Interval scale variables in R This is a question I found surprisingly hard to answer using Google: How is interval scaled data implemented in R? For nominal, its factor(), for ordinal, it's ordered(), and for ratio scale, it's numeric(). Now I understand that it's easy to use numeric for interval scale variables as well. But the point about these data types is that addition will fail on factor() and ordered() variables, and greater/lesser comparisons fail on factor(), but not on ordered(). Likewise, is there a datatype for interval data that allows for addition and subtraction, but not division and multiplication?
 A: Partially answered in comments:  

The meaning of a measurement scale is at best only loosely and
  indirectly connected with a computer data type. Conflating those two
  may be creating a lot of confusion--which explains the difficulty in
  researching this with Google. In particular, there is no sense of
  "failure" (of division, etc) in a measurement type. The definition of
  type depends on which relationships among numbers remain meaningful as
  the numeric representation is modified in an allowable way. Although
  your question raises many issues, as asked it really is unanswerable.

– whuber 

I suspect reading over Lord's paper might indicate the sense in which
  few statistical tests actually "rely on" or require data on a
  particular scale and reveal why creating such a datatype might be
  counterproductive. Even procedures designed for count data have been
  effectively applied to data represented as real numbers.

– whuber 
Another viewpoint: A-reanalysis-of-Lords-statistical-treatment-of-football-numbers

Thank you for sharing that. The literature is much larger--Lord's
  paper engendered many, many reactions. Although your particular
  reference decides Lord was wrong, their conclusion backs up my
  suggestion that this direction you are heading in--of attempting to
  enforce some kind of "measurement scale" as a computing data type--may
  be unwise. Don't misunderstand me: I think there is a place for
  strongly typed statistical computing languages (of which R is
  decidedly not an example). Just don't confuse measurement type with
  data type!

– whuber
