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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).

Matt

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    Tangentia$l$, 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.2012-12-22

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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.

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    @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](http://en.wikipedia.org/wiki/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.2012-12-22