Table 1.
Recommended sample sizes and decision rules for numbers of clusters up to n min for the community health worker data quality assessment example
|
Number of clusters | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | ||
| ICC = 0.01 |
samples per cluster, k |
13 |
7 |
5 |
4 |
5 |
3 |
4 |
3 |
2 |
2 |
3 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
| |
total sample size, n |
26 |
21 |
20 |
20 |
30 |
21 |
32 |
27 |
20 |
22 |
36 |
26 |
28 |
30 |
32 |
34 |
36 |
38 |
20 |
| |
decision rule, d |
4 |
3 |
3 |
3 |
4 |
3 |
5 |
4 |
3 |
3 |
5 |
4 |
4 |
4 |
5 |
5 |
5 |
5 |
3 |
| |
α |
0.093 |
0.081 |
0.096 |
0.095 |
0.040 |
0.077 |
0.073 |
0.069 |
0.092 |
0.062 |
0.036 |
0.081 |
0.056 |
0.038 |
0.071 |
0.050 |
0.035 |
0.024 |
0.091 |
| |
β |
0.048 |
0.091 |
0.079 |
0.078 |
0.065 |
0.087 |
0.022 |
0.045 |
0.076 |
0.096 |
0.034 |
0.040 |
0.050 |
0.062 |
0.021 |
0.027 |
0.033 |
0.041 |
0.075 |
| |
Expected Costs, Scenario 1 † |
$1,260 |
$1,710 |
$2,200 |
$2,700 |
$3,300 |
$3,710 |
$4,320 |
$4,770 |
$5,200 |
$5,720 |
$6,360 |
$6,760 |
$7,280 |
$7,800 |
$8,320 |
$8,840 |
$9,360 |
$9,880 |
$10,200 |
| |
Expected Costs, Scenario 2 ‡ |
$1,900 |
$1,950 |
$2,200 |
$2,500 |
$3,300 |
$3,150 |
$4,000 |
$4,050 |
$4,000 |
$4,400 |
$5,400 |
$5,200 |
$5,600 |
$6,000 |
$6,400 |
$6,800 |
$7,200 |
$7,600 |
$7,000 |
| ICC = 0.025 |
samples per cluster, k |
14 |
7 |
7 |
4 |
5 |
3 |
4 |
3 |
2 |
2 |
3 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
| |
total sample size, n |
28 |
21 |
28 |
20 |
30 |
21 |
32 |
27 |
20 |
22 |
36 |
26 |
28 |
30 |
32 |
34 |
36 |
38 |
20 |
| |
decision rule, d |
4 |
3 |
4 |
3 |
4 |
3 |
5 |
4 |
3 |
3 |
5 |
4 |
4 |
4 |
5 |
5 |
5 |
5 |
3 |
| |
α |
0.084 |
0.090 |
0.069 |
0.100 |
0.045 |
0.080 |
0.077 |
0.072 |
0.094 |
0.063 |
0.038 |
0.083 |
0.057 |
0.039 |
0.072 |
0.051 |
0.036 |
0.025 |
0.091 |
| |
β |
0.074 |
0.098 |
0.062 |
0.083 |
0.070 |
0.090 |
0.025 |
0.048 |
0.078 |
0.097 |
0.036 |
0.041 |
0.051 |
0.063 |
0.022 |
0.028 |
0.034 |
0.042 |
0.075 |
| |
Expected Costs, Scenario 1 |
$1,280 |
$1,710 |
$2,280 |
$2,700 |
$3,300 |
$3,710 |
$4,320 |
$4,770 |
$5,200 |
$5,720 |
$6,360 |
$6,760 |
$7,280 |
$7,800 |
$8,320 |
$8,840 |
$9,360 |
$9,880 |
$10,200 |
| |
Expected Costs, Scenario 2 |
$2,000 |
$1,950 |
$2,600 |
$2,500 |
$3,300 |
$3,150 |
$4,000 |
$4,050 |
$4,000 |
$4,400 |
$5,400 |
$5,200 |
$5,600 |
$6,000 |
$6,400 |
$6,800 |
$7,200 |
$7,600 |
$7,000 |
| ICC = 0.05 |
samples per cluster, k |
18 |
10 |
7 |
6 |
5 |
3 |
4 |
3 |
2 |
2 |
3 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
| |
total sample size, n |
36 |
30 |
28 |
30 |
30 |
21 |
4 |
27 |
20 |
22 |
36 |
26 |
28 |
30 |
32 |
34 |
36 |
38 |
20 |
| |
decision rule, d |
5 |
4 |
4 |
4 |
4 |
3 |
5 |
4 |
3 |
3 |
5 |
4 |
4 |
4 |
5 |
5 |
5 |
5 |
20 |
| |
α |
0.093 |
0.071 |
0.082 |
0.056 |
0.052 |
0.085 |
0.085 |
0.076 |
0.097 |
0.065 |
0.041 |
0.086 |
0.060 |
0.041 |
0.075 |
0.053 |
0.038 |
0.026 |
0.091 |
| |
β |
0.083 |
0.095 |
0.073 |
0.082 |
0.078 |
0.094 |
0.029 |
0.052 |
0.080 |
0.100 |
0.040 |
0.043 |
0.054 |
0.065 |
0.023 |
0.029 |
0.036 |
0.044 |
0.075 |
| |
Expected Costs, Scenario 1 |
$1,360 |
$1,800 |
$2,280 |
$2,800 |
$3,300 |
$3,710 |
$4,320 |
$4,770 |
$5,200 |
$5,720 |
$6,360 |
$6,760 |
$7,280 |
$7,800 |
$8,320 |
$8,840 |
$9,360 |
$9,880 |
$10,200 |
| |
Expected Costs, Scenario 2 |
$2,400 |
$2,400 |
$2,600 |
$3,000 |
$3,300 |
$3,150 |
$4,000 |
$4,050 |
$4,000 |
$4,400 |
$5,400 |
$5,200 |
$5,600 |
$6,000 |
$6,400 |
$6,800 |
$7,200 |
$7,600 |
$7,000 |
| ICC = 0.1 |
samples per cluster, k |
68‡‡ |
15 |
9 |
6 |
5 |
4 |
4 |
3 |
3 |
3 |
3 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
| |
total sample size, n |
136 |
45 |
36 |
30 |
30 |
28 |
32 |
27 |
30 |
33 |
36 |
26 |
28 |
30 |
32 |
34 |
36 |
38 |
20 |
| |
decision rule, d |
17 |
6 |
5 |
4 |
4 |
4 |
5 |
4 |
4 |
5 |
5 |
4 |
4 |
4 |
5 |
5 |
5 |
5 |
3 |
| |
α |
0.096 |
0.092 |
0.090 |
0.075 |
0.067 |
0.082 |
0.099 |
0.086 |
0.052 |
0.077 |
0.048 |
0.091 |
0.064 |
0.045 |
0.080 |
0.058 |
0.041 |
0.029 |
0.091 |
| |
β |
0.099 |
0.093 |
0.082 |
0.099 |
0.093 |
0.073 |
0.038 |
0.060 |
0.078 |
0.036 |
0.047 |
0.047 |
0.058 |
0.070 |
0.026 |
0.033 |
0.040 |
0.048 |
0.075 |
| |
Expected Costs, Scenario 1 |
$2,360 |
$1,950 |
$2,360 |
$2,800 |
$3,300 |
$3,780 |
$4,320 |
$4,770 |
$5,300 |
$5,830 |
$6,360 |
$6,760 |
$7,280 |
$7,800 |
$8,320 |
$8,840 |
$9,360 |
$9,880 |
$10,200 |
| |
Expected Costs, Scenario 2 |
$7,400 |
$3,150 |
$3,000 |
$3,000 |
$3,300 |
$3,500 |
$4,000 |
$4,050 |
$4,500 |
$4,950 |
$5,400 |
$5,200 |
$5,600 |
$6,000 |
$6,400 |
$6,800 |
$7,200 |
$7,600 |
$7,000 |
| ICC = 0.15 |
samples per cluster, k |
†† |
45‡‡ |
13 |
9 |
6 |
4 |
5 |
3 |
3 |
3 |
3 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
| |
total sample size, n |
|
135 |
52 |
45 |
36 |
28 |
40 |
27 |
30 |
33 |
36 |
26 |
28 |
30 |
32 |
34 |
36 |
38 |
20 |
| |
decision rule, d |
|
17 |
7 |
6 |
5 |
4 |
6 |
4 |
4 |
5 |
5 |
4 |
28 |
4 |
5 |
5 |
5 |
5 |
3 |
| |
α |
|
0.099 |
0.100 |
0.082 |
0.087 |
0.095 |
0.090 |
0.096 |
0.060 |
0.086 |
0.055 |
0.096 |
0.069 |
0.049 |
0.085 |
0.062 |
0.045 |
0.032 |
0.091 |
| |
β |
|
0.099 |
0.090 |
0.087 |
0.080 |
0.083 |
0.043 |
0.067 |
0.086 |
0.042 |
0.053 |
0.051 |
0.062 |
0.074 |
0.029 |
0.036 |
0.043 |
0.051 |
0.075 |
| |
Expected Costs, Scenario 1 |
|
$2,850 |
$2,520 |
$2,950 |
$3,360 |
$3,780 |
$4,400 |
$4,770 |
$5,300 |
5830.000 |
$6,360 |
$6,760 |
$7,280 |
$7,800 |
$8,320 |
$8,840 |
$9,360 |
$9,880 |
$10,200 |
| |
Expected Costs, Scenario 2 |
|
$7,650 |
$3,800 |
$3,750 |
$3,600 |
$3,500 |
$4,400 |
$4,050 |
$4,500 |
4950.000 |
$5,400 |
$5,200 |
$5,600 |
$6,000 |
$6,400 |
$6,800 |
$7,200 |
$7,600 |
$7,000 |
| ICC = 0.2 |
samples per cluster, k |
†† |
†† |
40 |
12 |
9 |
6 |
6 |
4 |
3 |
3 |
3 |
3 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
| |
total sample size, n |
|
|
160 |
60 |
54 |
42 |
48 |
36 |
30 |
33 |
36 |
39 |
28 |
30 |
32 |
34 |
36 |
38 |
20 |
| |
decision rule, d |
|
|
20 |
8 |
7 |
6 |
7 |
5 |
4 |
5 |
5 |
5 |
4 |
4 |
5 |
5 |
5 |
5 |
3 |
| |
α |
|
|
0.096 |
0.099 |
0.077 |
0.098 |
0.091 |
0.077 |
0.068 |
0.095 |
0.063 |
0.041 |
0.073 |
0.052 |
0.090 |
0.066 |
0.048 |
0.035 |
0.091 |
| |
β |
|
|
0.100 |
0.090 |
0.091 |
0.067 |
0.050 |
0.071 |
0.093 |
0.047 |
0.060 |
0.074 |
0.066 |
0.078 |
0.032 |
0.039 |
0.047 |
0.055 |
0.075 |
| |
Expected Costs, Scenario 1 |
|
|
$3,600 |
$3,100 |
$3,540 |
$3,920 |
$4,480 |
$4,860 |
$5,300 |
$5,830 |
$6,360 |
$6,890 |
$7,280 |
$7,800 |
$8,320 |
$8,840 |
$9,360 |
$9,880 |
$10,200 |
| Expected Costs, Scenario 2 | $9,200 | $4,500 | $4,500 | $4,200 | $4,480 | $4,500 | $4,500 | $4,950 | $5,400 | $5,850 | $5,600 | $6,000 | $6,400 | $6,800 | $7,200 | $7,600 | $7,000 | |||
This table assumes pu = 0.25, pl = 0.05, αmax = βmas = 0.1.
† Assuming costs of $500 per cluster and $10 per individual sampled. ‡ Assuming costs of $300 per cluster and $50 per individual sampled. †† Too few clusters to determine a system. ‡‡ May not be applicable to CHW problem, as recommended sample size exceeds average number of households per cluster.