Sample Sizes - Cannon & Roe
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ELECTRONIC FIELD SURVEY TABLES Version 1.0 The spreadsheets contained in this workbook represent direct calculations of each of the tables in Livestock Disease Surveys. A Field Manual for Veterinarians. by Cannon and Roe (Bureau of Rural Science, Department of Primary Industry 1982) The motivation for producing this workbook arose for several reasons, in particular the fact that Cannon and Roe is now out of print, and both authors have 'retired', the desire to generate specific answers not dependent on tables or reading off graphs, and to put the functionality of Cannon and Roe into the hands of all field veterinarians. Every attempt has been made to remain consistent with the approach taken by Rob Cannon and Dick Roe, while using the flexibility of Excel statistical functions, in a form that allows direct calculations, rather than table lookup. In some cases, a table has been calculated as well, although this is more of academic interest. The tables are as intuitive as I can make them. In most cases, pop-up comments indicate where/what should be placed in relevant cells. In addition, where specific inputs are required or desirable, drop-down boxes offer a range of choices. I wish to thank Tony Martin, and Mario D'Antuono for their kind assistance in producing this workbook.
DEDICATION Chris Hawkins Veterinary Epidemiologist WA Department of Agriculture April 2003
This workbook is dedicated to the lifetime of service to animal health and veterinary epidemiology provided by Rob Cannon and Dick Roe, whose cooperation in the production of Livestock Disease Surveys lifted a great burden from non-statistical field veterinarians!
Sample size required to detect disease Confidence limits for number positive Confidence
0.99
Population size (N) 1600
1.00% 399
Direct calculation Percentage of diseased animals in the population, OR Percentage sampled and found clean
Cannon and Roe Table 1 Table format: desired confidence:
0.9
Percentage of diseased animals in the population, OR percentage sampled and found c Population Size (N) 10 20 30 40 50 60 70 80 90 100 120 140 160 180 200 250 300 350 400 450 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000
50% 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
40% 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
30% 5 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
25% 6 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9
20% 7 8 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
10% 9 13 16 17 18 19 19 20 20 20 20 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22
5% 10 18 23 27 30 32 33 35 36 36 38 39 40 40 41 42 42 43 43 43 43 44 44 44 44 44 45 45 45 45 45 45 45 45 45
7000 8000 9000 10000 "Infinite"
4 4 4 4 4
5 5 5 5 5
7 7 7 7 7
9 9 9 9 9
11 11 11 11 11
22 22 22 22 22
45 45 45 45 45
OR percentage sampled and found clean 2% 10 20 30 38 45 51 56 61 65 68 74 78 82 85 87 92 95 98 100 101 102 104 106 107 107 108 109 110 110 111 111 112 113 113 113
1% 10 20 30 40 50 59 68 76 83 90 102 113 122 130 137 150 160 168 175 180 184 191 196 200 203 205 209 212 214 216 217 221 223 224 225
0.5% 10 20 30 40 50 60 70 80 90 99 118 135 151 166 180 210 235 256 273 288 301 321 337 350 360 369 382 392 400 406 411 426 434 439 443
0.1% 10 20 30 40 50 60 70 80 90 100 120 140 160 180 200 250 300 350 399 448 495 587 674 755 830 900 1024 1130 1220 1299 1367 1607 1750 1845 1912
114 114 114 114 114
226 226 227 227 230
445 447 448 449 460
1962 2000 2031 2056 2302
0.9 0.95 0.98 0.99 1 1
Chance of detecting positives with various intensities of monitoring Sampling proportion:
0.2
No. Population Sampled 10 2 20 4 30 6 40 8 50 10 60 12 70 14 80 16 90 18 100 20 1000 200
Cannon & Roe formula, p 30 Number of positives in the population. 1 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199
2 0.377 0.367 0.364 0.363 0.362 0.362 0.361 0.361 0.361 0.360 0.359
3 0.532 0.507 0.500 0.496 0.494 0.493 0.492 0.491 0.491 0.490 0.487
4 0.665 0.623 0.611 0.605 0.602 0.599 0.598 0.597 0.596 0.595 0.589
5 0.776 0.716 0.700 0.692 0.688 0.685 0.683 0.681 0.680 0.679 0.672
6 0.864 0.792 0.772 0.762 0.757 0.753 0.751 0.749 0.748 0.746 0.737
7 0.931 0.851 0.828 0.818 0.812 0.808 0.805 0.803 0.801 0.800 0.790
8 0.975 0.896 0.873 0.862 0.855 0.851 0.848 0.846 0.844 0.843 0.832
Using Excel function HYPGEOMDIST Note limitations to the use of HYPGEOMDIST Number of positives in the population No. Population Sampled 1 2 3 4 5 6 7 8 10 2 0.200 0.378 0.533 0.667 0.778 0.867 0.933 0.978 20 4 0.200 0.368 0.509 0.624 0.718 0.793 0.852 0.898 30 6 0.200 0.366 0.501 0.612 0.702 0.773 0.830 0.874 40 8 0.200 0.364 0.498 0.607 0.694 0.764 0.819 0.863 50 10 0.200 0.363 0.496 0.603 0.689 0.758 0.813 0.857 60 12 0.200 0.363 0.495 0.601 0.686 0.755 0.809 0.853 70 14 0.200 0.362 0.494 0.599 0.684 0.752 0.807 0.850 80 16 0.200 0.362 0.493 0.598 0.683 0.751 0.804 0.847 90 18 0.200 0.362 0.492 0.597 0.682 0.749 0.803 0.846 100 20 0.200 0.362 0.492 0.597 0.681 0.748 0.802 0.844 1000 200 0.200 0.360 0.488 0.591 0.673 0.739 0.791 0.833 "N/A" is inserted when the requirements of the HYPGEOMDIST function are not met. With discretion, in such cases assume the probability of detecting at least one positive is close to 1.
onitoring
ulation.
0.05 9 0.997 0.930 0.907 0.896 0.890 0.885 0.882 0.880 0.878 0.877 0.866
10 0.997 0.955 0.934 0.923 0.916 0.912 0.909 0.907 0.905 0.904 0.893
the use of HYPGEOMDIST ulation 9 N/A 0.932 0.909 0.897 0.891 0.887 0.884 0.881 0.879 0.878 0.867
on are not met. positive is close to 1.
10 N/A 0.957 0.935 0.924 0.917 0.913 0.910 0.908 0.906 0.905 0.894
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
Probability of Failure to Detect Disease at a Given Prevalence Assumes sampling from a very large population.
Prevalence 0.01
5 0.951
10 0.904
15 0.860
Number of animals in the sample tested 20 25 50 75 100 200 0.818 0.778 0.605 0.471 0.366 0.134
Hint: vary the prevalence as you wish; alter the number of animals as required.
250 0.081
500 0.007
1000 0.000
Sample size for estimation of disease prevalence Level of confidence Expected Desired Prevalence accuracy 0.01
0.1 7
Finite Population Correction Populaton size: 1600 7
0.99 0.05 26
0.01 657
0 65685
26
466
1562
BINOMIAL CONFIDENCE LIMITS Estimating disease prevalence Limits:
Upper 0.99
Lower 0.01
Two sided 98%
Sample size:
134
Number positive:
Proportion positive:
0.04
Proportion of the pop'n sampled:
Upper Lower
Limits* 0.095 0.010
Corrected 0.067 0.007
5 0.5
Critbinom 11 1
N/C Not calculated
*See Agresti A, and Coull BA (1998) Approximate is Better than "Exact" for Interval Estimation of Binomial Proportions. The American Statistician 52:(2) 119-126
DEDICATION Chris Hawkins Veterinary Epidemiologist WA Department of Agriculture April 2003
This workbook is dedicated to the lifetime of service to animal health and veterinary epidemiology provided by Rob Cannon and Dick Roe, whose cooperation in the production of Livestock Disease Surveys lifted a great burden from non-statistical field veterinarians!
Sample size required to detect disease Confidence limits for number positive Confidence
0.99
Population size (N) 1600
1.00% 399
Direct calculation Percentage of diseased animals in the population, OR Percentage sampled and found clean
Cannon and Roe Table 1 Table format: desired confidence:
0.9
Percentage of diseased animals in the population, OR percentage sampled and found c Population Size (N) 10 20 30 40 50 60 70 80 90 100 120 140 160 180 200 250 300 350 400 450 500 600 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 6000
50% 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
40% 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
30% 5 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
25% 6 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9
20% 7 8 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
10% 9 13 16 17 18 19 19 20 20 20 20 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22
5% 10 18 23 27 30 32 33 35 36 36 38 39 40 40 41 42 42 43 43 43 43 44 44 44 44 44 45 45 45 45 45 45 45 45 45
7000 8000 9000 10000 "Infinite"
4 4 4 4 4
5 5 5 5 5
7 7 7 7 7
9 9 9 9 9
11 11 11 11 11
22 22 22 22 22
45 45 45 45 45
OR percentage sampled and found clean 2% 10 20 30 38 45 51 56 61 65 68 74 78 82 85 87 92 95 98 100 101 102 104 106 107 107 108 109 110 110 111 111 112 113 113 113
1% 10 20 30 40 50 59 68 76 83 90 102 113 122 130 137 150 160 168 175 180 184 191 196 200 203 205 209 212 214 216 217 221 223 224 225
0.5% 10 20 30 40 50 60 70 80 90 99 118 135 151 166 180 210 235 256 273 288 301 321 337 350 360 369 382 392 400 406 411 426 434 439 443
0.1% 10 20 30 40 50 60 70 80 90 100 120 140 160 180 200 250 300 350 399 448 495 587 674 755 830 900 1024 1130 1220 1299 1367 1607 1750 1845 1912
114 114 114 114 114
226 226 227 227 230
445 447 448 449 460
1962 2000 2031 2056 2302
0.9 0.95 0.98 0.99 1 1
Chance of detecting positives with various intensities of monitoring Sampling proportion:
0.2
No. Population Sampled 10 2 20 4 30 6 40 8 50 10 60 12 70 14 80 16 90 18 100 20 1000 200
Cannon & Roe formula, p 30 Number of positives in the population. 1 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199 0.199
2 0.377 0.367 0.364 0.363 0.362 0.362 0.361 0.361 0.361 0.360 0.359
3 0.532 0.507 0.500 0.496 0.494 0.493 0.492 0.491 0.491 0.490 0.487
4 0.665 0.623 0.611 0.605 0.602 0.599 0.598 0.597 0.596 0.595 0.589
5 0.776 0.716 0.700 0.692 0.688 0.685 0.683 0.681 0.680 0.679 0.672
6 0.864 0.792 0.772 0.762 0.757 0.753 0.751 0.749 0.748 0.746 0.737
7 0.931 0.851 0.828 0.818 0.812 0.808 0.805 0.803 0.801 0.800 0.790
8 0.975 0.896 0.873 0.862 0.855 0.851 0.848 0.846 0.844 0.843 0.832
Using Excel function HYPGEOMDIST Note limitations to the use of HYPGEOMDIST Number of positives in the population No. Population Sampled 1 2 3 4 5 6 7 8 10 2 0.200 0.378 0.533 0.667 0.778 0.867 0.933 0.978 20 4 0.200 0.368 0.509 0.624 0.718 0.793 0.852 0.898 30 6 0.200 0.366 0.501 0.612 0.702 0.773 0.830 0.874 40 8 0.200 0.364 0.498 0.607 0.694 0.764 0.819 0.863 50 10 0.200 0.363 0.496 0.603 0.689 0.758 0.813 0.857 60 12 0.200 0.363 0.495 0.601 0.686 0.755 0.809 0.853 70 14 0.200 0.362 0.494 0.599 0.684 0.752 0.807 0.850 80 16 0.200 0.362 0.493 0.598 0.683 0.751 0.804 0.847 90 18 0.200 0.362 0.492 0.597 0.682 0.749 0.803 0.846 100 20 0.200 0.362 0.492 0.597 0.681 0.748 0.802 0.844 1000 200 0.200 0.360 0.488 0.591 0.673 0.739 0.791 0.833 "N/A" is inserted when the requirements of the HYPGEOMDIST function are not met. With discretion, in such cases assume the probability of detecting at least one positive is close to 1.
onitoring
ulation.
0.05 9 0.997 0.930 0.907 0.896 0.890 0.885 0.882 0.880 0.878 0.877 0.866
10 0.997 0.955 0.934 0.923 0.916 0.912 0.909 0.907 0.905 0.904 0.893
the use of HYPGEOMDIST ulation 9 N/A 0.932 0.909 0.897 0.891 0.887 0.884 0.881 0.879 0.878 0.867
on are not met. positive is close to 1.
10 N/A 0.957 0.935 0.924 0.917 0.913 0.910 0.908 0.906 0.905 0.894
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
Probability of Failure to Detect Disease at a Given Prevalence Assumes sampling from a very large population.
Prevalence 0.01
5 0.951
10 0.904
15 0.860
Number of animals in the sample tested 20 25 50 75 100 200 0.818 0.778 0.605 0.471 0.366 0.134
Hint: vary the prevalence as you wish; alter the number of animals as required.
250 0.081
500 0.007
1000 0.000
Sample size for estimation of disease prevalence Level of confidence Expected Desired Prevalence accuracy 0.01
0.1 7
Finite Population Correction Populaton size: 1600 7
0.99 0.05 26
0.01 657
0 65685
26
466
1562
BINOMIAL CONFIDENCE LIMITS Estimating disease prevalence Limits:
Upper 0.99
Lower 0.01
Two sided 98%
Sample size:
134
Number positive:
Proportion positive:
0.04
Proportion of the pop'n sampled:
Upper Lower
Limits* 0.095 0.010
Corrected 0.067 0.007
5 0.5
Critbinom 11 1
N/C Not calculated
*See Agresti A, and Coull BA (1998) Approximate is Better than "Exact" for Interval Estimation of Binomial Proportions. The American Statistician 52:(2) 119-126
