It's interesting that you place such a high value on statistical analysis.
Well I did
said "if it checks out". I can't buy the claims made in the article without a lot
more research than I have time for right now (thankfully I am following some smart folk who do).
There was an earlier claim for statistical evidence of fraud based on Benford's Law
that I didn't find very convincing. Here's the paper on it:
BENFORD’S LAW ANOMALIES IN THE 2009 IRANIAN PRESIDENTIAL ELECTION By Boudewijn F. Roukema [pdf]
And here is a very good analysis of it's relevance by Nate Silver
that contributed greatly towards my rejection of it as a form of evidence. Even so, it was an interesting hypothesis because it tied together with another bit of evidence (about the turnouts being greater than 100% in many cities).
So I don't know whether the claims they made in the article I posted this thread about check out they seem to on the surface but these kinds of things often are spoiled by "gotchas" that weren't immediately obvious (at least in my experience). However if they are correct in saying that the results they analyzed should only happen 4% of the time naturally I would find it compelling evidence, together with the rest, that it is likely to have been fraudulent.
For myself, I require a preponderance of evidence. No single source does it for me. And at this point I'm still not sure what happened over there, which is why I started my other thread to ask how voting fraud may have been done and how it can be hidden so effectively.
I'm leaning toward fraud based on the other bits of evidence I posted to your other thread, and frankly I am a lot more suspicious about statistical analysis being able to conclusively say whether it was fraud one way or another than anything else in this election. I've seen miracles where such conclusions are
teased out of the data but this is a case where there's just not much of the data itself to work with.
But the biggest reason statistical analysis can't be conclusive is because it simply can't rule out many kinds of fraud. They could just switch the names on the results for very natural numbers that would conceal the fraud against statistical analysis nicely.
However I have seen statistical analysis give very solid conclusions about fraud using similar techniques, and I know it can be done. I just am not very hopeful that it can in this particular case. But if their claims check out, and the odds of these results being natural are 4% I would take that into consideration and yes it would be the last straw that leads me to believe that fraud did occur.
One thing I am convinced of however is that a lot of Iranians are very angry, and I figure they know their country better than I do. And that piece of information, along with a handful of other suspicious aspects of the vote count (including what you have listed above), as well as an inherently flawed verification process in place over there (the Guardian Council) make me think that the election results are probably (but not definitely) inaccurate.
I am cautious against bias on the part of the Iranians as well. They were distributing a very dubious-looking document that purported to be a letter to Khamenei with the "real" results and they too might be engaging in wishful thinking as well. Maybe the progressives have just had enough of the regime while still being in the minority and due to the lack of political transparency are lashing out at the validity of the results.
In many such political systems with little transparency the losing party alleges fraud almost invariably. Hell, even in the US you'll have huge swaths of people who believe in fraud at times even with all the checks and balances we have. I can just as easily envision this anger taking place with or without fraud if the narrative that the educated metropolitan folk were outnumbered by the rural folk is true.
But you bring up a good point here, in that they are angry and don't feel adequately represented and maybe that's all that matters. If enough believe it was illegitimate then that may just create the facts on the ground. I for one wouldn't mind if the regime finally cracks over this accusation even if it wasn't true.