### Math 225 Course Notes

### Section 1.3: Measurement and Measurement Scales

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

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.

Last modified: Jan 15, 1996

Bret Larget,
larget@mathcs.duq.edu