ONE IN 4.5 BILLION? IT'S ACTUALLY MUCH, MUCH WORSE THAN THAT.

[TruthIsAll]

In the interest of mathematical accuracy, I must confess: My original analysis was actually too conservative when I estimated that the odds were 1 in 4.5 billion that 16 of 51 states would move beyond the Exit Poll Margin of Error to the actual Bush vote.

In the calculation, I used the probability of 5% that a single state would deviate beyond the MOE as input to the Excel Binomial Distribution function. That was actually correct on its face – but it's the probability of a move beyond the MOE, regardless of whether the move is favorable to Bush OR Kerry.

In fact, what we really want is the probability that the vote would deviate beyond the MOE to Bush, not Kerry. This is exactly what happened. So that is why we must use 2.5% and NOT 5.0% as our input probability. We just split the probability in half, the half that would go to Bush..

So, what is the effect of this seemingly small, innocuous change on our final probability estimate? Well, it means that the probability these 16 deviations could be due to CHANCE alone becomes EVEN MORE REMOTE. And this is actually an understatement of BIBLICAL PROPORTIONS.

Get ready. Grab your chair. Hold your hat.

Here are the odds that 16 out of 51 states would move beyond the MOE in favor of Bush, again using the Binomial Distribution. But this time with .025 (rather than .05) as the probability that a given state would move beyond the MOE to Bush:

The probability P is: P =1-BINOMDIST(16,51,0.025,TRUE)

P = 0.0000000000004996%

The odds are 1/P or 1 out of 200.159 TRILLION that these changes could have occurred due to chance alone.

ONE out of 4.5 BILLION?
ONE out of 200 TRILLION?

There is NO practical difference.
But the second one is MATHEMATICALLY CORRECT.

Here are the odds for N states moving beyond the MOE in favor of Bush:

N The odds are 1 out of:
1- 3
2- 7
4- 113
6- 3,715
8- 223,016
10- 22,192,000
12- 3,432,782,579
14- 788,997,832,405

16- 200,159,983,438,689

That's right. You are seeing correctly. Don't laugh. Don't cry.
It's 1 out of 200 trillion.