and
By Benford's analysis you can examine large data sets on their digit distribution and notice deviations in the Benford distribution. Quality criterion is the mean absolute deviation (MAD), which states the average deviation to the theoretically expected frequency. Usually the mean square error (MSE) is used too as quality criterion. MSE has the advantage that it evaluates larger deviations more because of the squaring.[1]
If h(i)observed or h(i)expectet are as observed the expected relative frequency of the ?rst digit i, so the deviations are denoted as:
and
[1] See Posch (2004), Page 10 and Page 20.