My understanding is that data can either be qualitative (ordinal/nominal) or quantitative (discrete/ continuous).
But I’ve read also that quantitative data can be interval/ratio – but where does this fall into the hierarchy? Can a discrete variable be interval/ratio? Are there any examples? My brain hurts.
In: Mathematics
>My understanding is that data can either be qualitative (ordinal/nominal) or quantitative (discrete/ continuous).
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>But I’ve read also that quantitative data can be interval/ratio – but where does this fall into the hierarchy? Can a discrete variable be interval/ratio? Are there any examples? My brain hurts.
Nominal (categorical) data is qualitative — it is simply some indication of a given observation having a characteristic or not. An easy example from social science is race: someone in the US could be denoted as white, black, Asian, etc. — these labels may covary systematically with other data, but racial/ethnic categorization is not *quantifiable* in the sense that is has no absolute or relative natural ordering.
Ordinal data is quantitative, but only in a relative way via natural ordering. For example, we might ask a survey respondent how much they agree or disagree with a given statement and ask them to give their response on an integer scale of 1-5. When comparing different responses, we will be able to make assertions about how each response is more/less emphatic in a given direction, but we will not be able to precise answer *how much*. Things like ordered preference among categories also fall here — we could ask people to order their preference for five different types of soft drink, for example, and then try to make assertions about their relative popularity based on the aggregated responses.
Continuous data (including interval) is data for which more precise measurement allows for both the above *ordinality* of responses as well as *cardinality* — that is, *how much* more/less a given response is compared to others. Measuring income in dollar amounts, for example, allows us to make more exact assertions about the covariance between income and other variables (e.g. if age/income have a linear relationship, we can try to model it and get an estimate for exactly how much more income to expect given each additional unit of age or vice-versa).
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