The scale of measurement that you use depends on the method of
measurement that you use and not on the characteristic that you
are measuring. A basic understanding of scales of measurement is
essential in order to know something about presenting, interpreting
and analysing data. There are four well-known scales of
measurement:
nominal,
ordinal,
interval, and
ratio.
Categorical or qualitative variables
tend to be reported in nominal and ordinal
scales.
Nominal scale
A nominal scale tells you to which group a unit/individual belongs.
A nominal scale can be used to categorise. For example, gender can
be categorised as male or female, and religion can be categorised
as Jewish, Muslim, Christian, Buddhist, and ‘other’.
Sometimes a numerical code is assigned to nominal variables (e.g.
1 = female, 2 = male) but the code does not imply order.
Ordinal scale
An ordinal scale extends the information of a nominal scale to
show order, i.e. that one unit has more of a certain characteristic
than another unit. For example, an ordinal scale can be used
to rank job applicants from the best to the worst,
to categorise people according to their level of education,
or
to measure people's feelings about some matter using a measure
like ‘strongly agree’, ‘agree’, ‘neutral’,
‘disagree’, ‘strongly disagree’.
Quantitative variables are reported in interval
or ratio scales.
Interval scale
Interval scales are not simply ordinal. They give a deeper meaning
to order. An interval scale is a scale of measurement in which the
magnitude of difference between measurements of any two units is
meaningful. If weights are measured in kilograms (kg), then the
difference in weights between two people whose weights are respectively
82kg and 69kg is the same as that between people whose respective
weights are 64kg and 51kg. That is, the 'intervals' are the same
(13kg) and have the same meaning. Further, someone who weighs 100
kilograms is twice as heavy as someone who weighs 50 kilograms.
Consequently, most interval scales are also meaningful on a ratio
scale.
Ratio Scale
A ratio scale is a special form of interval scale that has a true
zero. For some interval scales, measurement ratios are not meaningful.
For example, 40° C does not represent a temperature which has
twice the heat of 20° C because the zero on the Celsius scale
is arbitrary, and does not represent an absence of heat. However,
when we consider the metric system for temperature (known as ‘degrees
Kelvin’), then there is a true zero (called ‘absolute
zero’). Therefore, a measure of 40K (i.e. 40 degrees Kelvin)
is twice as hot as 20K.
Another example of a ratio scale measurement is cash money, which
has an absolute zero. You cannot hold in your hand anything less
than a five cent coin (the smallest legal coin)!
The relationship between numbers and nominal, ordinal,
interval and ratio scales
Numbers can be used to represent measurements on any of the four
scales mentioned in this section. However, the relative values of
these numbers have a deeper meaning as the scale goes progressively
through nominal, ordinal, interval and ratio scales. For example,
suppose the numbers 1, 2, and 3 represent 3 measurements on any
one of those scales. On a nominal scale, the numbers could have
been replaced equally by the same numbers in a different order such
as 3, 1, 2 or three arbitrarily chosen different numbers such as
6, 4, 8. On an ordinal scale, the order of the numbers 1, 2, 3 is
important, but the order tells us nothing about the magnitude of
difference between 1 and 2 and 2 and 3. However, on an interval
scale, the difference between 1 and 2 is the same as that between
2 and 3 and half of that between 1 and 3.
SCENARIO
A sociologist wishes to conduct a study on suburban households. She decides to survey a sample of households.
Some of the variables that she decides to measure include:
the language background of the householders (English, Mandarin, Greek, Italian);
annual household income; and
the highest level of education completed (primary school, up to 3 years of high school, completed high school, TAFE, university, higher).
Identify the scales of measurement that you would apply to each of these variables.
