= Difference in errors adjusted for overall number when the errors have different signs =
Suppose we have error scores which can take positive or negative values, of equal importance, on two conditions, baseline (B) and treatment (T) then assuming at least one of B and T are non-zero the difference in the errors adjusted for total number can be expressed using absolute values, abs(), as
{{{
sgn(T-B)[abs(T-B)] / [(abs(B) + abs(T)] if T and B have different signs or
[abs(T) - abs(B)] / [(abs(B) + abs(T)] if T and B have the same sign
}}}
Alternatively, provided B is nonzero, we can express the difference in errors as a percentage change (PC) by
{{{
sgn(T-B) 100[abs(T-B)] / abs(B) if T and B have different signs or
100[abs(T) - abs(B)]/abs(B) = 100(SF - 1) if T and B have the same sign
}}}
where SF is the scaling factor relating to T and B.
For example if T and B both have the same sign and the number of errors doubles (SF=2) it follows abs(T) - abs(B) = 2 abs(B) so abs(T) = 2 abs(B) which gives a 100 (2abs(B)- abs(B))/abs(B) = 100% increase in errors from baseline.
If we ignore the absolute values in the above formulae we can end up with misleading values due to failing to ignore the signs of B and T. For example if we have scores of -3 for B and +2 for T then the total number of errors equal to B+A equals -1 when in fact there are 5 errors made in total.