sample costs+sizes+CO+MN+PA

	A	B	C	D	E	F	G	H
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	300	900	0	Sample size needed for 90% chance of detecting error
81	Error level	Risk of missing errors in the image files or CVRs
82	5%	8%	21%	0%	0%	0%	100%	45
83	4%	13%	29%	0%	0%	0%	100%	57
84	3%	22%	40%	1%	0%	0%	100%	76
85	2.28%	32%	50%	3%	0%	0%	100%	100
86	2%	36%	55%	5%	0%	0%	100%	114
87	1%	61%	74%	22%	5%	0%	100%	230
88	0.60%	74%	83%	41%	16%	0%	100%	383
89	Risk of missing the error level shown with sample shown	Error level
90	11%	4.32%	7.09%	1.46%	0.73%	0.24%
91	10%	4.50%	7.39%	1.52%	0.76%	0.26%
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