Table 1.
RUL | GLL | α (0.05), β (0.2) | α (0.05), β (0.1) | α (0.05), β (0.05) | |||
---|---|---|---|---|---|---|---|
% | % | n | Ac (%) | n | Ac (%) | n | Ac (%) |
10 | 20 | 79 | 12.3 (15.6) | 111 | 16.3 (14.7) | 143 | 20.2 (14.1) |
15 | 25 | 101 | 21.1 (20.8) | 140 | 28.0 (20.0) | 179 | 34.7 (19.4) |
15 | 30 | 49 | 11.5 (23.4) | 68 | 15.0 (22.1) | 87 | 18.5 (21.3) |
20 | 30 | 119 | 31.0 (26.0) | 165 | 41.5 (25.1) | 209 | 51.3 (24.6) |
20 | 35 | 57 | 16.4 (28.7) | 78 | 21.4 (27.5) | 99 | 26.3 (26.6) |
20 | 40 | 34 | 10.6 (31.3) | 46 | 13.7 (29.7) | 59 | 16.9 (28.6) |
25 | 35 | 134 | 41.7 (31.2) | 185 | 55.9 (30.2) | 234 | 69.4 (29.7) |
25 | 40 | 63 | 21.4 (34.0) | 86 | 28.1 (32.7) | 109 | 34.7 (31.8) |
25 | 45 | 37 | 13.6 (36.7) | 51 | 17.8 (35.0) | 64 | 21.7 (33.9) |
25 | 50 | 25 | 9.8 (39.2) | 33 | 12.3 (37.4) | 42 | 15.1 (36.0) |
30 | 40 | 146 | 52.9 (36.2) | 201 | 71.0 (35.3) | 253 | 87.9 (34.7) |
30 | 45 | 68 | 26.6 (39.1) | 93 | 35.2 (37.8) | 117 | 43.3 (37.0) |
30 | 50 | 39 | 16.4 (42.1) | 54 | 21.7 (40.3) | 67 | 26.3 (39.2) |
30 | 55 | 26 | 11.6 (44.8) | 35 | 15.0 (42.7) | 44 | 18.2 (41.4) |
30 | 60 | 18 | 8.6 (47.8) | 25 | 11.3 (45.1) | 30 | 13.1 (43.8) |
35 | 45 | 155 | 64.0 (41.3) | 212 | 85.6 (40.4) | 267 | 106.3 (39.8) |
35 | 50 | 71 | 31.5 (44.3) | 97 | 41.7 (43.0) | 121 | 51.0 (42.1) |
35 | 55 | 41 | 19.4 (47.3) | 56 | 25.5 (45.5) | 69 | 30.7 (44.4) |
35 | 60 | 27 | 13.5 (50.1) | 36 | 17.3 (48.1) | 44 | 20.6 (46.8) |
35 | 65 | 19 | 10.1 (53.0) | 25 | 12.7 (50.7) | 31 | 15.2 (49.1) |
40 | 50 | 160 | 74.2 (46.4) | 219 | 99.5 (45.4) | 275 | 123.4 (44.9) |
40 | 55 | 73 | 36.1 (49.4) | 99 | 47.6 (48.1) | 124 | 58.6 (47.2) |
40 | 60 | 42 | 22.0 (52.4) | 56 | 28.4 (50.8) | 70 | 34.7 (49.6) |
40 | 65 | 27 | 15.0 (55.5) | 36 | 19.2 (53.4) | 44 | 22.9 (52.1) |
40 | 70 | 19 | 11.1 (58.5) | 25 | 14.0 (56.1) | 30 | 16.4 (54.7) |
45 | 55 | 163 | 83.8 (51.4) | 222 | 112.1 (50.5) | 278 | 138.7 (49.9) |
45 | 60 | 74 | 40.3 (54.5) | 100 | 53.2 (53.2) | 124 | 64.9 (52.3) |
45 | 65 | 42 | 24.2 (57.6) | 56 | 31.3 (55.9) | 69 | 37.8 (54.9) |
45 | 70 | 27 | 16.4 (60.7) | 36 | 21.1 (58.6) | 44 | 25.2 (57.3) |
45 | 75 | 19 | 12.1 (63.8) | 24 | 14.8 (61.7) | 29 | 17.5 (60.2) |
50 | 60 | 162 | 91.5 (56.5) | 220 | 122.2 (55.5) | 275 | 151.5 (55.0) |
50 | 65 | 73 | 43.5 (59.6) | 98 | 57.1 (58.3) | 121 | 69.5 (57.5) |
50 | 70 | 41 | 25.8 (62.8) | 55 | 33.6 (61.1) | 67 | 40.2 (60.0) |
50 | 75 | 27 | 17.8 (65.8) | 34 | 21.8 (64.1) | 42 | 26.3 (62.7) |
55 | 65 | 159 | 97.8 (61.5) | 214 | 129.7 (60.6) | 267 | 160.2 (60.0) |
55 | 70 | 71 | 45.9 (64.7) | 94 | 59.6 (63.4) | 117 | 73.2 (62.6) |
55 | 75 | 40 | 27.2 (67.9) | 52 | 34.5 (66.3) | 64 | 41.7 (65.2) |
60 | 70 | 152 | 101.1 (66.5) | 204 | 133.9 (65.6) | 253 | 164.6 (65.1) |
60 | 75 | 68 | 47.4 (69.8) | 89 | 61.0 (68.5) | 109 | 73.8 (67.7) |
60 | 80 | 38 | 27.8 (73.1) | 48 | 34.4 (71.6) | 59 | 41.6 (70.5) |
65 | 75 | 142 | 101.6 (71.6) | 189 | 133.6 (70.7) | 234 | 164.1 (70.1) |
65 | 80 | 63 | 47.2 (74.9) | 81 | 59.7 (73.7) | 99 | 72.2 (72.9) |
65 | 85 | 34 | 26.7 (78.5) | 44 | 33.8 (76.8) | 52 | 39.5 (75.9) |
70 | 80 | 129 | 98.9 (76.6) | 170 | 128.8 (75.8) | 209 | 157.2 (75.2) |
70 | 85 | 56 | 44.8 (80.1) | 72 | 56.8 (78.9) | 87 | 67.9 (78.1) |
75 | 85 | 113 | 92.3 (81.7) | 147 | 118.9 (80.9) | 179 | 143.8 (80.3) |
75 | 90 | 48 | 40.9 (85.3) | 60 | 50.5 (84.2) | 71 | 59.3 (83.5) |
80 | 90 | 93 | 80.7 (86.8) | 119 | 102.4 (86.0) | 143 | 122.3 (85.5) |
RUL upper limit of RED zone (expressed as percentage of total sample), GLL lower limit of GREEN zone (expressed as percentage of total sample), AC AMBER-statistical significance threshold (within the AMBER zone) where an observed estimate below the cut-point will result in a non-significant result (p ≥ 0.05) and figures at or above the cut-point will be significant (p < 0.05) (%, as a percentage of n)
Sample sizes were derived using the normal approximation to the binomial distribution (with continuity correction) formula given in the Appendix, which by convention is stable for np > 5 and n(1 − p) > 5.
For this approach, AC% is calculated from the 1-sided upper 95% confidence limit for the null proportion: 100% × (RUL + z1−α√((RUL(1 − RUL))/n)) [e.g. for RUL = 20% v GLL = 35%, n = 78, power 90%: AC% = 100% × (0.2 + 1.645√((0.2(1 − 0.2))/78)) = 27.5%. In the example this is expressed as a proportion (0.275)]
The AC values do not account for the continuity correction (− 0.5 deduction) which would need to be applied to the observed count from a study prior to cross-checking against the AC cut-offs provided here