| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | AA | AB | AC | AD | AE | AF | AG | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | Number of Ballot Sheets in Sample, for graph | |||||||||||||||||||||||||||||||||
2 | Chance of detecting issue | Errors detectable at several confidence levels | 50 | 58 | 70 | 80 | 90 | 100 | 120 | 170 | 220 | 270 | 320 | 370 | 420 | 470 | 520 | 1,000 | 5,000 | |||||||||||||||
3 | 95% | Sample has 95% chance to detect errors at left | 5.8% | 5.0% | 4.2% | 3.7% | 3.3% | 3.0% | 2.47% | 1.7% | 1.4% | 1.1% | 0.9% | 0.8% | 0.7% | 0.6% | 0.6% | 0.30% | 0.1% | |||||||||||||||
4 | 90% | Sample has 90% chance to detect errors at left | 4.5% | 3.9% | 3.2% | 2.8% | 2.5% | 2.3% | 1.90% | 1.3% | 1.0% | 0.8% | 0.7% | 0.6% | 0.5% | 0.5% | 0.4% | 0.23% | 0.05% | |||||||||||||||
5 | 75% | Sample has 75% chance to detect errors at left | 2.7% | 2.4% | 2.0% | 1.7% | 1.5% | 1.4% | 1.15% | 0.8% | 0.6% | 0.5% | 0.4% | 0.4% | 0.3% | 0.3% | 0.3% | 0.14% | 0.0% | |||||||||||||||
6 | 50% | Sample has 50% chance to detect errors at left | 1.4% | 1.2% | 1.0% | 0.9% | 0.8% | 0.7% | 0.58% | 0.4% | 0.3% | 0.3% | 0.2% | 0.2% | 0.2% | 0.1% | 0.1% | 0.1% | 0.0% | |||||||||||||||
7 | 25% | Sample has 25% chance to detect errors at left | 0.6% | 0.5% | 0.4% | 0.4% | 0.3% | 0.3% | 0.24% | 0.2% | 0.1% | 0.1% | 0.1% | 0.1% | 0.1% | 0.1% | 0.1% | 0.0% | 0.0% | |||||||||||||||
8 | ||||||||||||||||||||||||||||||||||
9 | Errors Detectable, for Confidence & Sample Shown | |||||||||||||||||||||||||||||||||
10 | Number of Ballots Sheets in Sample, for Table | 49,311 | ||||||||||||||||||||||||||||||||
11 | Sample Size | 50 | 100 | 200 | 300 | 600 | 1,000 | 2,000 | 38,011 | |||||||||||||||||||||||||
12 | Chance of detecting issue | Errors Detectable, for Confidence & Sample Shown | 22,972 | |||||||||||||||||||||||||||||||
13 | 95% | 5.8% | 3.0% | 1.5% | 1.0% | 0.5% | 0.30% | 0.15% | 11,519 | |||||||||||||||||||||||||
14 | 90% | 4.5% | 2.3% | 1.1% | 0.8% | 0.4% | 0.23% | 0.12% | 4,789 | |||||||||||||||||||||||||
15 | 75% | 2.7% | 1.4% | 0.7% | 0.5% | 0.23% | 0.14% | 0.07% | ||||||||||||||||||||||||||
16 | 50% | 1.4% | 0.7% | 0.3% | 0.23% | 0.12% | 0.07% | 0.03% | ||||||||||||||||||||||||||
17 | 25% | 0.6% | 0.3% | 0.14% | 0.10% | 0.05% | 0.03% | 0.01% | ||||||||||||||||||||||||||
18 | ||||||||||||||||||||||||||||||||||
19 | ||||||||||||||||||||||||||||||||||
20 | ||||||||||||||||||||||||||||||||||
21 | ||||||||||||||||||||||||||||||||||
22 | ||||||||||||||||||||||||||||||||||
23 | ||||||||||||||||||||||||||||||||||
24 | ||||||||||||||||||||||||||||||||||
25 | ||||||||||||||||||||||||||||||||||
26 | ||||||||||||||||||||||||||||||||||
27 | SRS - Simple Random Samples | |||||||||||||||||||||||||||||||||
28 | Risk that sample misses errors | Chance sample catches error | ||||||||||||||||||||||||||||||||
29 | Error Level | winning margin | 595 | 298 | 595 ballots compared to electronic records | 298 ballots compared to records | sample size | |||||||||||||||||||||||||||
30 | 0.20% | 0.4% | 30% | 55% | 70% | 45% | ||||||||||||||||||||||||||||
31 | 0.30% | 0.6% | 17% | 41% | 83% | 59% | ||||||||||||||||||||||||||||
32 | 0.40% | 0.8% | 9% | 30% | 91% | 70% | ||||||||||||||||||||||||||||
33 | 0.50% | 1.0% | 5% | 22% | 95% | 78% | ||||||||||||||||||||||||||||
34 | 0.60% | 1.2% | 3% | 17% | 97% | 83% | ||||||||||||||||||||||||||||
35 | 0.70% | 1.4% | 2% | 12% | 98% | 88% | ||||||||||||||||||||||||||||
36 | 0.80% | 1.6% | 1% | 9% | 99% | 91% | ||||||||||||||||||||||||||||
37 | 0.90% | 1.8% | 0% | 7% | 100% | 93% | ||||||||||||||||||||||||||||
38 | 1.00% | 2.0% | 0% | 5% | 100% | 95% | ||||||||||||||||||||||||||||
39 | 1.50% | 3.0% | 0% | 1% | 100% | 99% | ||||||||||||||||||||||||||||
40 | 2.00% | 4.0% | 0% | 0% | 100% | 100% | ||||||||||||||||||||||||||||
41 | 2.50% | 5.0% | 0% | 0% | 100% | 100% | ||||||||||||||||||||||||||||
42 | 3.00% | 6.0% | 0% | 0% | 100% | 100% | ||||||||||||||||||||||||||||
43 | 3.50% | 7.0% | 0% | 0% | 100% | 100% | ||||||||||||||||||||||||||||
44 | 4.00% | 8.0% | 0% | 0% | 100% | 100% | ||||||||||||||||||||||||||||
45 | 4.50% | 9.0% | 0% | 0% | 100% | 100% | ||||||||||||||||||||||||||||
46 | 6.0% | 12.0% | 0% | 0% | 100% | 100% | ||||||||||||||||||||||||||||
47 | ||||||||||||||||||||||||||||||||||
48 | Risk of not detecting error level shown | |||||||||||||||||||||||||||||||||
49 | flaws | margin | 50 | 60 | 70 | 80 | 90 | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 | 550 | 600 | 650 | |||||||||||||||
50 | 60 ballots in sample | 600 ballots in sample | ||||||||||||||||||||||||||||||||
51 | 0.10% | 0.2% | 95% | 94% | 93% | 92% | 91% | 90% | 86% | 82% | 78% | 74% | 70% | 67% | 64% | 61% | 58% | 55% | ||||||||||||||||
52 | 0.20% | 0.4% | 90% | 89% | 87% | 85% | 84% | 82% | 74% | 67% | 61% | 55% | 50% | 45% | 41% | 37% | 33% | 30% | ||||||||||||||||
53 | 0.30% | 0.6% | 86% | 84% | 81% | 79% | 76% | 74% | 64% | 55% | 47% | 41% | 35% | 30% | 26% | 22% | 19% | 16% | ||||||||||||||||
54 | 0.40% | 0.8% | 82% | 79% | 76% | 73% | 70% | 67% | 55% | 45% | 37% | 30% | 25% | 20% | 16% | 13% | 11% | 9% | ||||||||||||||||
55 | 0.50% | 1.0% | 78% | 74% | 70% | 67% | 64% | 61% | 47% | 37% | 29% | 22% | 17% | 13% | 10% | 8% | 6% | 5% | ||||||||||||||||
56 | 0.60% | 1.2% | 74% | 70% | 66% | 62% | 58% | 55% | 41% | 30% | 22% | 16% | 12% | 9% | 7% | 5% | 4% | 3% | ||||||||||||||||
57 | 0.70% | 1.4% | 70% | 66% | 61% | 57% | 53% | 50% | 35% | 25% | 17% | 12% | 9% | 6% | 4% | 3% | 2% | 1% | ||||||||||||||||
58 | 0.80% | 1.6% | 67% | 62% | 57% | 53% | 49% | 45% | 30% | 20% | 13% | 9% | 6% | 4% | 3% | 2% | 1% | 1% | ||||||||||||||||
59 | 0.90% | 1.8% | 64% | 58% | 53% | 49% | 44% | 40% | 26% | 16% | 10% | 7% | 4% | 3% | 2% | 1% | 1% | 0% | ||||||||||||||||
60 | 1.00% | 2.0% | 61% | 55% | 49% | 45% | 40% | 37% | 22% | 13% | 8% | 5% | 3% | 2% | 1% | 1% | 0% | 0% | ||||||||||||||||
61 | 2.00% | 4.0% | 36% | 30% | 24% | 20% | 16% | 13% | 5% | 2% | 1% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
62 | 3.00% | 6.0% | 22% | 16% | 12% | 9% | 6% | 5% | 1% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
63 | 4.00% | 8.0% | 13% | 9% | 6% | 4% | 3% | 2% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
64 | 5.00% | 10.0% | 8% | 5% | 3% | 2% | 1% | 1% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
65 | 6.00% | 12.0% | 5% | 2% | 1% | 1% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
66 | 7.00% | 14.0% | 3% | 1% | 1% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
67 | 8.00% | 16.0% | 2% | 1% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
68 | 9.00% | 18.0% | 1% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
69 | 10.00% | 20.0% | 1% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 0% | ||||||||||||||||
70 | ||||||||||||||||||||||||||||||||||
71 | ||||||||||||||||||||||||||||||||||
72 | Risk that a % sample will not detect fixed number of flaws, for different numbers of ballots. Fixed % sample does not give exactly the same risk for the same # of flaws, but very close. | |||||||||||||||||||||||||||||||||
73 | Univers | 10,000 | 100,000 | 2,000,000 | 10,000 | 100,000 | 2,000,000 | 10,000 | 100,000 | 2,000,000 | 10,000 | 100,000 | 2,000,000 | 10,000 | 100,000 | 2,000,000 | 10,000 | 100,000 | 2,000,000 | 10,000 | 100,000 | 2,000,000 | 10,000 | 100,000 | 2,000,000 | |||||||||
74 | sample% | 0.10% | 0.10% | 0.10% | 0.50% | 0.50% | 0.50% | 1.0% | 1.0% | 1.0% | 1.20% | 1.20% | 1.20% | 2.00% | 2.00% | 2.00% | 6 times cube root of ballot sheets | |||||||||||||||||
75 | sample | 10 | 100 | 2,000 | 50 | 500 | 10,000 | 100 | 1,000 | 20,000 | 120 | 1,200 | 24,000 | 200 | 2,000 | 40,000 | 129 | 278 | 756 | 120 | 120 | 120 | ||||||||||||
76 | flaws | flaw rate | flaw rate | flaw rate | ||||||||||||||||||||||||||||||
77 | 50 | 0.50% | 0.05% | 0.003% | 95.11% | 95.12% | 95.12% | 77.83% | 77.88% | 77.88% | 60.58% | 60.65% | 60.65% | 54.80% | 54.87% | 54.88% | 36.70% | 36.78% | 36.79% | 52.31% | 87.00% | 98.13% | 54.80% | 94.18% | 99.70% | |||||||||
78 | 115 | 1.15% | 0.12% | 0.01% | 89.08% | 89.13% | 89.14% | 56.08% | 56.25% | 56.27% | 31.45% | 31.64% | 31.66% | 24.96% | 25.14% | 25.16% | 9.89% | 10.01% | 10.03% | 22.42% | 72.58% | 95.75% | 24.96% | 87.10% | 99.31% | |||||||||
79 | 190 | 1.90% | 0.19% | 0.01% | 82.54% | 82.68% | 82.70% | 38.32% | 38.64% | 38.67% | 14.69% | 14.93% | 14.96% | 10.01% | 10.21% | 10.23% | 2.16% | 2.23% | 2.24% | 8.38% | 58.88% | 93.07% | 10.01% | 79.60% | 98.87% | |||||||||
80 | 230 | 2.30% | 0.23% | 0.01% | 79.24% | 79.43% | 79.45% | 31.24% | 31.62% | 31.66% | 9.76% | 10.00% | 10.02% | 6.13% | 6.31% | 6.33% | 0.95% | 1.00% | 1.00% | 4.94% | 52.66% | 91.67% | 6.13% | 75.86% | 98.63% | |||||||||
81 | 300 | 3.00% | 0.30% | 0.02% | 73.74% | 74.05% | 74.08% | 21.81% | 22.26% | 22.31% | 4.76% | 4.96% | 4.98% | 2.59% | 2.72% | 2.73% | 0.23% | 0.25% | 0.25% | 1.95% | 43.31% | 89.28% | 2.59% | 69.73% | 98.22% | |||||||||
82 | 450 | 4.50% | 0.45% | 0.02% | 63.10% | 63.70% | 63.76% | 10.00% | 10.49% | 10.54% | 1.00% | 1.10% | 1.11% | 0.40% | 0.45% | 0.45% | 0.01% | 0.01% | 0.01% | 0.26% | 28.48% | 84.36% | 0.40% | 58.20% | 97.34% | |||||||||
83 | 900 | 9.00% | 0.90% | 0.05% | 38.94% | 40.49% | 40.65% | 0.90% | 1.09% | 1.11% | 0.01% | 0.01% | 0.01% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 8.06% | 71.16% | 0.00% | 33.79% | 94.74% | |||||||||
84 | 1,800 | 18.00% | 1.80% | 0.09% | 13.74% | 16.26% | 16.52% | 0.00% | 0.01% | 0.01% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.64% | 50.63% | 0.00% | 11.31% | 89.76% | |||||||||
85 | 1,900 | 19.00% | 1.90% | 0.10% | 12.16% | 14.69% | 14.94% | 0.00% | 0.01% | 0.01% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.48% | 48.75% | 0.00% | 10.01% | 89.22% | |||||||||
86 | 4,000 | 40.00% | 4.00% | 0.20% | 0.60% | 1.69% | 1.82% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 22.02% | 0.00% | 0.75% | 78.64% | |||||||||
87 | 6,000 | 60.00% | 6.00% | 0.30% | 0.01% | 0.21% | 0.25% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 10.32% | 0.00% | 0.06% | 69.73% | |||||||||
88 | 8,000 | 80.00% | 8.00% | 0.40% | 0.00% | 0.02% | 0.03% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 4.83% | 0.00% | 0.00% | 61.82% | |||||||||
89 | 16,000 | 100.00% | 16.00% | 0.80% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.23% | 0.00% | 0.00% | 38.14% | |||||||||
90 | 38,000 | 100.00% | 38.00% | 1.90% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 10.01% | |||||||||
91 | 76,000 | 100.00% | 76.00% | 3.80% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.96% | |||||||||
92 | 152,000 | 100.00% | 100.00% | 7.60% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.01% | |||||||||
93 | 304,000 | 100.00% | 100.00% | 15.20% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | |||||||||
94 | 608,000 | 100.00% | 100.00% | 30.40% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | |||||||||
95 | 1,216,000 | 100.00% | 100.00% | 60.80% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | |||||||||
96 | ||||||||||||||||||||||||||||||||||
97 | ||||||||||||||||||||||||||||||||||
98 | ||||||||||||||||||||||||||||||||||
99 | ||||||||||||||||||||||||||||||||||
100 |