Mitch Nolan writes:
I’m not a statistician, but I’m looking at the Egypt vote results using Benford testing (the name of which I just learned today, to warn you of what a novice I am). First, here are the official results in Arabic. And here‘s an unofficial Google spreadsheet in English (the first page with the original data is locked, other pages are editable).
Nolan may not be a statistician, but I know nothing about Egypt. So I’m just posting his numbers below without comment.
OK, so here’s what Nolan sent me. Make of it what you will:
Distribution of trailing numbers in the “valid” vote results:
1 x
2 xx
3 xxx
4
5 xxxxx
6 xxxx
7 xxxxxx
8 xxxxx
9 x
0 xx
(Lots of 7s…)
Distribution of trailing numbers in the “invalid” vote results:
1 xx
2 xxxx
3 xx
4 xx
5 x
6 xxxxxx
7 xxxxx
8 xxx
9 xxxx
0
(No round numbers)
Valid and invalid, combined:
1 xxxxxxxxxxxxx
2 xxxxxxxxxx
3 xxxxxxx
4 xxxxxxxxxxxx
5 xxxxxxxxxxxxxx
6 xxxxxxxxxxxxxxxx
7 xxxxxxxxxxxxxx
8 xxxxxxxxxxxxxx
9 xxxxxxxxxx
0 xxxxxx
(6 zeros, 16 sixes?)
Valid, invalid, and yes votes, combined (still looking at trailing digits):
1 xxxxxxxxx
2 xxxxxxxxx
3 xxxxxx
4 xxxxxxxx
5 xxxxxxxx
6 xxxxxxxxxxxx
7 xxxxxxxxxxxx
8 xxxxxxxxxxxx
9 xxxxxxxx
0 xxx
(Four times as many 6s, 7s, and 8s as 0s?)
I’m going to skip over the no votes, because those would just be a
calculation of valid votes minus yes votes, and not numbers picked out
of the air in any case. Sticking with that data set of valid, invalid
and yes votes, here are some other results:
Leading digit:
1 xxxxxxxxxxxxxxxxx
2 xxxxxxxxxxxxxxx
3 xxxxxxxxxx
4 xxxxxxx
5 xxxxxxx
6 xxxxxxxxxxxxx
7 xxxxxx
8 xxxxxx
9 xxxxxx
0
(Those 6s pop out a bit…)
Leading two digits:
1 xxxxxxxxxxxxxxxxxxxxxx
2 xxxxxxxxxxxxxxxxxxxxxxxxx
3 xxxxxxxxxxxxxxxxxx
4 xxxxxxxxxxxxxxxxxxx
5 xxxxxxxxxxxxxxxxx
6 xxxxxxxxxxxxxxxxxxx
7 xxxxxxxxxxxxxxxx
8 xxxxxxxxxxxxxx
9 xxxxxxxxxxxxxx
0 xxxxxxxxxx
(Seems ok?)
Leading three digits:
1 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
2 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
3 xxxxxxxxxxxxxxxxxxxxxxxxxxx
4 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
5 xxxxxxxxxxxxxxxxxxxxxxx
6 xxxxxxxxxxxxxxxxxxxxxxxxxxxx
7 xxxxxxxxxxxxxxxxxxx
8 xxxxxxxxxxxxxxxxxxxxxxxxxxx
9 xxxxxxxxxxxxxxxxxxxxxxxx
0 xxxxxxxxxxxxxxx
(Not sure if the bias toward even numbers between 2 and 8 means anything.)
Trailing two digits:
1 xxxxxxxxxxxxxxxxxx
2 xxxxxxxxxxxxxxxxx
3 xxxxxxxxxxxxxxxx
4 xxxxxxxxxxxxxxxxxxx
5 xxxxxxxxxxxxxxxx
6 xxxxxxxxxxxxxxxxx
7 xxxxxxxxxxxxxxxxx
8 xxxxxxxxxxxxxxxxxxxxxxxx
9 xxxxxxxxxxxxxxxxxxx
0 xxxxxxxxxxx
(A bit of a bias toward 8s, but not a huge one.)
Second digit:
1 xxxxx
2 xxxxxxxxxx
3 xxxxxxxx
4 xxxxxxxxxxxx
5 xxxxxxxxxx
6 xxxxxx
7 xxxxxxxxxx
8 xxxxxxxx
9 xxxxxxxx
0 xxxxxxxxxx
(Seems ok?)
Third digit:
1 xxxxxxxxxxxxx
2 xxxxxxxx
3 xxxxxxxxx
4 xxxxxxxxxxx
5 xxxxxx
6 xxxxxxxxx
7 xxx
8 xxxxxxxxxxxxx
9 xxxxxxxxxx
0 xxxxx
(What happened to the 7s?)
Third digit, excluding the four 3-digit numbers in the set (where the
third digit is also the last digit):
1 xxxxxxxxxxxxx
2 xxxxxxxx
3 xxxxxxxxx
4 xxxxxxxxxxx
5 xxxxxx
6 xxxxxxxx
7 x
8 xxxxxxxxxxxx
9 xxxxxxxxxx
0 xxxxx
(NOW what happened to the 7s?)
OK, it’s me (Andy) again. Let me repeat that I did not do the analysis nor do I have any opinions on it. I just wanted to pass it on, and to Except to say that I think it’s a good thing that data and statistical ideas are becoming so generally accessible.