You say, “Made-up number sequences look different from real random sequences (e.g. numbers from McCain/Obama).” It’s hard to decide whether the e.g. refers to made-up seq’s or real seq’s but if you think McCain/Obama was real it shows how far into anal darkness your head is.

However, go look at the authors’ previous work on elections in Nigeria and, assuming you have ever honestly used statistical tests, you’ll see the flaw in their analysis. They apply a different test to the Nigerian data; in fact, the psychological studies they cite in that work directly belie the Iranian data. They posit that a fraudulent set of random numbers will have too many 1s, 2s, and 3s and not enough high digits. Yet here they see an excess of 7s and a paucity of 9s – neither number is discussed in their earlier work. The nonadjacent numbers test was discussed, but not applied, to the Nigerian data – why is it used here?

The most likely answer is that the authors here looked at every possible thing they’ve identified as diagnostic of a fraudulent election, picked the ones that occurred, and calculated the probability of that occurrence. As a statistical test of fraud, that’s completely worthless.

Ask yourself: had this phenomena occurred in the penultimate digit instead of the last digit, would the authors have written the same article?

In fact, in the 2008 Obama/McCain election (set of 102 state totals form Wikipedia) the 20% of the numbers are 7 and only 5% of them are 8 in the penultimate digit. This is rarer than the 7s and 9s observation here.

If you look at any set of 116 similar, random numbers, you’ll find an apparently paradoxical pattern; it would be much, much more unlikely, in fact, not to see such a pattern. Would fraud be less likely if each digit were used exactly 11 or 12 times out of the 116 numbers? That’s a much less likely outcome than having one digit occur 17% of the time and another occur 4% of the time.

I took the text from this post, then looked at the last digit of the ASCII code for each column (ie: the ones-column). Here is the histogram for that data:

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Clearly, there are too many characters that end with a code of “2″ in this post, which makes me suspect that it wasn’t generated from a valid sample.

Hmmmm….

Somewhat related to this, I just finished an election map of Iran. I found it odd that I didn’t see anything like it in the news, so I decided to make one myself. Geographic visualization isn’t my usual thing, but the data is really compelling.