1.3. Measurement level

Each variable has also a measurement level. These are used to classify the variables and depending on the type of measurement level different statistical techniques can be used. The classification described by Stevens (1946) is the one most frequently used and also described here.

Nominal has ‘no’ in it. It is used for variables that have no logical order (besides perhaps alphabetical). An example of a variable on a nominal level is TV shows. The order we put the TV shows in, does not really matter.
For variables on nominal level we can only compare groups based on the quantity.

As the name implies, for ordinal variables there is a logical order, but note that numbers are not yet being used. An example is Educational Level. There is a clear order in this.
Besides comparing the different groups, we can now also make statements about greater or less (e.g. 45 respondents had secondary school or less).

Interval is for variables that are using numbers, but the zero of the scale was somewhat arbitrary chosen. For example temperature in degrees Celsius (or Fahrenheit) is at an interval level. The zero was somewhat arbitrary chosen as the boiling point of water (and later flipped to be the freezing point).
This level is called ‘interval’ because there are equal intervals between values. The difference between 5 degrees Celsius and 10 degrees, is the same as the difference between 20 and 25. Note that for ordinal variables this is not the case, the difference between Strongly disagree and Agree, might be different than the difference between Agree and Neutral.
At an interval level the zero does not really mean nothing. For example at 0 degrees Celsius there is still a temperature, and also someone with an IQ of 0, still has intelligence (but nothing much). This means we can also add and subtract the values on an interval level.

The last level is ratio, for variables that are using number, and have a true zero. This means that zero really means nothing. If your income is zero, you are really not earning anything. Ratio variables are also relative speaking equal (hence the name ratio). If you earn 200 one day, and 400 the next than this is really twice as much (no matter which currency), while for example 10 degrees Celsius is not twice as much as 5 if you would convert them to Fahrenheit. There is one temperature scale that is considered ratio, which is Kelvin who uses the absolute zero as a starting point.
At ratio level we can now also divide and multiply.

Sometimes no distinction is made between nominal and ordinal, and the term categorical is used. Similar SPSS does not make a distinction between interval and ratio and simply calls these scale.

Another way to classify variables is into discrete and continuous. A discrete variable is a variable where the values are distinct from each other. This means that both nominal and ordinal variables will also be discrete. However interval and ratio variables could either be continuous or discrete. A continuous variable is if there are no interruptions. The number of people is a discrete variable, but also interval. Money, weight and length are examples of continuous variables.

Note that the measurement level classification from Stevens is not without criticism. Velleman & Wilkinson (1993) give a nice overview of various problems with Stevens classification. For those interested in reading more on measurement levels the article from Sarle (1997) might be a nice starting point.

>>Next chapter: Descriptive Statistics

References
Sarle, W. S. (1997, September 14). Measurement theory: Frequently asked questions. Retrieved May 3, 2015, from ftp://ftp.sas.com/pub/neural/measurement.html
Stevens, S. S. (1946). On the Theory of Scales of Measurement. Science, 103(2684), 677–680. doi:10.1126/science.103.2684.677
Velleman, P. F., & Wilkinson, L. (1993). Nominal, Ordinal, Interval, and Ratio Typologies are Misleading. The American Statistician, 47(1), 65–72. http://doi.org/10.1080/00031305.1993.10475938