How might one measure the difficulty of formulae?

[Vladimir Batagelj]

<<<-------- James Hartley-------->>>

> A colleague of mine has asked about whether or not it is possible to
> measure
> the difficulty of formulae in a statistics text.  He writes thus:
>
>  > I certainly agree that it would be helpful if we could
>> apply a way of measuring the complexity of a textbook statistics
>> formula,
>> rather than simply noting its occurrence.  I don’t know of any such
>> metric
>> (the only thing that I can think of is the number of alphanumeric
>> characters in the equation), but I will check into this. (Do you know
>> anyone to ask about this?)  It would certainly be helpful if we had a
>> cardinal measure of equation complexity, similar to the way that a
>> Flesch
>> score gives a cardinal measure of word content complexity.
>>
>>Anyone any ideas!

  Every formula can be represented by a tree.
  For example
   (-b+sqrt(b^2-4ac))/(2a)

     6                         /
                           /       \
     5                    +         *
                        /   \     /   \
     4                 -   sqrt  2     a
                      /       \
     3               b         -
                            /     \
     2                    ^2       *
                          /      / | \
     1                   b      4  a  c

  A simple measure of its complexity could be its height (or depth) -
  in our case  h = 6.
  For a better measure it should be combined in some way with
  branching structure of the tree.
  For example:
     a+b+c+d+e             h=2  b=5
     f(g(h(p(q(x)))))      h=6  b=1

  Vlado

-- 
Vladimir Batagelj, University of Ljubljana, FMF, Department of Mathematics
  Jadranska 19, 1000 Ljubljana, Slovenia
http://vlado.fmf.uni-lj.si