It is useful to distinguish between four **levels of
measurements** for data, from weakest to strongest:

1. Nominal (no ordering)

2. Ordinal (ordering exists, but not distance)

3. Interval (distance exists, but not ratios)

4. Ratio (ratios exist)

Sex is a *nominal* variable, since
`Male' and `Female' are just names of categories. There
is no intrinsic ordering between them.

A student's level of standing (freshman, sophomore, junior,
or senior) is *ordinal*; they are also names of categories
but, unlike sex, they are rank-ordered. However,
subtraction cannot be done and distances do not make sense.

GPA is an *interval* measurement; subtraction can be done
and distances make sense. For example, the distance from
2.3-2.4 is the same distance as 3.7-3.8. However,
ratios do not make sense; is 4.0 `twice as high' as 2.0?
The answer is no. The grading system would work just as well
on the scale (A, B, C)=(5.0, 4.0, 3.0) instead of (4.0, 3.0, 2.0).

Finally, number of credit hours is a *ratio* measurement.
A student who has completed 90 credit hours has TWICE as many
as 45 credit hours, and 3 times as many as 30 credit hours

It is useful to recognize a hierarchy of information
in the sense that *a measurement level contains an amount of
information greater than or equal to the level below it*.
At lower levels of
measurement, data analyses tend to be less sensitive and sophisticated.
A statistical study should aim for the highest levels of
measurement possible or affordable.

Interval and ratio variables together are often called *numerical*
variables because they provide a number which measures `quantity'
(how much, how many) of something.

Nominal and ordinal variables together are often called
*categorical* variables because they
classify into categories rather then count or measure.
It is tempting to think of categorical variables as
`non-numerical' but sometimes they do consist of numbers.
For example, `social security number' consists of numbers,
but are used more as labels rather than quantities.