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
I actually have an exam regarding this tomorrow and I am not as ready as I should be lol! So here we go (Please note that I have learned these in my native language so mention any errors or mistakes):
– There is no “Hierarchy” per se. Meaning that there is no inherent value comparison between these data types. The major difference is the mathematical and statistical operations that you are allowed to perform on the data.
For example, when you have Ordinal data, you are allowed to use Spearman’s correlation coefficient, but when you have Interval Scale data, you are allowed to use Pearson’s formula.
– When you have ordinal or nominal data, you are not allowed to perform mathematical operations mostly, since the distance between numbers is meaningless. But in Interval and Ratio scales, you can. Also, in Interval Scales, there is no defined 0. For example:
Imagine person A scores 70 out of 100 in an English test, person B scores 40, and person C scores 0.
This is considered an Interval scale, you can add and subtract (Person A scored 30 points more than Person B). But there is no defined 0. The reason is that you can not say that person C has 0 knowledge of the English language!
But imagine a ratio scale. Height is one. When you say object A is 5 meters and object B is 10 meters, Object B is twice long. And when you say Object C has the height of 0, it means it is literally zero (it does not exist).
Check out more here:
[https://en.wikipedia.org/wiki/Level_of_measurement](https://en.wikipedia.org/wiki/Level_of_measurement)
>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.
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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