Levels of Measurement

The seminal paper that first set out levels of measurement was "On the theory of scales of measurement" by S.S. Stevens (1946) you can download a copy from here. He argues that all measurements have to fit one of his four levels of measurement, nominal, ordinal, interval or ratio. They can also be characterised more broadly into Categorical and Continuous

Categorical variables

These are variables that come in categories as they are not able to be quantified in a meaningful sense. For instance if you are using countries you could code China as 3 but there is no rational basis to do this because to randomly attach numbers to countries would have no meaning. The writing in italics are Stevens' own descriptions

• Nominal: Determination of equality. More than 2 categories in no particular order eg. Types of transport bicycle, car, train

• Binary: Data in only 2 categories eg. Pregnancy, pregnant or not pregnant

• Ordinal: Determination of greater or less. More than 2 categories with logical order eg. Social class A,B,C1,C2,D,E
  

Continuous

This are numerical variables.

• Interval, Determination of equality of intervals or differences. It is like an ordinal variable in that it is ranked but additionally it is a measurement where the difference between two values is meaningful. An example would be temperature in degrees Celsius
  

• Ratio, Determination of equality of ratios. Must be ranked like ordinal, like interval the difference must be meaningful but also there must be a non arbitrary absolute zero and have a ratio so that you can multiply and divide the data. In social research most "count" variables are ratio, for example, the number of sales in the past month. Why? Because you can have zero customers and because it is meaningful to say that "we had twice as many customers in the past month as we did in the previous month."

• Discrete variables uses whole numbers. A variable can be continuous and discrete or just continuous.
  

What type of measurement used effects the the type of statical analysis that should be used on the data. Nominal is the least statistically useful then ordinal and interval. Finally ratio is the most useful for doing analysis on.