Title: Ambiguities in defining levels of measurement
Course: UGQuants (SSPS) > Section: Introduction to Quantitative Analysis

Ambiguities in defining levels of measurement

It is important to be aware that defining level of measurement is not always a straightforward matter, and this has implications for analysis. At the extremes, it is often possible to identify variables that are straightforwardly nominal or ratio in character. For example, only if we adopted an avowedly sexist or racist position could we argue that ‘male’ could be ranked higher than ‘female’ or ‘white’ higher than ‘black’: these values are distinct, nothing more, and therefore represent the nominal level of measurement.

Similarly, if we were to measure income to the last penny or cent, we could confidently say that this was an example of a ratio variable. However, in practice in social and political research we rarely do record income in such detail, and we would certainly never record age to the exact day, hour, minute or second, even if such a thing were possible. But for the purposes of analysis, we usually treat a case with a value for age in years of 60 as being three times as old as someone with a value of 20, even though this might not be strictly true.

But ordinal and interval measures sometimes generate greater complexities. Take our example of highest educational qualification as an ordinal level of measurement. Often such a variable will include a category for cases with ‘foreign’ qualifications. Where would such cases fit in the rank order? It seems difficult to come to a firm and justifiable solution. One way to address this would be to exclude such cases from our analysis, especially if (as is common) they represent only a very small number of cases.

But, to follow the same example, what about those with qualifications related to an apprenticeship for a skilled manual occupation? Are such qualifications ‘higher’ or ‘lower’ in the hierarchy than, e.g. school qualifications? Rank order is not always entirely clear-cut and we must be aware of this when analysing data.

A rather different dilemma is presented by the kind of scales that are quite often used in social and political research. Imagine that, e.g. we ask people to express, on a numerical scale from 1-10, their level of satisfaction with the Prime Minister or President; or how safe they feel going out in their neighbourhood after dark; or whether they take a broadly negative or positive position with regard to the impact of immigration on the country in which they live. While it seems fairly clear that, e.g., cases with a value of 4 for satisfaction with the Prime Minister are expressing a higher level of satisfaction than cases with a value of 2, would we be justified in arguing that the difference between values 2 and 4 was equal to that between 4 and 6, or even that those with a value of 6 were three times more satisfied than those with a value of 2? There is no clear-cut answer, but what is clear is that our decision may have a profound impact on the kind of analysis we can use with such variables.