical Ordinal scale qualitative / "seemingly quantitative" not numerical/numerical Interval scale quantitative cardinal/metric numerical Ratio scale quantitative

Please note that the definitions in our statistics encyclopedia are simplified explanations of terms. Our goal is to make the definitions accessible for a broad audience; thus it is possible that some definitions do not adhere entirely to scientific standards.

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