Benford's Law: Applicability with rates per country?

[irenea99]

Hello,

As part of the IB program, students have to complete a mathematical investigation. I am investigating Benford's Law and hoping to construct a data set and then test out the Law on it, and then subsequently justify why it worked or didn't using statistical ideas like invariance and orders of magnitude.
It would be much more helpful if I knew if it would work beforehand.
If I compiled a list of the domestic violence rates per country in, say, 100 countries? Would the Law work on the leading digit?

Thank you

 

[stapel]

I am investigating Benford's Law and hoping to construct a data set and then test out the Law on it, and then subsequently justify why it worked or didn't using statistical ideas like invariance and orders of magnitude.
It would be much more helpful if I knew if it would work beforehand.
If I compiled a list of the domestic violence rates per country in, say, 100 countries? Would the Law work on the leading digit?

You're working with this, right? Isn't it kind of the point of a "law" that it is expected to work all the time, at least approximately? But:

According to the introduction here, it works best "when values are distributed across multiple orders of magnitude", so your results may vary from this Law a bit more than expected, since percentages from 0% to 100%, by their nature, don't vary in magnitude much. Perhaps this might suggest a more useful data-set type?

Note: Since this Law can be used to detect fraud in purported research results and data sets, one may probably safely conclude that, yes, this Law is fairly reliable.