Scales of Measurement
Ratio – this scale has an
absolute
zero point and equal intervals between the scale scores
correspond to equal intervals in the variable being measure. For example, think of money. You
can have absolutely no money, so there is a true zero point. Also, if you have $1 and then a day
later you have $2, you have increased by $1. If someone else has $6,482,291 and then a day later
has $6,482,292, then they have also increased by exactly $1. So the intervals stay equal across
the range of possible scores. Other examples are
weight and
height.
Interval – this kind of scale has
equal intervals between the scale scores which
correspond to equal intervals in the variable being measured. However, there is
no true zero
point. Think about the days of a
calendar. The amount of time that passes from Feb 2
nd
at 6am to
Feb 6
th
at 6am is exactly equal to the amount of time that passes from November 4
th
at 6am to
November 8
th
at 6am. But the calendar date has no true zero point. Other interval scales are
degrees
Celsius and degrees
Fahrenheit.
Ordinal – Ordinal scales only tell us the
order of variable values. Imagine you have three
animals – an elephant, a rhino, and a flea, and you are measuring their weights using an ordinal
scale, with the
heaviest animal getting a 1 and the
lightest animal getting a 3. These three
animals would receive the scores 1, 2, and 3 in an ordinal scale. However, the difference between
1 and 2 (elephant and rhino) is much smaller than the difference between 2 and 3
(rhino and
flea). Therefore, the
intervals are not equal.
Nominal – For a nominal scale, all we know is that the “scores” are different, but the
“scores” have
no mathematical meaning except that they are not equal to each other. Imagine we
have four
nationalities: Canadians, Americans, Mexicans, and Cubans and we assign them the
values 1, 2, 3, and 4. We know that 1 is not 2, and 2 is not 3, and 3 is not 4, and 1 is not 3, and
(etc, etc), but we cannot say that 1<2, or 2<3, or 3<4, or etc, etc. So the numbers are
mathematically meaningless, except to indicate the value of the variable to which the number
pertains. We would be just as well off to use letters A, B, C, and D instead of the numbers 1, 2,
3, and 4.
Types of measures and converging operations