ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAG
1
Number of Ballot Sheets in Sample, for graph
2
Chance of detecting issueErrors detectable at several confidence levels50587080901001201702202703203704204705201,0005,000
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
501002003006001,0002,00038,011
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 errorsChance sample catches error
29
Error Levelwinning margin595298595 ballots compared to electronic records298 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
flawsmargin5060708090100150200250300350400450500550600650
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
sample101002,0005050010,0001001,00020,0001201,20024,0002002,00040,000129278756120120120
76
flawsflaw rateflaw rateflaw 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