Dimensional analysis (also used in Physics) can be used to check statistical formulae.
Define the dimensions
Now define the dimension function by:
Note that, like the complexity notation in computing, these are just notation, and not really formulae in that they can’t be written in reverse; likewise, constant factors are ignored.
Thus, we can check some terms:
— this is what we’d expect: for example, if the are velocities (for example), then is also a velocity.
we see that the sub-terms are of like dimension and thus may be added or subtracted.
(*) remember: constants factors disappear.