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. 2021 Feb 3;7:40. doi: 10.1186/s40814-021-00770-x

Table 1.

Sample size and significance cut-points for (GLL-RUL) differences for a one-sample test, power (80%, 90%, 95%) and 1-tailed 5% significance level based on normal approximation (with continuity correction)

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