Dimensional analysis (also used in Physics) can be used to check statistical formulae.

Define the dimensions

: frequency;

: data.

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*.

Checking

(*),

we see that the sub-terms are of like dimension and thus may be added or subtracted.

(*) remember: constants factors disappear.

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