Actually, it's NOT a big difference. Consider this: there were 5816467 total Bush and Gore voters in Florida, as of the current tally, with 1805 the count in Bush's favor.
The possibilities:
1) All Florida Bush or Gore voters went to their polling stations yesterday and punched a line out on the ballot for their candidate. The individual ballots were tallied.
2) All Florida Bush or Gore voters went to their polling stations yesterday and flipped a fair coin. A heads was tallied for Bush, a tails for Gore.
Are these possibilities distinguishable statistically? As it currently stands, no.
The distribution of random processes such as a coin toss are goverened by Poisson statistics, also known as the counting statistics. The mean width of such a distribution is simply the square root of the total counts. In this case, thats:
sqrt(5816467)=2412
Larger than the difference between them! So, independent of finer-grained district-based tallying in Florida, the coin-toss hypothesis is just as likely as the voter choice hypothesis. If you gave the numbers to a statistician, and asked them to prove a bias in either direction, he would be unable to.
If you doubt the accuracy of this statistic, pick your favorite programming language with an accurate pseudo-random number generator with large enough cycle period, generate 5816467 0's or 1's randomly, count them into n[0] and n[1], and look at the difference between n[0] and n[1]. Repeat this many times, and average the absolute difference. Your answer will converge to the square root in several hundred runs.
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Actually, it's NOT a big difference. Consider this: there were 5816467 total Bush and Gore voters in Florida, as of the current tally, with 1805 the count in Bush's favor.
The possibilities:
1) All Florida Bush or Gore voters went to their polling stations yesterday and punched a line out on the ballot for their candidate. The individual ballots were tallied.
2) All Florida Bush or Gore voters went to their polling stations yesterday and flipped a fair coin. A heads was tallied for Bush, a tails for Gore.
Are these possibilities distinguishable statistically? As it currently stands, no.
The distribution of random processes such as a coin toss are goverened by Poisson statistics, also known as the counting statistics. The mean width of such a distribution is simply the square root of the total counts. In this case, thats:
sqrt(5816467)=2412
Larger than the difference between them! So, independent of finer-grained district-based tallying in Florida, the coin-toss hypothesis is just as likely as the voter choice hypothesis. If you gave the numbers to a statistician, and asked them to prove a bias in either direction, he would be unable to.
If you doubt the accuracy of this statistic, pick your favorite programming language with an accurate pseudo-random number generator with large enough cycle period, generate 5816467 0's or 1's randomly, count them into n[0] and n[1], and look at the difference between n[0] and n[1]. Repeat this many times, and average the absolute difference. Your answer will converge to the square root in several hundred runs.
This is scary.