Can nominal data have uncountably many values?

Are categorical data the same as nominal data?

Are discrete data the same as nominal data?


  • 1
    $\begingroup$ There's no r in nominal. $\endgroup$ – Marc Claesen Aug 10 '13 at 13:35

Let's see:

1) I think it depends on how you mean "uncountably". In a strict sense, no. You could count every atom in the universe, at least in theory. But in a more practical sense - sure. A list of all possible molecules is finite but it's so big that the finiteness is not practical.

2) Categorical data can certainly be nominal; they can also be ordinal (e.g. opinions given on a Likert scale). You can even categorize (and people frequently do) data that is interval or ratio, and sometimes you can uncategorize it.

3) As @Gung pointed out, a count variable is discrete but not categorical. They are also not nominal - indeed, counts don't fit perfectly into Stevens' classification - they are discrete but ratio, in that e.g. a person with 3 cars has 3 times more than a person who has 1.

  • $\begingroup$ This is good info, but note that a count (eg, the number of complications per month in a surgical center) is discrete, but is not categorical data. $\endgroup$ – gung Aug 10 '13 at 14:42
  • $\begingroup$ Oh, good example, +1. I will modify my answer. Counts are tricky $\endgroup$ – Peter Flom Aug 10 '13 at 14:48
  • $\begingroup$ What's the difficulty with counts? Ratios of counts make sense as zero is a natural origin for counts and so they are ratio scale. Discrete vs continuous is a distinction independent of nominal-ordinal-interval-ratio. (Whether there are interval scale measurements that are discrete is an interesting question.) Categories can of course be counted in many cases, just as the amount of a category can be measured. $\endgroup$ – Nick Cox Aug 10 '13 at 15:28
  • $\begingroup$ The opening sections of Agresti, Alan. 2013. Categorical data analysis. Hoboken, NJ: John Wiley are good on these minor terminological issues. They are visible via amazon.com/Categorical-Analysis-Series-Probability-Statistics/… $\endgroup$ – Nick Cox Aug 10 '13 at 15:37
  • $\begingroup$ @gung Agreed, but paradoxically or not most of the analysis of categorical data is focused on counts of categories (even if the counts are 0,1). $\endgroup$ – Nick Cox Aug 10 '13 at 15:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.