AlchemyToday

In the Washington Post, two Columbia political science students claim to “use statistics more systematically to show [that the Iranian elections results were altered behind closed doors].”  They are confident that this leaves “very little room for reasonable doubt” that the results were not at least partially fabricated.  They identify two unexpected occurrences in the last two digits of the number of votes received by the four candidates in Iran’s provinces (116 total numbers):

1. In the last digit, the number 7 occurs 17% of the time (N=20) and the number 5 occurs 4% of the time (N=5).  The probability of this phenomena for 116 random numbers is 3.5%.

2. The last digit and the penultimate digit are non-adjacent only 62% of the time (0 is adjacent to both 9 and 1, so there is a 70% probability that a random number will be adjacent to any other number).  The probability of this is 4.2%

3. The probability of both occurrences happening simultaneously is 0.5% [sic - it is actually 0.15%, the product of the probabilities of each event]

They correctly state that the odds of this happening in a fair election are extremely low; they incorrectly infer that this leaves little doubt of fraud.  Focusing on the first point, let’s see what the authors have to say here:

Why would fraudulent numbers look any different? The reason is that humans are bad at making up numbers. Cognitive psychologists have found that study participants in lab experiments asked to write sequences of random digits will tend to select some digits more frequently than others.

…

The numbers look suspicious. We find too many 7s and not enough 5s in the last digit. We expect each digit (0, 1, 2, and so on) to appear at the end of 10 percent of the vote counts. But in Iran’s provincial results, the digit 7 appears 17 percent of the time, and only 4 percent of the results end in the number 5.

Indeed, cognitive psychologists say this.  What’s more, the authors previously looked into possible Nigerian election fraud and discussed this further:

We showed that we can expect the last digits of electoral results to occur with equal frequency given a wide range of distributional assumptions, and we then emphasized the fact that humans tend to be biased in the production of random numbers: They tend to select small digits, avoid repetition, and favor adjacent numerals.

None of the literature they cite says anything about the numbers 5 and 7, and the phenomenon observed here actually runs counter to experimental evidence of human attempts at producing random numbers.

They equate the probability of seeing one number too frequently and one number too infrequently with the probability that the last digits are random.  These probabilities are not equivalent.  It’s easy to see that there are any number of equivalent, similarly improbable events:

1. X appears too frequently and Y appears too infrequently

2. Both X and Y appear too frequently

3. Both X and Y appear too infrequently

4. X, Y, and Z appear too frequently

5. X, Y, and Z appear too infrequently

etc.

It’s trivial to continue and think of dozens of equivalent events all with a 3.5% probability.  In fact, there is a 100% chance that a string of 116 random digits will feature such a pattern (update: I suspect this, but I’m not remotely capable of proving it).

The correct way to investigate whether a set of numbers might be random is using Pearson’s chi-square test.  We first calculate the chi-square test statistic for an expected digit frequency of 11.6 per 116 numbers.  The digits 0 through 9 are observed 9, 11, 8, 9, 10, 5, 14, 20, 17, and 13 times.  The test statistic is 15.6.  Since our data has 10 possible values there are 9 degrees of freedom, and the critical value required to reject the null hypothesis at a 95% confidence level is 16.9 – you simply can’t conclude with a high degree of confidence that the numbers aren’t entirely random.

What’s more, here is the authors’ example of the results for a fair election:

As a point of comparison, we can analyze the state-by-state vote counts for John McCain and Barack Obama in last year’s U.S. presidential election. The frequencies of last digits in these election returns never rise above 14 percent or fall below 6 percent, a pattern we would expect to see in seventy out of a hundred fair elections.

Why look at the last digit when the second-to-last digit should also be random?  If you look at the second-to-last digit in this same data set, you’ll find 20% 7s and 5% 8s.  The odds of this happening are 1.5% – well below the odds of the 7s and 5s phenomenon in Iran.

Derbeshire approvingly posts this e-mail at the Corner, writing, “For sure, decade by decade, universal adult suffrage is looking like a worse and worse idea.”

From Radio Derb:  “‘No taxation without representation!’ The Tea Party protestors of our time don’t have that cry available to them. We do have representation. The destruction of freedom and prosperity is proceeding with the full support of our elected representatives in Congress, under the leadership of a President easily elected by a majority of voters.”

Methinks an appropriate cry today might be “No representation without taxation.” That would eliminate over 40 percent of the electorate, leaving the productive 60 percent in charge.

Sorry, the 24th amendment beat you to the punch.

The right of citizens of the United States to vote in any primary or other election for President or Vice President, for electors for President or Vice President, or for Senator or Representative in Congress, shall not be denied or abridged by the United States or any State by reason of failure to pay any poll tax or other tax.

Eliminating property requirements with the 24th amendment was an “idea” only in the sense that it was a way to eliminate end-arounds of the 15th amendment by racists.

Then again, I didn’t know how the truck I saw with the Obama for Change sticker made it out of town, either.

The only tragic thing about these protests for me is that I’m now hedging on whether I’m going to raise a Join or Die flag out my window and make someone get the wrong message.  You’d think that Join or Die is antithetical to the Tea Party protests, but apparently that doesn’t matter.

h/t The Daily Record

But apparently that wasn’t a fair sample?

h/t Not Larry Sabato

What does it say about America that the night-vision footage of a navy seal raid rescuing this captain will be the biggest boost for Obama’s approval rating out of everything accomplished in the first hundred days?

Just made spätzle dough only to realize that I had nothing even remotely resembling a spätzle press (had assumed my colander would work; holes were way too small).  After a bit of futility trying to squeeze the dough into very small pieces, I gave up and tore it off by hand (not easy with sticky dough) and made bits of boiled dough that were something of a cross between spätzle and superballs.  Fried up in oil and butter and then added blanched brussel sprouts.  A bit chewy, but not bad — I definitely see the appeal of spätzle, but need to acquire better tools before trying again.  Also pictured, tofu w/ garbanzo, spring onion, and garlic.

From the Cherry Blossom 10 miler on Sunday

My endorsement for champion of NCAA hoops:

I believe I am finally over hating State out of my love for UMich; also, it’s somewhat unfair that Danny Green has made every three point shot except for one that I’ve seen him take in the tournament.  Looking at his stats, he’s actually right around his 41.5% season average, so it must just be good luck (for him) when I watch.

It’s interesting to see some people in a tizzy over indulging in the ceremonies of our uneasy ally Saudi Arabia.  Anyone claiming that we American’s don’t bow down to anyone is ignorant of history:

Didn’t anyone tell President Obama that Americans don’t bow down to anyone? Didn’t anyone tell President Obama that the President of the United States especially doesn’t bow down to anyone?

Didn’t anyone tell President Obama that Americans fought a long and bloody war so we wouldn’t have to bow down to a king anymore?

Or at least ignorant of the recent John Adams miniseries, which dramatized the day when King George III received Adams as the first American minister to Britain in 1785:

On July 4, 1776, John Adams, delegate to the Continental Congress from Massachusetts, voted to adopt the Declaration of Independence, proclaiming the British King unfit to be ruler of a free people. The King had proclaimed the rebellious colonists to be traitors. Could Adams possibly have imagined that, after eight years of warfare, he would stand before that same King, as a respected diplomat on the world stage, presenting his credentials as the first United States Minister Plenipotentiary to Britain?

On June 1, 1785, King George formally received John Adams, representative of the fledgling nation that had dealt the British Empire a bitter defeat. The meeting, as Adams recounted in this official account, was marked by the pomp and ceremony required by the occasion of a royal audience. But beneath the pageantry, Adams described a strong undercurrent of emotion as the King and his former subject—who once reviled each other as bitter enemies—met face to face, as statesmen.

In a letter to Sec. State John Jay, Adams recounts going through the formalities in having an audience with the King:

I went with his Lordership thro’ the Levee Room into the King’s Closet, the Door was shut and I was left with his Majesty and the Secretary of State alone.  I made the three Reverences, one at the Door, another about half way and the third before the Presence, according to the usage established at this and all the Northern Courts of Europe, and then addressed myself to his Majesty in the following words–

So perhaps this is all just kinda silly.  If not, here’s a video of Bush bowing, kissing, and receiving a medal from King Abdullah.  Big deal.  More importantly, John Adams had preternaturally outstanding handwriting.