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Can nominal data have uncountably many values?

Are categorical data the same as nominal data?

Are discrete data the same as nominal data?

Thanks!

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

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  • $\begingroup$ 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

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