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richardcharnin.com

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http://www.electionmathematics.org/em-exitpolls/Exit_Polls_2004_Edison-Mitofsky.pdf

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 Margin of Error and corresponding Win Probability over a range of respondents and vote shares

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N= poll sample respondents

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S= winning 2-party poll share

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C= Cluster effect (exit poll only, zero for pre-election polls)

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Formulas:

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MoE = (1+C) * .98 / sqrt (N) is a good approximation when S is 50-60%

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MoE = Margin of error = (1+C) * 1.96 * sqrt (S* (1-S) / N) is a more general formula used below.

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Win Probability = NORMDIST(S, .5, MoE/1.96, true)

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The confidence level (probability) is 95% that the True Vote will fall within the range: S - MoE < S < S + MoE

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Sample Input:2-party

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N - respondents136601366052.38%National Exit

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S - EP win share52.4%52.4%51.78%State Aggregate

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C- cluster effect30%30%

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Calculations:

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Margin of Error 1.09%

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Win Probability100.00%

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2-party Winning Poll Share (S)

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51.8%52.4%53%54%62%70%80%90%

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2004 NEP2004 Ohio2008 NEP

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Margin of Error

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N-Sample

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5005.69%5.69%5.69%5.68%5.53%5.22%4.56%3.42%

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10004.03%4.02%4.02%4.02%3.91%3.69%3.22%2.42%

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15003.29%3.29%3.28%3.28%3.19%3.01%2.63%1.97%

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2004 Ohio20202.83%2.83%2.83%2.83%2.75%2.60%2.27%1.70%

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30002.32%2.32%2.32%2.32%2.26%2.13%1.86%1.40%

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100001.27%1.27%1.27%1.27%1.24%1.17%1.02%0.76%

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2004 NEP136601.09%1.09%1.09%1.09%1.06%1.00%0.87%0.65%

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2008 NEP178360.95%0.95%0.95%0.95%0.93%0.87%0.76%0.57%

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Win Probability

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50073.22%79.58%84.94%91.63%100.00%100%100%100%

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100080.96%87.88%92.81%97.45%100%100%100%100%

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150085.84%92.39%96.33%99.16%100%100%100%100%

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2004 Ohio202089.35%95.17%98.11%99.72%100%100%100%100%

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300093.55%97.86%99.43%99.96%100%100%100%100%

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1000099.72%99.99%100.00%100%100%100%100%100%

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2004 NEP1366099.94%100.00%100.00%100%100%100%100%100%

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2008 NEP1783699.99%100.00%100%100%100%100%100%100%