| A | B | C | D | E | F | G | H | I | J | K | |
|---|---|---|---|---|---|---|---|---|---|---|---|
1 | SAMPLE OF ELECTION RECORDS | ||||||||||
2 | Winning margin, as % of all ballots | 1.25% | 2.50% | 5% | 10% | 20% | 40% | ||||
3 | Error rate to detect | 0.63% | 1.25% | 2.50% | 5% | 10% | 20% | ||||
4 | You can word that as 1 error in this many records | 1 in 160 | 1 in 80 | 1 in 40 | 1 in 20 | 1 in 10 | 1 in 5 | ||||
5 | This random sample of ballots gives 63.2% chance of detecting the error (sample = 2 divided by the winning margin) | 160 | 80 | 40 | 20 | 10 | 5 | ||||
6 | A bigger random sample of ballots gives 90% chance of detecting the error (sample ≈ 4.5 divided by the winning margin) | 368 | 184 | 91 | 45 | 22 | 11 | ||||
7 | 4.60 | 4.60 | 4.55 | 4.50 | 4.40 | 4.40 | |||||
8 | Winning margin, as % of all ballots | 1.25% | 2.50% | 5% | 10% | 20% | 40% | ||||
9 | Error rate to detect | 0.63% | 1.25% | 2.50% | 5% | 10% | 20% | ||||
10 | Size of random sample | Probability that sample size at left will detect the error rate above | |||||||||
11 | 1 | 0.62% | 1.25% | 2.5% | 5.0% | 10.0% | 20.0% | ||||
12 | 2 | 1.25% | 2.5% | 4.9% | 9.8% | 19.0% | 36.0% | ||||
13 | 11 | 6.7% | 12.9% | 24.3% | 43.1% | 68.6% | 91.4% | ||||
14 | 22 | 12.9% | 24.2% | 42.7% | 67.6% | 90.2% | 99.3% | ||||
15 | 45 | 24.6% | 43.2% | 68.0% | 90.1% | 99.1% | 100.0% | ||||
16 | 91 | 43.5% | 68.2% | 90.0% | 99.1% | 100.0% | 100.0% | ||||
17 | 184 | 68.5% | 90.1% | 99.1% | 100.0% | 100.0% | 100.0% | ||||
18 | 368 | 90.0% | 99.0% | 100.0% | 100.0% | 100.0% | 100.0% | ||||
19 | 500 | 95.6% | 99.8% | 100.0% | 100.0% | 100.0% | 100.0% | ||||
20 | 1,000 | 99.8% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | ||||
21 | |||||||||||
22 | |||||||||||
23 | Winning margin, as % of all ballots | 1.25% | 2.50% | 5% | 10% | 20% | 40% | ||||
24 | Erroneous ballots | 0.63% | 1.25% | 2.50% | 5% | 10% | 20% | ||||
25 | If worst batches are 100% wrong, this fraction of batches are erroneous | 0.63% | 1.25% | 2.50% | 5% | 10% | 20% | ||||
26 | If worst batches are 50% wrong, this fraction of batches are erroneous | 1.25% | 2.50% | 5% | 10% | 20% | 40% | ||||
27 | If worst batches are 25% wrong, this fraction of batches are erroneous | 2.50% | 5% | 10% | 20% | 40% | 80% | ||||
28 | If worst batches are 100% wrong, this random sample of batches gives 90% chance of detecting error | 368 | 184 | 91 | 45 | 22 | 11 | ||||
29 | If worst batches are 50% wrong, this random sample of batches gives 90% chance of detecting error | 184 | 91 | 45 | 22 | 11 | 5 | ||||
30 | If worst batches are 25% wrong, this random sample of batches gives 90% chance of detecting error | 91 | 45 | 22 | 11 | 5 | 2 | ||||
31 | |||||||||||
32 | |||||||||||
33 | |||||||||||
34 | |||||||||||
35 | |||||||||||
36 | |||||||||||
37 | Sample of batches | Erroneous batches as % of all batches | |||||||||
38 | 1% | 5% | 10% | 20% | |||||||
39 | Number of batches in sample | Chance sample will miss all the erroneous batches | |||||||||
40 | 1 | 99.00% | 95.00% | 90.00% | 80.00% | ||||||
41 | 2 | 98.01% | 90.25% | 81.00% | 64.00% | ||||||
42 | 4 | 96.06% | 81.45% | 65.61% | 40.96% | ||||||
43 | 10 | 90.44% | 59.87% | 34.87% | 10.74% | ||||||
44 | 20 | 81.79% | 35.85% | 12.16% | 1.15% | ||||||
45 | 40 | 66.90% | 12.85% | 1.48% | 0.01% | ||||||
46 | |||||||||||
47 | factor | Average number of ballots switched, in batches with switches | |||||||||
48 | 30% | 25% | 20% | 5% | |||||||
49 | winning margin as % | Number of batches needed in sample depends on how many ballots switched | |||||||||
50 | 3% | 22 | 18 | 14 | 3 | ||||||
51 | 1% | 68 | 56 | 45 | 10 | ||||||
52 | 0.60% | 114 | 95 | 76 | 18 | ||||||
53 | |||||||||||
54 | |||||||||||
55 | error level detectible, at 10% risk, with sample of 2 | 0.68 | 20.51% | 17.09% | 13.68% | 3.42% | |||||
56 | error level detectible, at 10% risk, with sample of 14 | 0.15 | 4.55% | 3.79% | 3.03% | 0.76% | |||||
57 | error level detectible, at 10% risk, with sample of 18 | 0.12 | 3.60% | 3.00% | 2.40% | 0.60% | |||||
58 | error level detectible, at 10% risk, with sample of 45 | 0.05 | 1.50% | 1.25% | 1.00% | 0.25% | |||||
59 | |||||||||||
60 | ballots switched, in batches with switches | 25% | |||||||||
61 | number of batches | 100.00 | 500.00 | 1,000.00 | 3,000.00 | ||||||
62 | 1% sample | 1.00 | 5.00 | 10.00 | 30.00 | ||||||
63 | ballots switched overall | Odds of missing errors | |||||||||
64 | 0.5% | 98.0% | 90.4% | 81.7% | 54.5% | ||||||
65 | 1.0% | 96.0% | 81.5% | 66.5% | 29.4% | ||||||
66 | 2.0% | 92.0% | 65.9% | 43.4% | 8.2% | ||||||
67 | 4.0% | 84.0% | 41.8% | 17.5% | 0.5% | ||||||
68 | 8.0% | 68.0% | 14.5% | 2.1% | 0.0% | ||||||
69 | chance of missing errors | error level to give chance of missing as shown at left, assuming up to 25% of batch in error | |||||||||
70 | 70% | 7.5% | 1.7% | 0.9% | 0.3% | ||||||
71 | 67.0% | 8.3% | 1.9% | 1.0% | 0.3% | ||||||
72 | 80.0% | 5.0% | 1.1% | 0.6% | 0.2% | ||||||
73 | chance of missing errors | erroneous batches to give chance of missing as shown at left | |||||||||
74 | 70% | 30.0% | 6.9% | 3.5% | 1.2% | ||||||
75 | 67.0% | 33.0% | 7.7% | 3.9% | 1.3% | ||||||
76 | 80.0% | 20.0% | 4.4% | 2.2% | 0.7% | ||||||
77 | |||||||||||
78 | |||||||||||
79 | Sample of individual ballots | ||||||||||
80 | Sample size | 50 | 30 | 150 | 240 | 600 | 1,000 | Sample size needed for 90% chance of detecting error | |||
81 | Error level | ||||||||||
82 | 5% | 8% | 21% | 0% | 0.0% | 0.0% | 0.0% | 45 | |||
83 | 4% | 13% | 29% | 0% | 0.0% | 0.0% | 0.0% | 57 | |||
84 | 3% | 22% | 40% | 1% | 0.1% | 0.0% | 0.0% | 76 | |||
85 | 2.28% | 32% | 50% | 3% | 0.4% | 0.0% | 0.0% | 100 | |||
86 | 2% | 36% | 55% | 5% | 0.8% | 0.0% | 0.0% | 114 | log formula for sample from conf.level/(1-err.rate) | ||
87 | 1% | 61% | 74% | 22% | 9.0% | 0.2% | 0.0% | 459 | 229 | ||
88 | 0.50% | 78% | 86% | 47% | 30.0% | 4.9% | 0.7% | 460 | |||
89 | Risk of missing the error level shown with sample shown | Error level | |||||||||
90 | 11% | 4.32% | 7.09% | 1.46% | 0.92% | 0.37% | |||||
91 | 10% | 4.50% | 7.39% | 1.52% | 0.95% | 0.38% | |||||
92 | |||||||||||
93 | good items | errors | cum chance of missing errors | ||||||||
94 | Example: total ballots or batches | 200 | |||||||||
95 | erroneous ballots or batches | 10 | |||||||||
96 | chance of missing error in sample 1 | 0.95 | 190 | 10 | 0.95 | ||||||
97 | chance of missing error in sample 2 | 0.9497487437 | 189 | 10 | 0.9022613065 | ||||||
98 | chance of missing error in sample 3 | 0.9494949495 | 188 | 10 | 0.8566925537 | ||||||
99 | chance of missing error in sample 4 | 0.9492385787 | 187 | 10 | 0.813205622 | ||||||
100 | chance of missing error in sample 5 | 0.9489795918 | 186 | 10 | 0.7717155393 | ||||||