Testimony Proffered to New York Supreme Court Judge Ira Warshawsky Regarding the November 2010 Senate Contest in NY Senate District 7
Philip B. Stark, 4 December 2010
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The 3% audit gives very little statistical confidence that a full hand count of the ballots would show Mr. Martins to be the winner. The audit results would not be surprising even if a full hand count would show Mr. Johnson to be the winner.
Three of seven audited machines had errors: roughly 43%. Net, the errors favored Mr. Martins: correcting them decreases the apparent margin.
Because the audit examined only 7 machines, there is a substantial possibility that the machine with the largest error was not one of the machines that was audited. Indeed, there's a 97% chance that auditing 7 of 249 machines won't check the machine with the largest error.
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Because the margin is so small compared to the possible errors, a very large percentage of machines needs to be audited to give strong evidence that Mr. Martins is indeed the winner. 3% is not sufficient. 8% is not sufficient. To have 90% statistical confidence that Mr. Martins won requires auditing a minimum of 90% of the machines selected randomly: an additional 218 machines.
This is true if the audit finds that those 218 machines have counted perfectly. If the audit of those 218 machines found many errors, still more machines would have to be audited.
Here are some links to news reports:
http://portwashington.patch.com/articles/supreme-court-certifies-7th-senate-race-for-martins-2 http://www.newsday.com/long-island/nassau/it-s-official-judge-declares-martins-victor-over-johnson-1.2516962 http://online.wsj.com/article/APdcf6dc2872e7425aaa027804b561aabe.html http://www.nytimes.com/2010/12/05/nyregion/05elect.html P.B. Stark. Last modified 9 December 2010.
http://statistics.berkeley.edu/~stark/Preprints/nysd7-4-12-10.htm