Brief Background/Motivation: I am looking at an Income vs. Education table that is adapted from a dissertation and was used in developing a curriculum in a social justice mathematics program. In the dissertation, the author discusses using these data (income vs. education level, broken down by gender) to have students create a line of best fit, but does not explain how the categorical variable is treated or transformed into an ordinal variable.
The issue, as I see it, is that education level is categorical and not continuous; I have been unable to find a "standard" or even suggested approach regarding how to treat the categorical variable. I see two different ways:
Starting at 1, label each category 1-7. This assumes a uniform/linear step size (i.e., the difference between some high school and completing high school is the same as the difference between a master's degree and a doctorate) which is clearly problematic, but one possibility.
Approximate the number of years of schooling for each category. For example, "high school completion" would be 13, bachelor's degree would be 17, masters would be anything from 18 to 19, etc. Then you have to make some decisions about categories such as "some high school": is this a 10, 11 or 12? Also, how should you count the category of "no high school"? Is this a 7 or 8 or 9? This is also clearly subjective and has its own problematics, but is actually roughly the same as (1).
Question: Do either of the two approaches suggested above work? Or is there another, better way to treat these data?
Pointers to relevant papers or resources would be welcome, too.