2002 Senate Election Fraud Probability Analysis: re-written for clarity

[TruthIsAll]

THE PURPOSE OF THE ANALYSIS
A statistical analysis of the Senate 2002 elections has employed basic probability theory to determine the odds that four out of eight hotly contested Senate races would dramatically turn from the Democrat to the Republican, based on the latest polling numbers taken just prior to the election.

See: American Coup: Mid-Term Election Polls vs Actuals
http://www.scoop.co.nz/mason/stories/HL0211/S00078.htm

These results should be taken in the context of the paper "Analysis of an Electronic Voting System", written by four computer scientists. They assert that their analysis of the Diebold electronic voting system shows that "it is far below even the most minimal security standards applicable in other contexts".

The statistical analysis does NOT constitute proof of fraud, but nevertheless are highly incriminating as circumstantial evidence.

THE POLLING MARGIN OF ERROR
The probability that a given state poll will be correct within the +/- 3% margin of error (MOE) is 19 out of 20 or 95%.

The odds that 4 out of 8 elections would fall outside the MOE (and ALL go for the Repubs) is 1 out of 43,040.

THE STATES IN QUESTION
The four states which experienced these remarkable turnarounds were:

1-Minnesota: The Democrats were leading 47-39% in the final polls; the Republicans won by 50-47%, an 11 point switch.

2-Georgia: The Democrats were leading 49-44% in the final polls; the Republicans won by 53-46%, a 12 point switch.

3-Texas: The Democrats were trailing by 48-49% in the final polls; the Republicans won by 55-43%, an 11 point switch.

4-New Hampshire: The Democrats were leading by 46-40% in the final polls; the Republicans won by 51-47%, a 10 point switch.

Each of these races turned around with deviations significantly beyond the 6% margin of error range.

Out of 8 races, the probability that ALL would fall WITHIN the margin of error =66.3%, or 2 out of 3. Stated another way, the chances that 1 or more states would fall OUTSIDE the MOE =33.7%, or 1 out of 3.

THE CUMULATIVE DISTRIBUTION PROBABILITY FUNCTION
The statistical analysis utilized the Cumulative Binomial Distribution function. This function computes the probability that there would be at least (N) successes in a series of (T) independent trials, where (P) is the probability of success in any trial. For any values of N,T,and P the Probability is calculated using the Excel Function: =BINOMDIST(N,T,P,TRUE)

For the case of 4 out of 8, with 95% probability
= BINOMDIST(4,8,.95,TRUE)= 0.000371751

In addition, the probability is 1/2 (50%) that any given election falling outside the MOE would go for the Democrat (or Republican). Therefore, the probability that ALL four would fall for the Republican is the product 1/2*1/2*1/2*1/2= 1/16

SUMMARY OF RESULTS
The odds that 4 out of 8 hotly contested Senate elections would fall outside the MOE (all for the Repubs) is the Joint Probability: 1/16*.000371751= .0000232, or 1 out of 43,040.

Assuming that 16 elections were hotly contested, The odds that 4 out of 16 elections would fall outside the MOE (all for the Repubs) is
1 out of 2,284.

Assuming that ALL 34 elections were hotly contested, the odds that 4 out of 34 elections would fall outside the MOE(all for the Repubs) is
1 out of 182.