Solved – Convert ordinal data to continuous data

Some people I know conducted a survey. One of their goals is to estimate the hourly salary of a group of people. There are two questions in the survey that, supposedly, could answer this question:

  • What is you weekly salary?

  • How many hours do you work per week?

Well, this is easy, right? I have the salary per week and the number of worked hours. Hence, my first thought was to divide the salary by the number of hours.

However, the salary is not a quantitative variable. It is an ordinal variable. For example, suppose there are five categories and they are

  • less than $100,

  • $101-$200,

  • $201-$300

  • $301-$600

  • over $600

Yes, the categories have unequal ranges. How can I convert these data do quantitative? I know a lot of information was lost, but there is a way to estimate some of the salaries, at least? I've been searching the internet for an answer without luck.

The simple answer to your question is that what you want can't be done. You were interested in hourly salary, but you didn't ask participants that. Obviously, creating ratios would create some bizarre overlapping categories. Sometimes they can be coarsened into a larger category, so for instance, individuals working full time for $200 or less could be clustered with individuals working half-time for $100 or less for an hourly salary. But I have also found you will obtain interesting discrepancies from how participants would have responded to "what is your hourly salary?". All signs point to not creating a transformed variable.

There's no reason why salary can't be treated as a grouped linear variable where a 1 indicates the lowest salary and 5 indicates the highest, in prediction and inference this approach has been discussed extensively as a valid approach. Similarly, with enough participants, it can be treated ordinally without a problem.

Furthermore, there's no reason why hours worked per week couldn't be considered a separate factor in any model. Suppose for instance you were interested in modeling self-reported happiness, both hours-worked-per-week would be predictors of happiness as well as weekly salary for different albeit correlated reasons. Allowing an interaction (eq. a product term) between these values would tell you if there is a time-money tradeoff for happiness.

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