# Standardizing versus percentile rank with survey data

I am currently working with survey data, collected across different locations, but with slightly different units of measurement.

For example, on questions such as "What is your level of education", some participants had the choice between only 3 categories, others 5 categories etc. The categories are always ordered in the same direction (less to more education) but their number vary.

The categories are:

• in some locations, High School, Bachelor's degree, Master’s/PhD

• in other locations, No high school degree, high school, some university education, bachelor's degree, Master's/PhD

I would like to include this variable in a regression. I am wondering if standardizing the variables (using z-scores) will help? I know it can help compare scores when measurement varies, but here I am worried that the categorical nature of the data makes this solution unreliable.

I know that this will "erase" differences between the different locations, but I am mostly interested in comparing how being in the lower part of the distribution vs. higher part affects the dependent variable.

• Welcome to the site. This is at least two questions: One about education and one about income (and maybe more if you have other variables). The methods I would suggest would vary. Please separate the questions and please list the categories. – Peter Flom May 7 at 10:38
• Sorry about this. I have narrowed down my question and listed the categories as requested. – Charlotte Manin May 7 at 17:17
• Not meaning to sound facetious, but will help what precisely? That is, what is or are the problems that this will supposedly solve? I get that how common or rare a PhD may affect what difference it makes having one, and so forth, but I don't see how you could do anything but code that the score for PhDs is a certain constant score, whether it's a percent rank or a quantile of some distribution corresponding to that. In other words, you would be mapping an ordinal scale to another ordinal scale that is quite arbitrarily defined. Just using indicator variables is cleaner and more general. – Nick Cox May 7 at 17:57
• @Nick Recoding evidently won't solve anything--except perhaps to make it possible to combine the data in a simple way--but there may be an underlying issue of uncertainty, because we can conceive of the five-category scale as being around twice as precise as the three-category scale. To the extent the analysis recognizes this imprecision, there's an interesting question to discuss. However, I would suspect that a more important question would be whether (and to what extent) the two scales are even commensurable: people might be responding entirely differently depending on the scale. – whuber May 7 at 18:48

## 1 Answer

I don't think standardizing (by taking z scores or anything else) makes sense here. The variable is not just ordinal, it is very ordinal. There are some ordinal variables (such as Likert type questions) where treating them as interval makes some sense, even though it is technically incorrect to do so.

But here, that is not true. The difference between "high school" and "BA" is not really quantifiable (but see below) and can't really be compared to the difference between "BA" and "MA/PHD".

So, what would I do?

in some locations, High School, Bachelor's degree, Master’s/PhD

in other locations, No high school degree, high school, some university education, bachelor's degree, Master's/PhD


Three of the matches are easy: HS = HIS, BA = BA, MA/PhD = MA/PHD.

But, in the first location, what happened to people who had no HS degree? What did they mark? What about those who had some university? The best solution depends on that, but you have to come up with labels that reflect both locations, which might be

1. HS or less
2. At least some university
3. Grad degree

The exceptions I can think of are if you are asking about education in some specific context that allows quantificaction. For instance, if your research is about salaries, you might be able to get the median salary at each level of education in each location and use that.