Section 1.3: Measurement and Measurement Scales

Key Concepts

Data can be measured according to several different measurement scales. Be able to identify which measurement scale is used for any variable.

Measurement Scales

Categorical variables are measured according to either the nominal scale or the ordinal scale.

The nominal scale corresponds to when there is no natural ordering to the categories. Examples are gender, race, and survival.

The ordinal scale corresponds to when there is a natural ordering to the categories. An example is degree of burn.

Quantitative variables are measured according to either the interval scale or the ratio scale. In almost all instances, the ratio scale is used.

The interval scale corresponds to when it makes sense to take a difference between two measurements, but not to take a ratio of them. An example is temperature. 100 degrees is 80 degrees higher than 20 degrees Fahrenheit, but 100 degrees Fahrenheit does not represent five times as much heat as 20 degress Fahrenheit. A measurement of 0 on the interval scale does not represent an absence of the characteristic being measured.

The ratio scale corresponds to when it makes sense to take differences or ratios. Age and percent burned are examples. A forty-year-old is thirty years older than a ten-year-old, and is also four times as old. A measurement of 0 does represent an absence of the characteristic being measured.