From a post on the Democratic Underground forums:
ONE OUT OF 4.5 BILLION!
Those are the odds that Kerry's EXIT poll percentage would EXCEED his ACTUAL reported vote percentage by MORE THAN THE MARGIN OF ERROR in 16 out of 51 States by chance alone. That is exactly what occurred on Nov. 2.
I know that is hard to fathom. But here is the data. And here is the calculation, based on the number of individuals polled in each state and the corresponding Margin of Error (MOE).
The chances of a given state falling outside the MOE = 1/20 = .05. The calculation for the probability that 16 out of 51 states would fall outside the MOE is a simple one which uses the BINOMIAL DISTRIBUTION FUNCTION:
The Probability (P) that at least 16 out of 51 states would deviate beyond the exit poll MOE is:
P = 1-BINOMDIST(16,51,0.05,TRUE)
This returns P= 0.0000000218559% or 1 out of 4,575,415,347!
Here is how the odds decrease as the number of states (N) exceeding the MOE increase:
N>MOE Odds
3: 1 out of 4
5: 1 out of 24
8: 1 out of 139
10: 1 out of 2707
12: 1 out of 1,037,879
14: 1 out of 57,503,169
15: 1 out of 490,978,624
16: 1 out of 4,575,415,347
The individual state probabilities are calculated using the Normal distribution Function.
For example, consider Florida: The probability that Kerry's 50.51% exit poll percentage would decline to 47.47% in the actual vote (a 4.04% deviation, far outside the 1.84% MOE) is equal to .06%.
This calculation is based on the FL exit poll sample size of 2846, which produces a MOE of 1.84%. The corresponding standard deviation (StDev) is 0.94%. The StDev is plugged into the normal distribution function, along with the exit poll and reported vote percentages.
The probability that this deviation would occur due to chance is:
.06% = 100*NORMDIST(47.47%,50.51%,.94%,TRUE)
Here are the Exit Poll and Voting Results for all the states:
Size refers to the exit poll sample size for the given state. The percentages are Kerry's Exit Polls and reported Votes.
............Kerry
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 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 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 Bush ID 559 33.50% 30.61% -2.89% 2.11% 4.14% 8.60 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 Bush LA 1669 44.50% 42.42% -2.08% 1.22% 2.40% 4.49 Bush IL 1392 57.00% 55.00% -2.00% 1.34% 2.63% 6.78 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 Kerry KS 654 35.00% 37.37% 2.37% 1.96% 3.83% 88.76 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
