More on measurement!

In lecture, I stressed that some variables can be measured with more precision than others—hence there are “levels” of measurement.  And the level(s) at which we can measure depends on the nature of the variable—i.e., how it has been operationalized (this is important later!)

There are two types of variables (discrete & continuous) and four levels of measurement (nominal, ordinal, interval & ratio).  Discrete variables are fixed and descriptive while continuous variables have infinite attributes.  Each type of variable contains two levels of measurement.  Discrete variables are nominal or ordinal while continuous variables are interval or ratio.

Nominal measures contain attributes or “qualities” that are either present or they are not.  There is no inherent hierarchy for the attributes.  For example, sex/gender is a nominal measure with two attributes: male and female.  The attributes are not ranked or privileged in any way; they’re simply qualities that you either are or are not.

Ordinal measures are ranked according to some characteristic.  For example, “happiness” has attributes that can be ranked from most to least happy: ‘very happy’, ‘sort of happy’, ‘not too happy’, and ‘the world sucks’.  It’s not a very precise ranking, but it is nonetheless a ranking.  She who is ‘sort of happy’ is clearly having a better day than he who thinks ‘the world sucks’.

The shortcoming with ordinal measures is that we don’t know the exact distance between the levels.  For example, the difference between ‘very happy’ and ‘sort of happy’ the same as the distance between ‘not too happy’ and ‘the world sucks’?  This brings us to continuous variables as the distance or difference between attributes is fixed and can be precisely measured.

Interval measures are ranked but also tell us how far apart the attributes are on some scale.  Temperature and IQ scores are common examples.  The distance between an IQ score of 100 and 101 is the same as the distance between a score of 115 and 116.  Likewise, the distance between a temperature of 50 and 60 Fahrenheit is the same the distance between 90-100F.  The key point is that interval measures have no meaningful “zero”—an IQ score of 0 doesn’t mean you have zero intelligence nor does 0 degrees F mean you have no warmth.  Interval measures are uncommon in sociology though one example you might come across is time measured in years.  For example, the distance between the years 1980-85 is the same as the distance between 1995-2000.

Ratio measures can be ranked, the difference between attributes is fixed, and they have a meaningful zero.  You can be 0 years old and the difference between 10-12 years is the same as the distance between 20-22 years.  Income is another popular ratio measure.

Finally, I has stressed the difference between measurement precision and measurement detail.  Nominal level measures are considered the least detailed while ratio measures are considered the most detailed.  However, that doesn’t mean that ratio measures are necessarily more precise.  For example, it doesn’t make sense to say that knowing someone is male is more precise than knowing that his annual salary is $15K.  These are different variables.  Precision and detail become more meaningful when a single variable is measured at different levels.  For example, an ordinal measure of annual income is “a little” while a ratio measure is $15k.  The latter is certainly more precise than the former.

Consider another example—height.  Ordinal measures of height are: very tall, tall, medium, short, and very short.  Ratio level measures are 84 inches, 83 inches, 82 inches, etc.  The second measure is much more precise.  Ideally, we’d always like to have such precision but it in reality this is not always feasible.  More important is that we understand different levels of measurement so that we can better work with the data we are presented.  And that’s the moral of this posting!