It makes it all so easy to raise the eyebrows of those who
refuse to believe.
Historically, exit polls have been much more accurate than
standard polls. In prior calculations, I have
(conservatively) used the standard polling MOE methodology to
compute probabilities based on deviations from the Exit polls.
Using standard polling MOE's does not make much sense
intuitively. We should consider historically proven EXIT POLL
accuracy.
So let's be a little more realistic this time and assume that
the Exit Poll margin of error in each state is 2.0%, even
though all historical evidence indicates that it's less than
half that (see Germany, Ukraine, France etc.) So we are still
being very CONSERVATIVE in this assumption.
Now let's take another look at the election results:
For Bush, vote tallies in 23 states were outside the 2.0% MOE
- all in his favor.
For Kerry, vote tallies in 2 states were outside the 2.0% MOE
- all in his favor.
So here we go again. I'm almost sorry to do have to do this.
Let's calculate the probability (for Bush) of this occurring
under the 2.0% MOE criteria.
I ran the numbers in Excel as before, with a single input
parameter changed to calculate the odds that at least 23
states would be beyond the the MOE.
We input 22 as the number of states inclusive. The probability
is still .025 that the MOE would be exceeded. See the
description of the BINOMDIST below.
So, once again, let's calculate the probability:
Probability= P = 1-BINOMDIST(22, 51, 0.025, TRUE)
P = 0.000000000000000000000000000000E+00
IT'S A BIG FAT ZERO.ZILCH.NADA! THIRTY OF THEM.
EXCEL WON'T PRINT ANY MORE THAN 30 DECIMALS!
To compute the odds, we must calculate 1/P.
But wait!
P = ZERO
We can't divide by ZERO. No can do.
What does this mean?
It's BEYOND INFINITESMAL!
It's IMPOSSIBLE!
THE DEVIATIONS IN FAVOR OF BUSH COULD NOT HAVE OCCURRED BY
CHANCE!
THE PROBABILITY THAT IT COULD HAVE BEEN DUE TO CHANCE IS ZERO!
THANK YOU, BILL GATES, FOR GIVING EXCEL TO AMERICA.
OH, AND THANK YOU, TOO, LOTUS.
I USED 1-2-3 LONG BEFORE EXCEL.
********************************************************************
Notes:
BINOMDIST(number_s,trials,probability_s,cumulative)
Number_s is the number of successes in trials = 22 (at most
22 would fall within the MOE, at least 23 above)
Trials is the number of independent trials = 51
Probability_s is the probability of success on each trial=
.025.
If cumulative is TRUE (which it is), then BINOMDIST returns
the cumulative distribution function, which is the probability
that there are at most number_s successes; if FALSE, it
returns the probability mass function, which is the
probability that there are number_s successes.
*********************************************************************
Size refers to the exit poll sample size for the given state.
The percentages are Kerry's Exit Polls and reported Votes.
State Size Exit Vote Diff StDev MoE Prob >MoE? Favor
DE 770 58.50% 53.54% -4.96% 1.80% 3.53% 0.29 yes Bush
NH 1849 55.40% 50.51% -4.89% 1.16% 2.28% 0.00 yes Bush
VT 685 65.00% 60.20% -4.80% 1.91% 3.74% 0.60 yes Bush
SC 1735 46.00% 41.41% -4.59% 1.20% 2.35% 0.01 yes Bush
NE 785 36.76% 32.32% -4.44% 1.78% 3.50% 0.64 yes Bush
AK 910 40.50% 36.08% -4.42% 1.66% 3.25% 0.38 yes Bush
AL 730 41.00% 37.00% -4.00% 1.85% 3.63% 1.53 yes Bush
NC 2167 48.00% 44.00% -4.00% 1.07% 2.11% 0.01 yes Bush
NY 1452 63.00% 59.18% -3.82% 1.31% 2.57% 0.18 yes Bush
CT 872 58.50% 55.10% -3.40% 1.69% 3.32% 2.24 yes Bush
RI 809 64.00% 60.61% -3.39% 1.76% 3.45% 2.68 yes Bush
MA 889 66.00% 62.63% -3.37% 1.68% 3.29% 2.21 yes Bush
PA 1930 54.35% 51.00% -3.35% 1.14% 2.23% 0.16 yes Bush
MS 798 43.26% 40.00% -3.26% 1.77% 3.47% 3.29 yes Bush
OH 1963 52.10% 49.00% -3.10% 1.13% 2.21% 0.30 yes Bush
FL 2846 50.51% 47.47% -3.03% 0.94% 1.84% 0.06 yes Bush
MN 2178 54.50% 51.52% -2.98% 1.07% 2.10% 0.27 yes Bush
UT 798 30.50% 27.55% -2.95% 1.77% 3.47% 4.78 yes Bush
ID 559 33.50% 30.61% -2.89% 2.11% 4.14% 8.60 yes Bush
AZ 1859 47.00% 44.44% -2.56% 1.16% 2.27% 1.38 yes Bush
VA 1000 47.96% 45.45% -2.50% 1.58% 3.10% 5.66 yes Bush
LA 1669 44.50% 42.42% -2.08% 1.22% 2.40% 4.49 yes Bush
IL 1392 57.00% 55.00% -2.00% 1.34% 2.63% 6.78 yes Bush
WI 2223 52.50% 50.51% -1.99% 1.06% 2.08% 3.00 Bush
WV 1722 45.25% 43.43% -1.82% 1.20% 2.36% 6.54 Bush
NM 1951 51.30% 49.49% -1.81% 1.13% 2.22% 5.54 Bush
CO 2515 49.10% 47.47% -1.63% 1.00% 1.95% 5.15 Bush
IN 926 41.00% 39.39% -1.61% 1.64% 3.22% 16.42 Bush
GA 1536 43.00% 41.41% -1.59% 1.28% 2.50% 10.69 Bush
MO 2158 47.50% 46.00% -1.50% 1.08% 2.11% 8.17 Bush
NJ 1520 55.00% 53.54% -1.46% 1.28% 2.51% 12.67 Bush
WA 2123 54.95% 53.54% -1.41% 1.09% 2.13% 9.70 Bush
IA 2502 50.65% 49.49% -1.15% 1.00% 1.96% 12.41 Bush
AR 1402 46.60% 45.45% -1.15% 1.34% 2.62% 19.55 Bush
KY 1034 41.00% 40.00% -1.00% 1.55% 3.05% 26.01 Bush
OK 1539 35.00% 34.00% -1.00% 1.27% 2.50% 21.63 Bush
MI 2452 52.50% 51.52% -0.98% 1.01% 1.98% 16.47 Bush
NV 2116 49.35% 48.48% -0.87% 1.09% 2.13% 21.29 Bush
ME 1968 54.75% 54.08% -0.66% 1.13% 2.21% 27.80 Bush
MD 1000 57.00% 56.57% -0.43% 1.58% 3.10% 39.18 Bush
DC 795 91.00% 90.91% -0.09% 1.77% 3.48% 47.96 Bush
MT 640 39.76% 39.80% 0.04% 1.98% 3.87% 50.72 Kerry
OR 1064 51.20% 52.00% 0.80% 1.53% 3.00% 69.91 Kerry
HI 499 53.30% 54.55% 1.25% 2.24% 4.39% 71.10 Kerry
TX 1671 37.00% 38.38% 1.38% 1.22% 2.40% 87.10 Kerry
TN 1774 41.50% 43.00% 1.50% 1.19% 2.33% 89.68 Kerry
CA 1919 54.00% 55.56% 1.56% 1.14% 2.24% 91.35 Kerry
SD 1495 37.76% 39.39% 1.63% 1.29% 2.53% 89.65 Kerry
ND 649 34.00% 36.36% 2.36% 1.96% 3.85% 88.58 yes Kerry
KS 654 35.00% 37.37% 2.37% 1.96% 3.83% 88.76 yes Kerry
Avg 1450 49.18% 47.38% -1.80% 1.42% 2.79% 21.67 Bush
Med 1507.5 49.23% 47.47% -1.81% 1.29% 2.52% 6.66 Bush
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