The DU Mathematicians have spoken: It's 1 out of 14 TRILLION !

[TruthIsAll]

I posted yesterday asking that mathematicians confirm or refute my calculation of the probability that AT LEAST 16 out of 51 states would move beyond the MOE in favor of Bush. Well, they refuted it.

Sort of.

I originally calculated the odds at 1 in 4.5 BILLION.
That was too conservative.
On further analysis, I calculated the odds as 1 in 200 TRILLION.
But I was still off.

Thanks to MathGuy and JFERN for checking (and fixing) my calculation of the odds.

MathGuy calculates: 1 in 13.5 TRILLION
JFERN has it as: 1 in 14.5 TRILLION

So which is mathematically correct? They BOTH seem right to me.
Maybe we should just split the difference and say:
1 in 14 TRILLION.

For the sake of mathematical purity (and the trolls), we had better get to the bottom of this discrepancy. Hehehehehehe.

Here is my original calculation for the odds that 16 out of 51 states would move beyond the MOE in favor of Bush, using the Binomial Distribution, with .025 as the probability that a given state would move beyond the MOE to Bush:

The Excel formula for P:
P = 1 – BINOMDIST ( 16, 51, 0.025, TRUE)
P = 0.000000000000004996
The odds: 1 / P or 1 out of 200.159 TRILLION
(that the deviations could have occurred due to chance).

MathGuy made this input parameter change (16 to 15) to the Binomial function:
P = 1-BINOMDIST (15, 51, 0.025, TRUE)
The odds: 1 in 13.5 TRILLION.

Then JFERN offered this elegant answer:
51 choose 16 * 0.025^16 * 0.975^35
The odds: 1 in 14.5 TRILLION.

If someone can resolve the 1 TRILLION discrepancy, please do so.

Here is my confirmation of JFERN’s calculation:
"51 choose 16" means the number of combinations of 51 states taken 16 at a time.

I used the Excel combinatorial function to calculate this:

COMBIN (number, number_chosen)
This function returns the number of combinations for a given number of items.

COMBIN is used to determine the total possible number of groups for a given number of items, where:
-number is the number of items.
-number_chosen is the number of items in each combination.

Here is the calculation sequence:

1. Number of combinations of 51 states taken 16 at a time:
C = COMBIN(51,16) = 7.17452E+12

2. The probabilties (16 beyond MOE, 35 within) for each combination:
JP = 0.025^16 * 0.975^35 = 9.59846E-27

3. Sum the total probabilities of all combinations:
P = C*JP = 0.0000000000000688643 = 6.88644E-14

4. Calculate the odds: 1 / P

***** 1 in 14,521,300,254,785 ******

[salinen]

1. TIA

you must realize that math is the enemy of the liar. Too much "schoolin" leads to a mindset that attempts to solve problems.

[NuttyFluffers]

4. exactly. math is fact and reality. that's therefore obviously wrong.

so, as useful as this exercise is, unfortunately it is antithetical to those who desire to persist in LaLa Land. therefore the numbers must be inherently wrong. so expect to see things like this from 'true believers' and freepers:

"has the number 0 found a savior in jesus christ? if not, then how can it be believed?"

"the digits need to 'testify' otherwise they are the work of the devil and weak-mindedness."

"true christians don't need numbers, they only need god."

"equations are ivory tower liberal creations used to subject ourselves to the UN's will and destroy america."

"them numbers are black, i don't like black."

"it's those muslims that gave us algebra, y'know. how can you trust that stuff?"

"math's unpopular, i like hanging around what's popular. like, oh my god, my roots are showing! quick get the peroxide."

"those numbers don't enslave anyone to raise my holdings' value. what's the point?"

"why do digits hate america?"

notice: if i left a whacked-out reactionary group of nutjobs that leaves you feeling 'left behind' from my little grind, please feel free to speak up and i'll quickly make restitution to include you.

[Snivi Yllom]

16. high on math

Why not call it 1 in 1 trillion trillion and just leave it at that, I mean it would sound more impressive.

Although it appears a great deal of thought has gone into this math, here is something just too fantastic about it.

[Dogmudgeon]

2. It can only mean one thing

Jeebus interceded in the election to allow His beloved servant, George W. Bush, to continue guiding our fair Republic unto righteousness.

Praise Jeebus!

Hail Bush!

--p!

[Roger_Otip]

3. you're calculating the odds that exactly 16 states

would be beyond the margin of error in favour of bush, but shouldn't you be calculating the odds that 16 or more states would be beyond the margin of error for bush?

eg toss a coin 10 times - the chance that you get exactly 3 heads is quite low, whereas the chance that you get 3 heads or more is quite likely.

with these exit polls, whatever the numbers it's clear there was some systemic factor involved and that this did not happen purely by chance. i don't think anyone doubts that, so what does it matter what the exact probability is?

[rock]

5. It is important that you see that chance is not an explanation

Just saying "highly unlikely" is not as convincing as an actual quote of (pretty well) impossible odds. So whatever the explanation, it's not chance.

[TruthIsAll]

6. I calculated the odds that AT LEAST 16 states...

would exceed the MOE in the final Bush tallies. Thanks, and I just fixed the wording.

Check the Excel functions: BINOMDIST and NORMDIST.
They both have TRUE and FALSE parameters.

I used the TRUE parameter in the Excel Binomial distribution function. This triggers the calculation of the CUMULATIVE probability that AT LEAST 16 states would exceed the Exit Poll MOE in favor of Bush. This is exactly what occurred. Not one exceeded the MOE for Kerry.

The FALSE parameter is used to calculate the probability THAT EXACTLY 16 states would exceed the MOE. That is not what we want.

I used NORMDIST to calculate the probability in each state that Bush would exceed the MOE.

I calculated the MOE based on the exit polling sample size.
Then I calculated the corresponding standard deviation for input to NORMDIST: StDev = MOE/1.96

[goldengreek]

7. Bush is amazing!!

Truly a comeback kid!! Holy Guacamole!!

[bones_7672]

8. Guess what! Virtually nobody cares!

In the end, the biggest ream of paper with stats on it won't mean a thing to a county board of election, to an individual Secretary of State, to a Senator, to an Elector, to 95% of the people who voted.

What matters is actual evidence of deliberate fraud, and there is precious little of that.

[goldengreek]

9. I don't think that's true.

It takes a few weeks to gather all that together and we're now starting to see it show up. We're just playing around with all the red flags indicating fraud for fun.

[understandinglife]

14. Incorrect. This rigorous analysis ....

....provided to Rep Conyers, Mr Arnebeck and others will give them very strong justification for forcing disclosure of the Edison-Mitofsky 'raw' exit poll data, now.

And, a pragmatic, highly relevant test of whether a 2% cutoff is still overly generous is WA State. 'Red shift' for WA state was 2.9; shifted to Bush; and 'truthisall' shows a diff in Bush's favor of -1.41%. Two counties in WA State used e-vote machines and are having to 'print out' ballots. That little factlet is likely one of the key reasons the republicans are shouting 'nuclear bomb' because obviously no one is going to except merely a 'print out' from those devices without also examing the logs, code and any evidence of disc 'erase/delete' of binary.

So, in WA State, an examination of the 'raw' Edison-Mitofsky exit poll data coupled with a State-wide inspection of each ballot, an inspection of voting machines in the two counties that used them, and a comparison of those results to the 'certified' tables from each county's central tabulating system could be 'the perfect storm' of national election 2004 -- and the WA state republican flak may have ironically chosen exactly the right metaphor for what is about to happen to their party.

Peace.

"Did Busk Know?"

[Nye Bevan]

10. Reconciling the 1 Trillion

Both of the computations are correct but they are calculating slightly different things.

Define as an "anomaly" a state where the Bush vote exceeds the margin of error. We are assuming that the probability of each state being an anomaly is 2.5%.

- The probability of 16 OR MORE anomalies is 1 in 13.5 trillion.

- The probability of PRECISELY 16 anomalies (JFERN's calculation above) is 1 in 14.5 trillion.

To test this you can run the JFERN algorithm for every N from 16 up to 51: i.e. compute

PROB(N) = (51 choose N) * (0.025^N) * (0.975^(51-N)) for N=16,17,18,....,49,50,51

and add up all of these PROB(N) for N=16 to 51. This TOTAL probability is 1 in 13.5 trillion. That is:

PROB(16) = 1 in 14.5 trillion, and
PROB(16)+PROB(17)+PROB(18)+.....+PROB(49)+PROB(50)+PROB(51) = 1 in 13.5 trillion.

Either way this is less likely than the Mets winning the World Series for the next 7 years in a row!

[TruthIsAll]

11. MathGuy, you nailed it. It's 1 out of 13.5 BILLION.

We need the cumulative probability for ALL the combinations 16 and over. I missed that one. Iv'e been out of school for too long.

MathGuy, do you mind if I inquire about your math background? Degrees, work, etc. Nothing too specific. Just curious.
You are a great asset to DU.
Stick around.

[Nye Bevan]

17. Thanks TIA

I have always liked math, I was a big fan of the Martin Gardner mathematical diversion & games books when I was a kid. I studied math at college in England; abstract algebra was my favorite field (fellow algebraists - little pun here!), but not much application for this in the real world so I'm now working in insurance-- a lot of probability, statistics, and Excel, as you would expect.

I enjoy math puzzles (which is why I first posted here). For example--- how many people do you need to have in a room so that there is a greater than 50% chance that at least 2 of the people share a birthday? The answer is surprisingly small-- 23. And if you have 41 people in a room there is a 90% chance that at least two people have the same birthday! (Excel is handy to analyze this problem).

Keep up the good work!

[newyawker99]

13. Hi MathGuy!!

Welcome to DU!! :toast:

[Nye Bevan]

15. Thanks NewYawker99

That looks like Guinness! (My favorite)

[texpatriot2004]

12. Thanks for crunching and posting the numbers. n/t

[Tripmann]

18. Thank you TIA and the rest of the number crunchers....

...for your tireless work on behalf of the truth.

Tripmann

[Kellis]

19. Kick

good work TIA & Mathguy~Its people like you that will convince the doubters that something doesn't "add up" about the election.

Welocme to DU Mathguy:hi: