Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

It is my understanding that in statistics one has 4 basic data types: nominal, ordinal, ratio, and interval.

I see cases where people refer to "count data" (which is a random variable whose range is the set of whole numbers, such as the number of accidents in a week or the number of passengers on a plane), which brings me to my question: is "count data" is really data. It seems to me that it is a statistic computed from nominal data for two reasons. First, it doesn't seem to fall into one of the four data type categories. Secondly, it is obtained not from a measurement or recording of single events but rather from an arithmetic operation (i.e. addition). So for example, the number of passengers in a plane is a statistic whch would be computed from the nominal data associated with each seat in the plane ("1" = occupied, "0" = unoccupied).


share|cite|improve this question
Tangential, but "count data" need not be a random variable. Counting the entries in a spreadsheet or database (based on attribute values of the contained data), whereas stochastic models (ie, randomness) are extraneous to the data. – alancalvitti Dec 22 '12 at 14:58

Certainly count data is data. The list of what you call four basic data types is not intended to be an enumeration of "data types". It is a list of what are called "levels of measurement". My sixth-grade teacher frequently iterated the assertion "Measurement is approximation; counting is exact." That would exclude count data from a list of "levels of measurement". The term "levels of measurement" seems to come from the discipline of psychophysics. It gets taught in statistics courses with very little if any of the theory that it emerged from, and usually without even citing any sources where one could read more about it. See "On the Theory of Scales of Measurement" by S. S. Stevens, Science, volume 103, number 2684, pages 677--680, June 7, 1946.

share|cite|improve this answer
I still have some difficulties making sense of these distinctions. On pg 678 in the article by Stevens, we read "the only statistic relevant to nominal scales of type A is the number of cases, e.g. the number of players assigned numerals", which seems to be exactly what I was saying earlier (counts are statistics). Secondly, it seems the statements "nominal is a level of measurement" and that "measurements are approximations" are not totally consistent. If a nominal variable has 2 categories where a subject is either unambiguously in one category or the other, there is no approximation. – Matt Brenneman Dec 18 '12 at 22:07
@MattBrenneman, +1 (also to M.H.). Fyi, there are other inconsistencies as well as increasingly subtleties in theories of scaling. But I think what you are asking about: data vs. measurement may be a false dichotomy. A statistic, being the image of input data produced by an estimator, is also data (eg, your FICO score based on your credit record data is data to banks). – alancalvitti Dec 22 '12 at 15:02
@MattBrenneman : I don't think "nominal is a level of measurement" and "measurements are approximations" necessarily conflict with each other. For example, I once attended a talk by Stephen Fienberg, the famous categorical data analyst, in which he mentioned a survey he designed of Jews living in the Pittsburgh area. The survey began with questions to ascertain whether a person should be considered Jewish. He was empatically unwilling to trust their assertions about this. There are uncertainties aobut the boundaries between categories. – Michael Hardy Dec 22 '12 at 19:52

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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