5

I have a question about how to interpret some discrete data. Some are very easy, like the number of children in a household: that is a discrete and numerical, measured as a ratio variable.

Other variables are not that easy, for example

  • age, measured in whole years: is that interval or ratio?
  • number of cigarettes smoked per day: is that interval, or ratio?

The difference between interval and ratio is that ratio has an absolute zero (when the measured property is absent). In case of the age measured in whole years, an infant aged 2 months has zero (whole) years, but that does not mean the person doesn't have an age... so is that ratio?

statstudent
  • 51
  • 1
    Why are you asking? Typically these questions have no applied value and people often discuss the distinctions only for interest sake or for arguments. Also, is this for an assignment? If so, I think this site has specific rules about asking for answers to an assignment. – Behacad Mar 25 '13 at 01:58
  • Hi Behacad, thanks for replying. Nope, this has nothing to do with any assignment, but only with our understanding of these issues. We're having heavy discussions around the topic, and if possible would like to have other opinions.

    Basically, age measured in whole years is a countable variable, but we cannot agree whether it is interval or ratio...

     – statstudent Mar 25 '13 at 15:00
  • 1
    What difference does it make (serious question)? Is this similar to arguing if a certain dish is a cake or a pie or does it actually have practical implications (e.g. do you have stats that depend on the answer)? This question comes up often and I have even asked this recently, but with a practical aspect. These concepts are immaterial and some argue the distinction is moot. – Behacad Mar 25 '13 at 15:33
  • Well, there are some (not sure if practical) implications. For example the coefficient of variation which is standard deviation divided by the mean. For a ratio variable, the mean is easy to calculate and it's fixed, but for an interval variable the mean is relative to the starting point (because there isn't an absolute zero anymore). Again, it's probably more a philosophical question than a statistical one, but still we'd love to have other opinions (if only to settle our conceptual arguments). Where can I find your other answers on the topic? Thanks! – statstudent Mar 26 '13 at 07:52
  • 1
    For some additional comments, pursuant to @Behacad's objections, please see http://stats.stackexchange.com/questions/23200/are-all-attributes-data-points-inherently-nominal/23266#23266. – whuber Apr 03 '13 at 17:31
  • I don't think this is such a bad question, or that it doesn't belong here. However, I agree that the concept of levels of measurement is generally flawed & not nearly as important as it's made out to be. You may find the following paper helpful in thinking through these issues: Velleman & Wilkinson (1993). Nominal, Ordinal, Interval, and Ratio Typologies are Misleading (pdf). – gung - Reinstate Monica Apr 03 '13 at 18:37

1 Answers1

6

I don't think there's a single correct answer to these sort of questions - it depends rather on the analysis you want to do. Age in whole years could be viewed as an approximation to a variable measured on a continuous ratio scale; or as a discrete count of the number of birthdays celebrated. Note that 'Count' is worth viewing as a type in its own right - for instance, you can't interpret a contingency table the same way if you replace units with tens or thousands, or identify a Poisson distribution from a histogram without looking at the labels on the abscissa.

Scortchi - Reinstate Monica
  • 29,907