Background
Minimisation with unequal allocation ratios and randomisation test
Methods
Sequence balance minimisation procedure
Characteristic | Treatment 1 (n = 10) | Treatment 2 (n = 20) |
---|---|---|
Gender | ||
Men | 7 | 11 |
Women | 3 | 9 |
Ethnic group | ||
White | 6 | 10 |
Other | 4 | 10 |
Next allocation | Factor 1: gender (women) | Factor 2: ethnic group (white) | Allocation probabilities | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Number allocated | Number required | Difference (required − allocated) | Imbalance scorea
| Weight | Number allocated | Number required | Difference (required − allocated) | Imbalance scorea
| Weight | ||
T1 | 0 | 1 | 1 − 0 | 1/3 | 0.4 | 0 | 1 | 1 − 0 | 1/2 | 0.6 | 0.42 |
T2 | 0 | 2 | 2 − 0 | 2/3 | 0.57 | 1 | 2 | 2 − 1 | 1/2 | 0.43 | 0.58 |
Simulation study
Results
Balancing properties and randomisation distribution of sequence balance minimisation
Random element | Number of factors | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
Sample size (n = 30), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 10) | |||||||||||
p = 0.5 | Mean (SE) | 10.7 (0.07) | 10.5 (0.04) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.04) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.04) |
Median (p1–p99) | 11 (6–16) | 10 (7.5–14) | 10 (8–13) | 10 (7–13) | 10 (8–13) | 10 (8–13) | 10 (7–13) | 10 (8–13) | 10 (8–13) | 10 (8–13) | |
p = 0.6 | Mean (SE) | 10.6 (0.06) | 10.4 (0.04) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.04) | 10.1 (0.04) | 10.1 (0.04) |
Median (p1–p99) | 11 (6–15) | 10 (8–13) | 10 (8–13) | 10 (8–12.5) | 10 (8–12) | 10 (8–13) | 10 (8–13) | 10 (7–13) | 10 (7–13) | 10 (8–13) | |
p = 0.7 | Mean (SE) | 10.5 (0.05) | 10.3 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.04) | 10.1 (0.03) |
Median (p1–p99) | 10 (7–14) | 10 (8–13) | 10 (8–12.5) | 10 (8–13) | 10 (7.5–12) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (7.5–13) | 10 (7.5–13) | |
p = 0.8 | Mean (SE) | 10.3 (0.04) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.04) | 10.1 (0.03) |
Median (p1–p99) | 10 (7–14) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (8–12) | 10 (8–13) | 10 (8–12.5) | 10 (7.5–12.5) | 10 (8–13) | 10 (8–13) | |
p = 0.85 | Mean (SE) | 10.3 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.04) | 10.1 (0.03) |
Median (p1–p99) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (7.5–13) | 10 (7–13) | |
p = 0.9 | Mean (SE) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) |
Median (p1–p99) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (7.5–12) | 10 (8–13) | |
p = 0.95 | Mean (SE) | 10.1 (0.02) | 10.1 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.04) |
Median (p1–p99) | 10 (9–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (7.5–12) | 10 (8–12.5) | 10 (8–12) | 10 (7.5–13) | 10 (8–13) | |
Sample size (n = 60), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 20) | |||||||||||
p = 0.5 | Mean (SE) | 21.3 (0.09) | 21.0 (0.07) | 20.8 (0.06) | 20.6 (0.05) | 20.3 (0.05) | 20.1 (0.05) | 20.2 (0.05) | 20.1 (0.05) | 20.0 (0.05) | 20.1 (0.05) |
Median (p1–p99) | 21 (14–29) | 21 (16.5–26) | 21 (17–25.5) | 21 (17–25) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–23) | 20 (17–23.5) | 20 (17–24) | |
p = 0.6 | Mean (SE) | 21.1 (0.08) | 20.9 (0.06) | 20.7 (0.06) | 20.4 (0.05) | 20.3 (0.05) | 20.2 (0.04) | 20.1 (0.05) | 20.0 (0.05) | 20.1 (0.05) | 20.2 (0.05) |
Median (p1–p99) | 21 (15–27) | 21 (17–26) | 21 (17–25) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–23) | 20 (17–24) | 20 (17–24) | |
p = 0.7 | Mean (SE) | 20.8 (0.07) | 20.7 (0.05) | 20.5 (0.05) | 20.3 (0.05) | 20.3 (0.05) | 20.1 (0.05) | 20.1 (0.05) | 20.1 (0.05) | 20.1 (0.05) | 20.2 (0.05) |
Median (p1–p99) | 21 (16–26) | 21 (17–24.5) | 20 (17–25) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (16.5–24) | 20 (16.5–24) | |
p = 0.8 | Mean (SE) | 20.5 (0.06) | 20.4 (0.05) | 20.5 (0.05) | 20.2 (0.04) | 20.1 (0.05) | 20.1 (0.05) | 20.1 (0.05) | 20.0 (0.05) | 20.2 (0.05) | 20.1 (0.05) |
Median (p1–p99) | 21 (17–25) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–23) | 20 (17–23.5) | 20 (17–24) | 20 (17–23) | 20 (17–24) | 20 (16–24) | |
p = 0.85 | Mean (SE) | 20.5 (0.05) | 20.3 (0.04) | 20.2 (0.05) | 20.3 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.2 (0.05) | 20.0 (0.05) | 20.1 (0.05) | 20.2 (0.05) |
Median (p1–p99) | 20 (17–24) | 20 (17–23.5) | 20 (17–24) | 20 (17–24) | 20 (17–23) | 20 (17–23.5) | 20 (17–23.5) | 20 (17–23) | 20 (17–24) | 20 (17–24) | |
p = 0.9 | Mean (SE) | 20.2 (0.04) | 20.2 (0.04) | 20.3 (0.05) | 20.2 (0.04) | 20.2 (0.04) | 20.0 (0.05) | 20.1 (0.05) | 20.2 (0.05) | 20.1 (0.05) | 20.1 (0.05) |
Median (p1–p99) | 20 (17.5–23) | 20 (17–23) | 20 (17–24) | 20 (17–23) | 20 (17–23) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–24) | |
p = 0.95 | Mean (SE) | 20.1 (0.03) | 20.1 (0.03) | 20.2 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.0 (0.04) | 20.1 (0.05) | 20.1 (0.05) | 20.0 (0.04) | 20.3 (0.05) |
Median (p1–p99) | 20 (18–23) | 20 (18–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (16.5–23) | 20 (17–23) | 20 (17–24) | 20 (17–24) | |
Sample size (n = 120), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 40) | |||||||||||
p = 0.5 | Mean (SE) | 42.2 (0.13) | 41.7 (0.10) | 41.1 (0.08) | 40.7 (0.07) | 40.4 (0.07) | 40.3 (0.07) | 40.4 (0.07) | 40.3 (0.07) | 40.3 (0.07) | 40.3 (0.07) |
Median (p1–p99) | 42 (33–52) | 42 (35–49) | 41 (35–47) | 41 (35–46) | 40 (36–46) | 40 (35–45) | 40 (35–46) | 40 (36–46) | 40 (35–45) | 40 (35–45.5) | |
p = 0.6 | Mean (SE) | 41.8 (0.12) | 41.6 (0.09) | 40.8 (0.07) | 40.5 (0.07) | 40.4 (0.07) | 40.5 (0.07) | 40.3 (0.07) | 40.3 (0.07) | 40.3 (0.07) | 40.4 (0.07) |
Median (p1–p99) | 42 (33–50) | 41 (35–48) | 41 (35–47) | 40 (36–45) | 40 (36–45) | 40 (36–46) | 40 (35–45) | 40 (35–46) | 40 (35–45) | 40 (35–46) | |
p = 0.7 | Mean (SE) | 41.4 (0.10) | 41.2 (0.08) | 40.7 (0.07) | 40.5 (0.07) | 40.3 (0.07) | 40.4 (0.07) | 40.4 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.1 (0.07) |
Median (p1–p99) | 41 (34–49) | 41 (35–47) | 41 (36–46) | 41 (35–46) | 40 (35.5–45) | 40 (35–46) | 40 (35–45) | 40 (35–46) | 40 (36–45) | 40 (36–46) | |
p = 0.8 | Mean (SE) | 40.8 (0.08) | 40.8 (0.07) | 40.6 (0.07) | 40.4 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.3 (0.07) | 40.4 (0.07) | 40.3 (0.07) |
Median (p1–p99) | 41 (35.5–46) | 41 (35–46) | 41 (35–46) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (35–46) | 40 (35–46) | 40 (35–45) | 40 (35–45) | |
p = 0.85 | Mean (SE) | 40.7 (0.07) | 40.5 (0.07) | 40.5 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.3 (0.07) | 40.2 (0.07) |
Median (p1–p99) | 41 (35–46) | 40 (36–45) | 40 (36–45) | 40 (35.5–45) | 40 (35.5–45) | 40 (35–45) | 40 (35–45.5) | 40 (35–45) | 40 (35–45) | 40 (35–45) | |
p = 0.9 | Mean (SE) | 40.5 (0.06) | 40.5 (0.06) | 40.3 (0.06) | 40.4 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.4 (0.07) | 40.2 (0.07) |
Median (p1–p99) | 40 (36–45) | 41 (36–45.5) | 40 (36–45) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (35–45) | |
p = 0.95 | Mean (SE) | 40.3 (0.04) | 40.3 (0.06) | 40.2 (0.06) | 40.2 (0.06) | 40.2 (0.07) | 40.4 (0.06) | 40.2 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.3 (0.07) |
Median (p1–p99) | 40 (38–44) | 40 (36–44) | 40 (36–44) | 40 (36–44.5) | 40 (35.5–45) | 40 (36–45) | 40 (35–46) | 40 (35–46) | 40 (35–45) | 40 (35–45) |
Random element | Treatment totals only | Number of factors | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |||
Sample size (n = 30), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 10) | ||||||||||||
p = 0.5 | Mean (SE) | 10.9 (0.07) | 10.8 (0.06) | 10.5 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.04) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 11 (6–16) | 11 (7–15) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (8–12) | 10 (8–13) | 10 (7–13) | 10 (8–13) | 10 (8–13) | 10 (8–13) | |
p = 0.6 | Mean (SE) | 10.7 (0.06) | 10.7 (0.05) | 10.4 (0.03) | 10.2 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 11 (7–15) | 11 (7–15) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (7–12) | 10 (8–12.5) | 10 (8–13) | 10 (8–13) | |
p = 0.7 | Mean (SE) | 10.5 (0.05) | 10.5 (0.04) | 10.3 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 10 (6–14) | 10 (7–14) | 10 (8–13) | 10 (8–12.5) | 10 (8–12.5) | 10 (8–12) | 10 (8–12) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (8–13) | |
p = 0.8 | Mean (SE) | 10.3 (0.04) | 10.4 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.2 (0.03) | 10.1 (0.04) |
Median (p1–p99) | 10 (7–14) | 10 (8–13) | 10 (8–13) | 10 (8–12) | 10 (8–13) | 10 (8–12) | 10 (8–12.5) | 10 (8–12) | 10 (8–13) | 10 (8–13) | 10 (7–13) | |
p = 0.85 | Mean (SE) | 10.3 (0.03) | 10.3 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) |
Median (p1–p99) | 10 (8–13) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12.5) | 10 (8–12) | 10 (8–13) | 10 (7.5–12.5) | 10 (7–13) | |
p = 0.9 | Mean (SE) | 10.2 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.0 (0.04) | 10.1 (0.03) |
Median (p1–p99) | 10 (8–12) | 10 (8–13) | 10 (8–12) | 10 (8–12.5) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (7.5–13) | 10 (7–13) | 10 (8–12) | |
p = 0.95 | Mean (SE) | 10.1 (0.02) | 10.1 (0.02) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 10 (9–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–13) | 10 (8–13) | 10 (8–13) | |
Sample size (n = 60), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 20) | ||||||||||||
p = 0.5 | Mean (SE) | 21.7 (0.09) | 21.4 (0.07) | 20.9 (0.06) | 20.6 (0.06) | 20.4 (0.05) | 20.3 (0.05) | 20 (0.05) | 20.1 (0.05) | 20.1 (0.05) | 20.1 (0.05) | 20.1 (0.05) |
Median (p1–p99) | 22 (15–29) | 21 (16–27) | 21 (17–25) | 21 (17–26) | 20 (17–24) | 20 (17–24) | 20 (17–23) | 20 (17–23.5) | 20 (17–23.5) | 20 (17–24) | 20 (16.5–24) | |
p = 0.6 | Mean (SE) | 21.3 (0.09) | 21.1 (0.07) | 20.9 (0.06) | 20.5 (0.05) | 20.4 (0.04) | 20.3 (0.05) | 20.1 (0.04) | 20.1 (0.05) | 20.1 (0.05) | 20.2 (0.05) | 20.1 (0.05) |
Median (p1–p99) | 21 (16–28) | 21 (16–27) | 21 (17–26) | 20 (17–24) | 20 (17–24) | 20 (17–23.5) | 20 (17–24) | 20 (17–24) | 20 (17–23) | 20 (17–24) | 20 (17–24) | |
p = 0.7 | Mean (SE) | 20.9 (0.07) | 21.0 (0.06) | 20.7 (0.05) | 20.4 (0.05) | 20.4 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.1 (0.05) | 20.0 (0.05) | 20.1 (0.05) | 20.2 (0.05) |
Median (p1–p99) | 21 (16–26) | 21 (17–26) | 21 (17–25) | 20 (17–24) | 20 (17–24) | 20 (17–23) | 20 (17–24) | 20 (17–23) | 20 (17–23) | 20 (17–24) | 20 (17–24) | |
p = 0.8 | Mean (SE) | 20.8 (0.06) | 20.6 (0.05) | 20.4 (0.04) | 20.3 (0.05) | 20.2 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.0 (0.04) | 20.0 (0.05) | 20.1 (0.05) | 20.1 (0.05) |
Median (p1–p99) | 21 (17–25) | 21 (17–24) | 20 (17–24) | 20 (17–24) | 20 (17–23) | 20 (17–24) | 20 (17–23) | 20 (17–23) | 20 (17–24) | 20 (17–24) | 20 (17–24) | |
p = 0.85 | Mean (SE) | 20.5 (0.05) | 20.5 (0.04) | 20.3 (0.04) | 20.2 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.1 (0.05) | 20.1 (0.04) | 20.1 (0.05) | 20.1 (0.05) | 20.2 (0.05) |
Median (p1–p99) | 21 (17–24) | 20 (18–24) | 20 (17–23) | 20 (17–24) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–24) | 20 (17–24) | 20 (17–24) | |
p = 0.9 | Mean (SE) | 20.4 (0.04) | 20.3 (0.04) | 20.1 (0.04) | 20.2 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.1 (0.05) | 20.2 (0.05) | 20.1 (0.05) | 20.1 (0.05) |
Median (p1–p99) | 20 (17–24) | 20 (17–23.5) | 20 (17–23) | 20 (17–23.5) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–24) | 20 (17–24) | 20 (17–24) | 20 (16–24) | |
p = 0.95 | Mean (SE) | 20.2 (0.03) | 20.2 (0.03) | 20.1 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.2 (0.05) | 20.1 (0.05) | 20.1 (0.05) |
Median (p1–p99) | 20 (18–23) | 20 (18–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23.5) | 20 (16.5–23) | 20 (17–23) | 20 (17–24) | 20 (16.5–24) | 20 (17–24) | |
Sample size (n = 120), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 40) | ||||||||||||
p = 0.5 | Mean (SE) | 43.4 (0.14) | 42.7 (0.09) | 41.2 (0.08) | 40.8 (0.07) | 40.5 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.1 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.3 (0.07) |
Median (p1–p99) | 43 (33–54) | 43 (36–49.5) | 41 (36–47) | 41 (36–46) | 40 (36–45) | 40 (35–46) | 40 (35–45) | 40 (35–45.5) | 40 (35–45) | 40 (35–46) | 40 (36–45) | |
p = 0.6 | Mean (SE) | 42.5 (0.12) | 42.1 (0.09) | 41.1 (0.07) | 40.7 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.4 (0.07) |
Median (p1–p99) | 42 (34–51.5) | 42 (36–49) | 41 (36–46) | 41 (36–46) | 40 (36–45) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (35–46) | 40 (36–45) | |
p = 0.7 | Mean (SE) | 42.0 (0.10) | 41.6 (0.08) | 40.8 (0.07) | 40.6 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.2 (0.07) | 40.2 (0.07) |
Median (p1–p99) | 42 (35–49) | 42 (36–47.5) | 41 (36–46) | 41 (36–45) | 40 (35–45) | 40 (36–45) | 40 (35–45) | 40 (35.5–45) | 40 (35–45) | 40 (35–45) | 40 (36–45) | |
p = 0.8 | Mean (SE) | 41.3 (0.08) | 41.1 (0.07) | 40.6 (0.06) | 40.4 (0.06) | 40.3 (0.06) | 40.1 (0.07) | 40.2 (0.06) | 40.2 (0.07) | 40.2 (0.07) | 40.2 (0.07) | 40.3 (0.07) |
Median (p1–p99) | 41 (36–47) | 41 (36–46) | 41 (36–45) | 40 (36–45) | 40 (35.5–45) | 40 (35–45) | 40 (36–45) | 40 (35–45) | 40 (35–45) | 40 (35.5–45) | 40 (36–45) | |
p = 0.85 | Mean (SE) | 41.0 (0.07) | 40.8 (0.06) | 40.5 (0.06) | 40.4 (0.06) | 40.3 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.4 (0.07) | 40.2 (0.07) | 40.3 (0.07) | 40.2 (0.07) |
Median (p1–p99) | 41 (36–46) | 41 (37–45) | 40 (36–45) | 40 (36–45) | 40 (36–45) | 40 (35–45) | 40 (35–45) | 40 (35–46) | 40 (35–45) | 40 (35–45) | 40 (35–45) | |
p = 0.9 | Mean (SE) | 40.7 (0.06) | 40.5 (0.06) | 40.2 (0.06) | 40.2 (0.06) | 40.2 (0.06) | 40.1 (0.06) | 40.2 (0.07) | 40.2 (0.07) | 40.2 (0.07) | 40.2 (0.07) | 40.2 (0.07) |
Median (p1–p99) | 41 (36–45) | 40 (36–45) | 40 (35–45) | 40 (36–44) | 40 (35–45) | 40 (36–45) | 40 (36–45.5) | 40 (36–45) | 40 (35–46) | 40 (35–45.5) | 40 (35–45.5) | |
p = 0.95 | Mean (SE) | 40.4 (0.04) | 40.3 (0.05) | 40.1 (0.06) | 40.2 (0.06) | 40.1 (0.06) | 40.2 (0.07) | 40.3 (0.06) | 40.1 (0.07) | 40.3 (0.07) | 40.2 (0.07) | 40.3 (0.07) |
Median (p1–p99) | 40 (37.5–43.5) | 40 (37–44) | 40 (36–44) | 40 (36–44) | 40 (36–45) | 40 (35–46) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (35–45) | 40 (36–45) |
Random element | Number of factors | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
Sample size (n = 30), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 10) | |||||||||||
p = 0.5 | Mean (SE) | 10.8 (0.06) | 10.5 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 11 (7–15) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | |
p = 0.6 | Mean (SE) | 10.7 (0.06) | 10.5 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 11 (7–15) | 10 (8–13) | 10 (8–13) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12.5) | 10 (8–13) | 10 (8–13) | 10 (8–12) | |
p = 0.7 | Mean (SE) | 10.5 (0.05) | 10.3 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) |
Median (p1–p99) | 10 (7–14) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12.5) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | |
p = 0.8 | Mean (se) | 10.4 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 10 (8–13) | 10 (8–12) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | |
p = 0.85 | Mean (SE) | 10.3 (0.03) | 10.2 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 10 (8–13) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | |
p = 0.9 | Mean (SE) | 10.2 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 10 (8–13) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | |
p = 0.95 | Mean (SE) | 10.1 (0.02) | 10.1 (0.03) | 10.1 (0.03) | 10.0 (0.03) | 10.0 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) | 10.1 (0.03) |
Median (p1–p99) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | 10 (8–12) | |
Sample size (n = 60), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 20) | |||||||||||
p = 0.5 | Mean (SE) | 21.4 (0.07) | 21.0 (0.06) | 20.7 (0.05) | 20.4 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.0 (0.04) | 19.9 (0.04) | 20.0 (0.04) | 20.0 (0.04) |
Median (p1–p99) | 21 (16–27) | 21 (17–25.5) | 21 (17–25) | 20 (18–23) | 20 (17.5–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | |
p = 0.6 | Mean (SE) | 21.1 (0.07) | 20.8 (0.05) | 20.5 (0.05) | 20.3 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.1 (0.04) |
Median (p1–p99) | 21 (16–27) | 21 (17–25) | 20 (17–24) | 20 (17.5–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (18–23) | |
p = 0.7 | Mean (SE) | 21.0 (0.06) | 20.6 (0.05) | 20.4 (0.05) | 20.3 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.0 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.0 (0.04) |
Median (p1–p99) | 21 (17–26) | 21 (17–24) | 20 (17–24) | 20 (17–23.5) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | |
p = 0.8 | Mean (SE) | 20.6 (0.05) | 20.4 (0.04) | 20.2 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.0 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.0 (0.04) | 20.1 (0.04) |
Median (p1–p99) | 21 (17–24) | 20 (17.5–24) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | |
p = 0.85 | Mean (SE) | 20.5 (0.04) | 20.4 (0.04) | 20.2 (0.04) | 20.2 (0.03) | 20.1 (0.04) | 20.0 (0.04) | 20.0 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.1 (0.04) |
Median (p1–p99) | 20 (18–24) | 20 (17.5–23) | 20 (17–23) | 20 (18–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17.5–23) | 20 (17–23) | 20 (17–23) | |
p = 0.9 | Mean (SE) | 20.3 (0.04) | 20.3 (0.04) | 20.2 (0.04) | 20.1 (0.04) | 20.0 (0.04) | 20.0 (0.04) | 20.0 (0.04) | 20.1 (0.04) | 20.1 (0.04) | 20.1 (0.04) |
Median (p1–p99) | 20 (17–23.5) | 20 (18–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17.5–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | |
p = 0.95 | Mean (SE) | 20.2 (0.03) | 20.1 (0.03) | 20.2 (0.04) | 20.1 (0.04) | 20.0 (0.04) | 20.0 (0.04) | 20.0 (0.04) | 20.0 (0.04) | 20.1 (0.04) | 20.0 (0.04) |
Median (p1–p99) | 20 (18–23) | 20 (18–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | 20 (17–23) | |
Sample size (n = 120), the expected number of participants allocated to the treatment with smallest-allocation ratio (n = 40) | |||||||||||
p = 0.5 | Mean (SE) | 42.7 (0.09) | 41.5 (0.07) | 40.8 (0.06) | 40.4 (0.06) | 40.2 (0.06) | 40.1 (0.06) | 40.2 (0.06) | 40.1 (0.06) | 40.2 (0.06) | 40.2 (0.06) |
Median (p1–p99) | 43 (36–49.5) | 41 (36–47) | 41 (36.5–45) | 40 (36–45) | 40 (36–45) | 40 (36–44) | 40 (36–45) | 40 (36–44) | 40 (36–45) | 40 (36–44) | |
p = 0.6 | Mean (SE) | 42.1 (0.09) | 41.1 (0.07) | 40.6 (0.06) | 40.3 (0.06) | 40.0 (0.06) | 40.1 (0.06) | 40.1 (0.06) | 40.1 (0.06) | 40.2 (0.06) | 40.0 (0.06) |
Median (p1–p99) | 42 (36–49) | 41 (36–46) | 41 (37–45) | 40 (36–45) | 40 (36–44) | 40 (36–44) | 40 (36–44) | 40 (36–44) | 40 (36–45) | 40 (36–45) | |
p = 0.7 | Mean (SE) | 41.6 (0.08) | 40.8 (0.06) | 40.4 (0.06) | 40.2 (0.06) | 40.1 (0.06) | 40.1 (0.06) | 40.1 (0.06) | 40.0 (0.06) | 40.1 (0.06) | 40.1 (0.06) |
Median (p1–p99) | 42 (36–47.5) | 41 (36–45.5) | 40 (36–45) | 40 (36–44) | 40 (36–44) | 40 (36–44) | 40 (36–45) | 40 (36–45) | 40 (36–44) | 40 (36–45) | |
p = 0.8 | Mean (SE) | 41.1 (0.07) | 40.5 (0.06) | 40.3 (0.06) | 40.2 (0.06) | 40.1 (0.06) | 40.2 (0.06) | 40.1 (0.06) | 40.0 (0.06) | 40.2 (0.06) | 40.1 (0.06) |
Median (p1–p99) | 41 (36–46) | 40 (36–45) | 40 (36–44) | 40 (36–45) | 40 (35.5–44) | 40 (36–45) | 40 (36–44) | 40 (36–45) | 40 (36–44) | 40 (36–44) | |
p = 0.85 | Mean (SE) | 40.8 (0.06) | 40.4 (0.06) | 40.2 (0.05) | 40.3 (0.06) | 40.1 (0.06) | 40.1 (0.06) | 40.1 (0.06) | 40.2 (0.06) | 40.2 (0.06) | 40.2 (0.06) |
Median (p1–p99) | 41 (37–45) | 40 (36–45) | 40 (36–44) | 40 (36–44) | 40 (36–44) | 40 (36–44) | 40 (36–44) | 40 (36–45) | 40 (36–44) | 40 (36–44.5) | |
p = 0.9 | Mean (SE) | 40.5 (0.06) | 40.3 (0.06) | 40.1 (0.05) | 40.2 (0.06) | 40.1 (0.06) | 40.1 (0.06) | 40.2 (0.06) | 40.0 (0.06) | 40.2 (0.06) | 40.1 (0.06) |
Median (p1–p99) | 40 (36–45) | 40 (36–44.5) | 40 (36–44) | 40 (36–44.5) | 40 (36–44) | 40 (36–44) | 40 (36–45) | 40 (36–45) | 40 (36–44) | 40 (36–45) | |
p = 0.95 | Mean (SE) | 40.3 (0.05) | 40.1 (0.05) | 40.0 (0.05) | 40.1 (0.06) | 40.1 (0.05) | 40.2 (0.05) | 40.1 (0.06) | 40.1 (0.05) | 40.2 (0.06) | 40.1 (0.06) |
Median (p1–p99) | 40 (37–44) | 40 (36–44) | 40 (36–44) | 40 (36–45) | 40 (36–44) | 40 (36–44) | 40 (36–44.5) | 40 (36–44) | 40 (36–44) | 40 (36–45) |
Random element | Number of factors | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Treatment totals only (worst-case scenario) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
Sample size (n = 30), the expected number of participants allocated with the particular factor level n = 5 | ||||||||||||
p = 0.5 | Mean (SE) | 5.5 (0.05) | 5.4 (0.05) | 5.2 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 5.1 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–10) | 5 (2–9) | 5 (3–8) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2.5–8) | 5 (2.5–8) | |
p = 0.6 | Mean (SE) | 5.3 (0.05) | 5.3 (0.04) | 5.2 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.1 (0.03) | 5.0 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–9) | 5 (2–8) | 5 (3–8) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | |
p = 0.7 | Mean (SE) | 5.3 (0.05) | 5.3 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 5.0 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–9) | 5 (3–8) | 5 (3–7) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (3–8) | |
p = 0.8 | Mean (SE) | 5.2 (0.04) | 5.1 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.3 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 5.1 (0.04) | 5.0 (0.03) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–7) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (2.5–8) | 5 (2–8) | |
p = 0.85 | Mean (SE) | 5.1 (0.04) | 5.1 (0.03) | 5.0 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 4.9 (0.03) | 5.1 (0.04) | 5.1 (0.04) | 5.1 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–7) | 5 (3–7) | 5 (3–8) | 5 (3–7.5) | 5 (3–8) | 5 (2–8) | 5 (2–8) | 5 (2–8) | 5 (2–8) | |
p = 0.9 | Mean (SE) | 5.1 (0.04) | 5.1 (0.02) | 5.0 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 5.1 (0.04) | 4.9 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–7) | 5 (3–7) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (2.5–7.5) | 5 (2–8) | 5 (3–8) | 5 (2–8) | |
p = 0.95 | Mean (SE) | 5.0 (0.04) | 5.0 (0.02) | 5.0 (0.02) | 5.1 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 4.9 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 5.0 (0.04) | 5.0 (0.03) |
Median (p1–p99) | 5 (2–8) | 5 (4–6) | 5 (3–7) | 5 (3–7) | 5 (3–7.5) | 5 (3–8) | 5 (3–7) | 5 (2–7.5) | 5 (2–8) | 5 (2–8) | 5 (2–8) | |
Sample size (n = 60), the expected number of participants allocated with the particular factor level n = 10 | ||||||||||||
p = 0.5 | Mean (SE) | 10.9 (0.07) | 10.9 (0.07) | 10.6 (0.05) | 10.5 (0.05) | 10.2 (0.05) | 10.2 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) |
Median (p1–p99) | 11 (6–17) | 11 (6–16) | 11 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (6–14) | 10 (6.5–14) | 10 (6–14) | |
p = 0.6 | Mean (SE) | 10.6 (0.07) | 10.9 (0.07) | 10.6 (0.05) | 10.5 (0.05) | 10.2 (0.05) | 10.2 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) |
Median (p1–p99) | 11 (6–16) | 11 (6–16) | 11 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (6–14) | 10 (6.5–14) | 10 (6–14) | |
p = 0.7 | Mean (SE) | 10.4 (0.06) | 10.6 (0.05) | 10.4 (0.04) | 10.4 (0.05) | 10.2 (0.04) | 10.3 (0.05) | 10.2 (0.05) | 10.1 (0.05) | 10.2 (0.05) | 10.1 (0.06) | 10.2 (0.05) |
Median (p1–p99) | 10 (6–15) | 10 (7–15) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (6–14) | 10 (6–14) | 10 (7–14.5) | |
p = 0.8 | Mean (SE) | 10.4 (0.06) | 10.3 (0.04) | 10.3 (0.04) | 10.4 (0.04) | 10.0 (0.04) | 10.2 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (7–14) | 10 (8–14) | 10 (7–14) | 10 (7–13) | 10 (7–14) | 10 (7–14) | 10 (6–14) | 10 (7–14) | 10 (6–14) | 10 (6–14.5) | |
p = 0.85 | Mean (SE) | 10.2 (0.05) | 10.3 (0.03) | 10.2 (0.03) | 10.2 (0.04) | 10.2 (0.04) | 10.2 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.2 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (8–13) | 10 (8–13) | 10 (7–13) | 10 (7–13) | 10 (7–14) | 10 (7–14) | 10 (6.5–14) | 10 (7–14) | 10 (7–14) | 10 (6–14) | |
p = 0.9 | Mean (SE) | 10.1 (0.05) | 10.1 (0.03) | 10.2 (0.03) | 10.4 (0.04) | 10.1 (0.04) | 10.2 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.1 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (8–12) | 10 (7.5–13) | 10 (8–13.5) | 10 (7–13) | 10 (7–14) | 10 (7–13.5) | 10 (6.5–14) | 10 (6–14) | 10 (6.5–14) | 10 (6–14) | |
p = 0.95 | Mean (SE) | 10.1 (0.05) | 10.1 (0.02) | 10.1 (0.03) | 10.3 (0.04) | 10.1 (0.04) | 10.2 (0.05) | 10.1 (0.05) | 10.0 (0.05) | 10.2 (0.05) | 10.1 (0.05) | 10.3 (0.05) |
Median (p1–p99) | 10 (6–13.5) | 10 (9–12) | 10 (8–12) | 10 (7–13) | 10 (7–13.5) | 10 (6–14) | 10 (7–14) | 10 (6.5–14) | 10 (7–14) | 10 (7–14) | 10 (6–14) | |
Sample size (n = 120), the expected number of participants allocated with the particular factor level n = 20 | ||||||||||||
p = 0.5 | Mean (SE) | 22.0 (0.11) | 21.0 (0.10) | 21.0 (0.08) | 20.8 (0.07) | 20.5 (0.07) | 20.0 (0.08) | 20.2 (0.08) | 20.4 (0.08) | 20.3 (0.08) | 20.4 (0.08) | 20.6 (0.08) |
Median (p1–p99) | 22 (14–30) | 21 (14–29) | 21 (16–27) | 21 (16–26) | 21 (15–26) | 20 (14–25) | 20 (14–26) | 20 (15–26.5) | 20 (15–26) | 20 (14–26) | 21 (15–26) | |
p = 0.6 | Mean (SE) | 21.6 (0.10) | 20.8 (0.08) | 20.9 (0.07) | 20.7 (0.07) | 20.4 (0.07) | 20.2 (0.08) | 20.2 (0.08) | 20.3 (0.08) | 20.3 (0.08) | 20.5 (0.08) | 20.6 (0.09) |
Median (p1–p99) | 22 (14–30) | 21 (15–27) | 21 (16–26) | 21 (16–26) | 20 (16–26) | 20 (15–26) | 20 (15–26) | 20 (15–26) | 20 (14–27) | 21 (15–26.5) | 21 (14–27) | |
p = 0.7 | Mean (SE) | 21.1 (0.10) | 20.7 (0.07) | 20.6 (0.07) | 20.6 (0.07) | 20.4 (0.07) | 20.0 (0.08) | 20.1 (0.08) | 20.3 (0.08) | 20.4 (0.08) | 20.3 (0.08) | 20.6 (0.09) |
Median (p1–p99) | 21 (14–29) | 21 (16–26) | 21 (16–26) | 21 (16–25) | 20 (15–26.5) | 20 (14–26) | 20 (15–26) | 20 (15–26) | 20 (15–26.5) | 20 (15–27) | 21 (14–26) | |
p = 0.8 | Mean (SE) | 20.8 (0.09) | 20.3 (0.06) | 20.4 (0.06) | 20.6 (0.07) | 20.4 (0.07) | 20.1 (0.07) | 20.0 (0.08) | 20.2 (0.08) | 20.4 (0.08) | 20.5 (0.08) | 20.6 (0.08) |
Median (p1–p99) | 21 (14–28) | 20 (16–25) | 20 (16–25) | 21 (16–26) | 20 (15.5–25) | 20 (15–26) | 20 (14–26) | 20 (15–26) | 20 (14–26.5) | 20.5 (15–26) | 21 (15–26.5) | |
p = 0.85 | Mean (SE) | 20.4 (0.09) | 20.3 (0.05) | 20.3 (0.06) | 20.5 (0.06) | 20.2 (0.07) | 20.1 (0.08) | 20.1 (0.08) | 20.0 (0.08) | 20.3 (0.08) | 20.3 (0.08) | 20.5 (0.08) |
Median (p1–p99) | 20 (14–27) | 20 (17–24.5) | 20 (16–24) | 21 (16–25) | 20 (15–25) | 20 (15–26) | 20 (14.5–25.5) | 20 (14–26) | 20 (14.5–26) | 20 (15–27) | 20 (15–27) | |
p = 0.9 | Mean (SE) | 20.4 (0.09) | 20.2 (0.04) | 20.3 (0.05) | 20.5 (0.06) | 20.3 (0.07) | 20.2 (0.08) | 20.1 (0.08) | 20.3 (0.08) | 20.3 (0.08) | 20.4 (0.08) | 20.6 (0.08) |
Median (p1–p99) | 20 (14–27) | 20 (17–23) | 20 (16–25) | 21 (16–25) | 20 (15–25) | 20 (15–26) | 20 (14–25.5) | 20 (14.5–26.5) | 20 (15–26) | 20 (15–27) | 21 (14–26) | |
p = 0.95 | Mean (SE) | 20.2 (0.09) | 20.1 (0.03) | 20.1 (0.05) | 20.3 (0.06) | 20.2 (0.07) | 20.1 (0.07) | 20.1 (0.08) | 20.2 (0.08) | 20.3 (0.08) | 20.3 (0.08) | 20.6 (0.08) |
Median (p1–p99) | 20 (14–27) | 20 (18–22) | 20 (16–24) | 20 (16–25) | 20 (15–25) | 20 (15–25.5) | 20 (15–26) | 20 (14.5–26) | 20 (14.5–26) | 20 (14–26) | 21 (14.5–26) |
Random element | Number of factors | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Treatment totals only (worst-case scenario) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
Sample size (n = 30), the expected number of participants allocated with the particular factor level n = 5 | ||||||||||||
p = 0.5 | Mean (SE) | 5.5 (0.05) | 5.3 (0.04) | 5.4 (0.03) | 5.0 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.1 (0.04) | 5.0 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–10) | 5 (2–8) | 5 (3–8) | 5 (2–7) | 5 (3–7.5) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (2.5–8) | 5 (2–8) | |
p = 0.6 | Mean (SE) | 5.3 (0.05) | 5.3 (0.04) | 5.3 (0.03) | 5.0 (0.03) | 5.3 (0.03) | 5.2 (0.03) | 5.2 (0.04) | 5.0 (0.03) | 5.1 (0.04) | 5.0 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–9) | 5 (3–9) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2.5–8) | |
p = 0.7 | Mean (SE) | 5.3 (0.05) | 5.2 (0.04) | 5.3 (0.03) | 5.1 (0.03) | 5.2 (0.04) | 5.2 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.1 (0.04) | 5.0 (0.04) | 5.0 (0.03) |
Median (p1–p99) | 5 (2–9) | 5 (2.5–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2.5–8) | 5 (2.5–8) | |
p = 0.8 | Mean (SE) | 5.2 (0.04) | 5.2 (0.03) | 5.3 (0.03) | 5.0 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 4.9 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–7) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (2.5–8) | 5 (2.5–8) | 5 (2–8) | |
p = 0.85 | Mean (SE) | 5.1 (0.04) | 5.1 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.04) | 4.9 (0.04) | 5.1 (0.04) | 5.1 (0.03) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–7.5) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (2.5–8) | 5 (2–8) | 5 (2.5–8) | |
p = 0.9 | Mean (SE) | 5.1 (0.04) | 5.1 (0.02) | 5.2 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 5.0 (0.04) | 5.1 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–7) | 5 (3–7.5) | 5 (2.5–8) | 5 (2–8) | 5 (3–8) | |
p = 0.95 | Mean (SE) | 5.0 (0.04) | 5.0 (0.02) | 5.1 (0.03) | 5.0 (0.03) | 5.2 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.1 (0.04) | 5.0 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–6.5) | 5 (3–7) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–7.5) | 5 (2–8) | |
Sample size (n = 60), the expected number of participants allocated with the particular factor level n = 10 | ||||||||||||
p = 0.5 | Mean (SE) | 10.9 (0.07) | 10.6 (0.05) | 10.4 (0.05) | 10.3 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.0 (0.05) | 9.9 (0.05) | 10.0 (0.05) | 10.0 (0.05) | 10.1 (0.05) |
Median (p1–p99) | 11 (6–17) | 11 (7–14.5) | 10 (7–14) | 10 (7–14) | 10 (7–14) | 10 (7–13.5) | 10 (6–13.5) | 10 (7–14) | 10 (6–14) | 10 (6–14) | 10 (7–14) | |
p = 0.6 | Mean (SE) | 10.6 (0.07) | 10.5 (0.05) | 10.4 (0.04) | 10.2 (0.05) | 10.1 (0.05) | 10.0 (0.05) | 10.0 (0.05) | 9.9 (0.05) | 10.0 (0.05) | 10.1 (0.05) | 10.2 (0.05) |
Median (p1–p99) | 11 (6–16) | 10 (7–14) | 10 (7.5–14) | 10 (7–14) | 10 (7–13) | 10 (7–14) | 10 (6–14) | 10 (6–14) | 10 (6–14) | 10 (6–14) | 10 (6.5–14) | |
p = 0.7 | Mean (SE) | 10.4 (0.06) | 10.4 (0.04) | 10.4 (0.04) | 10.2 (0.05) | 10.1 (0.05) | 10.0 (0.05) | 10.0 (0.05) | 10.0 (0.05) | 10.0 (0.05) | 10.1 (0.05) | 10.2 (0.05) |
Median (p1–p99) | 10 (6–15) | 10 (7–14) | 10 (8–14) | 10 (7–14) | 10 (7–13.5) | 10 (7–13) | 10 (6.5–13) | 10 (7–14) | 10 (6–14) | 10 (6–14) | 10 (6.5–14.5) | |
p = 0.8 | Mean (SE) | 10.4 (0.06) | 10.2 (0.04) | 10.3 (0.04) | 10.1 (0.04) | 10.0 (0.04) | 10.0 (0.05) | 10.1 (0.05) | 9.9 (0.05) | 10.0 (0.05) | 10.1 (0.05) | 10.1 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (8–13) | 10 (8–13) | 10 (7–13) | 10 (7–13) | 10 (7–14) | 10 (7–14) | 10 (6–14) | 10 (7–14) | 10 (6–14) | 10 (7–14) | |
p = 0.85 | Mean (SE) | 10.2 (0.05) | 10.2 (0.03) | 10.2 (0.04) | 10.1 (0.04) | 10.0 (0.04) | 10.0 (0.05) | 10.0 (0.05) | 10.0 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.2 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (8–13) | 10 (7–13) | 10 (7–13) | 10 (7–14) | 10 (7–14) | 10 (6.5–14) | 10 (7–14) | 10 (6–14) | 10 (6.5–14) | 10 (7–14) | |
p = 0.9 | Mean (SE) | 10.1 (0.05) | 10.1 (0.03) | 10.2 (0.04) | 10.0 (0.04) | 9.9 (0.04) | 10.0 (0.05) | 10.0 (0.05) | 10.0 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.2 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (8–12) | 10 (7–13) | 10 (7–13) | 10 (7–13) | 10 (6–14) | 10 (7–14) | 10 (6–14) | 10 (6–14) | 10 (6–14) | 10 (6–14) | |
p = 0.95 | Mean (SE) | 10.1 (0.05) | 10.0 (0.03) | 10.0 (0.03) | 10.0 (0.04) | 9.9 (0.05) | 10.0 (0.05) | 10.0 (0.05) | 9.9 (0.05) | 10.1 (0.05) | 10.1 (0.05) | 10.2 (0.05) |
Median (p1–p99) | 10 (6–13.5) | 10 (8–12) | 10 (7–12) | 10 (7–13) | 10 (7–13) | 10 (7–13) | 10 (7–13) | 10 (6–14) | 10 (6–14) | 10 (6.5–14) | 10 (6–14) | |
Sample size (n = 120), the expected number of participants allocated with the particular factor level n = 20 | ||||||||||||
p = 0.5 | Mean (SE) | 22.0 (0.11) | 21.7 (0.06) | 20.6 (0.07) | 20.7 (0.07) | 20.3 (0.07) | 20.1 (0.08) | 20.1 (0.08) | 20.1 (0.08) | 20.4 (0.08) | 20.5 (0.08) | 20.5 (0.08) |
Median (p1–p99) | 22 (14–30) | 22 (17–26) | 20 (16–26) | 21 (15–26) | 20 (15–26) | 20 (14–26) | 20 (15–26) | 20 (14–26) | 20 (14–26) | 21 (15–27) | 20 (14–26) | |
p = 0.6 | Mean (SE) | 21.6 (0.10) | 21.3 (0.07) | 20.5 (0.07) | 20.6 (0.07) | 20.1 (0.07) | 20.0 (0.08) | 20.1 (0.08) | 20.1 (0.08) | 20.3 (0.08) | 20.4 (0.08) | 20.5 (0.08) |
Median (p1–p99) | 22 (14–30) | 21 (17–26) | 20 (16–26) | 21 (16–26) | 20 (15–25) | 20 (14–25.5) | 20 (14–26) | 20 (14–26) | 20 (13.5–26) | 20 (15–26) | 21 (14–26.5) | |
p = 0.7 | Mean (SE) | 21.1 (0.10) | 21.0 (0.06) | 20.4 (0.06) | 20.6 (0.07) | 20.1 (0.07) | 20.1 (0.08) | 20.1 (0.08) | 20.1 (0.08) | 20.4 (0.08) | 20.4 (0.09) | 20.5 (0.08) |
Median (p1–p99) | 21 (14–29) | 21 (17–26) | 20 (16–25) | 21 (16–25) | 20 (15–25) | 20 (15–26) | 20 (14–26) | 20 (14–26) | 20 (15–26) | 20 (14–27) | 20 (14.5–27) | |
p = 0.8 | Mean (SE) | 20.8 (0.09) | 20.7 (0.05) | 20.3 (0.06) | 20.6 (0.06) | 20.2 (0.07) | 20.0 (0.08) | 20.0 (0.08) | 20.1 (0.08) | 20.3 (0.08) | 20.4 (0.08) | 20.5 (0.09) |
Median (p1–p99) | 21 (14–28) | 21 (17–24) | 20 (16–25) | 21 (16–26) | 20 (15–25) | 20 (15–25.5) | 20 (14–26) | 20 (15–26) | 20 (15–26) | 20 (14–26) | 20 (14–27) | |
p = 0.85 | Mean (SE) | 20.4 (0.09) | 20.5 (0.05) | 20.2 (0.06) | 20.5 (0.07) | 20.2 (0.07) | 20.2 (0.08) | 20.1 (0.08) | 20.2 (0.08) | 20.4 (0.08) | 20.4 (0.08) | 20.5 (0.08) |
Median (p1–p99) | 20 (14–27) | 20 (17–24) | 20 (16–25) | 20 (16–26) | 20 (15–25) | 20 (14.5–26) | 20 (15–26) | 20 (14–26) | 20 (15–27) | 20 (14–26) | 21 (15–27) | |
p = 0.9 | Mean (SE) | 20.4 (0.09) | 20.2 (0.04) | 20.0 (0.06) | 20.4 (0.07) | 20.2 (0.07) | 20.1 (0.08) | 20.0 (0.08) | 20.1 (0.08) | 20.3 (0.08) | 20.5 (0.08) | 20.4 (0.08) |
Median (p1–p99) | 20 (14–27) | 20 (17–24) | 20 (16–24) | 20 (16–25) | 20 (15–25) | 20 (15–26) | 20 (14–26) | 20 (14–26) | 20 (14.5–26) | 21 (14–26) | 20 (14–26) | |
p = 0.95 | Mean (SE) | 20.2 (0.09) | 20.2 (0.04) | 20.0 (0.06) | 20.4 (0.06) | 20.2 (0.07) | 20.1 (0.08) | 20.1 (0.08) | 20.2 (0.08) | 20.4 (0.08) | 20.4 (0.08) | 20.5 (0.08) |
Median (p1–p99) | 20 (14–27) | 20 (17–23) | 20 (16–24) | 20 (16–25) | 20 (15–25) | 20 (14–26) | 20 (15–26) | 20 (14–26) | 20 (15–26.5) | 20.5 (15–26) | 20 (14–26) |
Random element | Number of factors | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Treatment totals only (worst case scenario) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
Sample size (n = 30), the expected number of participants allocated with the particular factor level n = 5 | ||||||||||||
p = 0.5 | Mean (SE) | 5.5 (0.05) | 5.3 (0.04) | 5.4 (0.03) | 5.0 (0.03) | 5.2 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.04) | 5.0 (0.04) | 5.0 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–10) | 5 (2–8) | 5 (3–8) | 5 (2–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | |
p = 0.6 | Mean (SE) | 5.3 (0.05) | 5.3 (0.04) | 5.4 (0.03) | 5.0 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 5.1 (0.04) | 5.1 (0.04) |
Median (p1–p99) | 5 (2–9) | 5 (3–9) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | |
p = 0.7 | Mean (SE) | 5.3 (0.05) | 5.2 (0.04) | 5.2 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.2 (0.04) | 5.1 (0.04) | 5.0 (0.04) | 5.0 (0.04) | 5.1 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–9) | 5 (2.5–8) | 5 (3–8) | 5 (2.5–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (2–8) | 5 (2.5–8) | 5 (3–8) | |
p = 0.8 | Mean (SE) | 5.2 (0.04) | 5.2 (0.03) | 5.3 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.2 (0.03) | 5.1 (0.04) | 5.1 (0.04) | 5.0 (0.03) | 5.1 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (3–8) | 5 (2–7) | 5 (2–8) | |
p = 0.85 | Mean (SE) | 5.1 (0.04) | 5.1 (0.03) | 5.3 (0.03) | 5.0 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.1 (0.03) | 5.0 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | |
p = 0.9 | Mean (SE) | 5.1 (0.04) | 5.1 (0.02) | 5.2 (0.03) | 5.1 (0.03) | 5.2 (0.04) | 5.2 (0.03) | 5.1 (0.03) | 5.1 (0.04) | 5.0 (0.04) | 5.1 (0.04) | 5.1 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–7) | 5 (3–7) | 5 (3–8) | 5 (2–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (3–8) | 5 (2–8) | |
p = 0.95 | Mean (SE) | 5.0 (0.04) | 5.0 (0.02) | 5.2 (0.03) | 5.1 (0.03) | 5.2 (0.03) | 5.1 (0.03) | 5.0 (0.03) | 5.0 (0.04) | 5.1 (0.03) | 5.1 (0.04) | 5.0 (0.04) |
Median (p1–p99) | 5 (2–8) | 5 (3–6.5) | 5 (3–7.5) | 5 (2.5–8) | 5 (3–8) | 5 (3–8) | 5 (3–8) | 5 (2–8) | 5 (3–8) | 5 (2.5–8) | 5 (2–8) | |
Sample size (n = 60), the expected number of participants allocated with the particular factor level n = 10 | ||||||||||||
p = 0.5 | Mean (SE) | 10.9 (0.07) | 10.6 (0.05) | 10.4 (0.05) | 10.1 (0.05) | 9.9 (0.05) | 9.8 (0.05) | 9.9 (0.05) | 9.7 (0.05) | 9.8 (0.05) | 9.9 (0.05) | 9.9 (0.05) |
Median (p1–p99) | 11 (6–17) | 11 (7–14.5) | 10 (7–14) | 10 (7–14) | 10 (7–13.5) | 10 (7–13) | 10 (7–13) | 10 (7–13) | 10 (6–13) | 10 (6–13) | 10 (6–13) | |
p = 0.6 | Mean (SE) | 10.6 (0.07) | 10.5 (0.05) | 10.3 (0.04) | 10.0 (0.05) | 9.8 (0.05) | 9.9 (0.05) | 9.8 (0.05) | 9.8 (0.05) | 9.9 (0.05) | 9.9 (0.05) | 9.9 (0.05) |
Median (p1–p99) | 11 (6–16) | 10 (7–14) | 10 (7–14) | 10 (7–13) | 10 (6–13) | 10 (6–14) | 10 (6–13) | 10 (7–14) | 10 (7–13.5) | 10 (6–14) | 10 (7–13) | |
p = 0.7 | Mean (SE) | 10.4 (0.06) | 10.4 (0.04) | 10.2 (0.04) | 10.1 (0.05) | 9.9 (0.05) | 9.8 (0.05) | 9.8 (0.05) | 9.7 (0.05) | 9.9 (0.05) | 9.8 (0.05) | 9.9 (0.05) |
Median (p1–p99) | 10 (6–15) | 10 (7–14) | 10 (7–13) | 10 (7–14) | 10 (7–14) | 10 (6–13) | 10 (6–13) | 10 (6–13) | 10 (6–13) | 10 (6–14) | 10 (6–14) | |
p = 0.8 | Mean (SE) | 10.4 (0.06) | 10.2 (0.04) | 10.2 (0.04) | 9.9 (0.05) | 9.9 (0.04) | 9.8 (0.05) | 9.8 (0.05) | 9.8 (0.05) | 9.8 (0.05) | 9.9 (0.05) | 9.9 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (8–13) | 10 (7–13) | 10 (6–13) | 10 (7–13) | 10 (6.5–13) | 10 (6–13.5) | 10 (6–14) | 10 (6.5–13) | 10 (7–13) | 10 (6.5–14) | |
p = 0.85 | Mean (SE) | 10.2 (0.05) | 10.2 (0.03) | 10.2 (0.04) | 9.9 (0.04) | 9.8 (0.04) | 9.8 (0.05) | 9.8 (0.05) | 9.8 (0.05) | 9.9 (0.05) | 9.9 (0.05) | 10.0 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (8–13) | 10 (7–13) | 10 (7–13) | 10 (7–13) | 10 (7–13) | 10 (6–13) | 10 (6–13) | 10 (7–14) | 10 (6–14) | 10 (6–14) | |
p = 0.9 | Mean (SE) | 10.1 (0.05) | 10.1 (0.03) | 10.1 (0.04) | 9.9 (0.04) | 9.7 (0.04) | 9.8 (0.05) | 9.8 (0.05) | 9.7 (0.05) | 9.8 (0.05) | 9.8 (0.05) | 10.0 (0.05) |
Median (p1–p99) | 10 (6–14) | 10 (8–12) | 10 (8–13) | 10 (7–13) | 10 (7–13) | 10 (7–13) | 10 (7–13) | 10 (6–13.5) | 10 (6–13) | 10 (6–14) | 10 (6–14) | |
p = 0.95 | Mean (SE) | 10.1 (0.05) | 10.0 (0.03) | 10.1 (0.03) | 9.9 (0.04) | 9.8 (0.04) | 9.7 (0.05) | 9.8 (0.05) | 9.8 (0.05) | 9.8 (0.05) | 9.9 (0.05) | 9.9 (0.05) |
Median (p1–p99) | 10 (6–13.5) | 10 (8–12) | 10 (8–13) | 10 (7–13) | 10 (7–13) | 10 (6–14) | 10 (6–13) | 10 (7–13) | 10 (6–13) | 10 (6–14) | 10 (6–14) | |
Sample size (n = 120), the expected number of participants allocated with the particular factor level n = 20 | ||||||||||||
p = 0.5 | Mean (SE) | 22.0 (0.11) | 21.7 (0.06) | 20.8 (0.07) | 20.7 (0.07) | 20.3 (0.08) | 19.9 (0.08) | 20.2 (0.08) | 20.2 (0.08) | 20.3 (0.08) | 20.5 (0.08) | 20.4 (0.08) |
Median (p1–p99) | 22 (14–30) | 22 (17–26) | 21 (16–26) | 21 (16–26) | 20 (15–26) | 20 (14–25.5) | 20 (15–26) | 20 (14–27) | 20 (15–26) | 20 (15–26.5) | 20 (15–27) | |
p = 0.6 | Mean (SE) | 21.6 (0.10) | 21.3 (0.07) | 20.6 (0.07) | 20.6 (0.07) | 20.3 (0.07) | 20.1 (0.08) | 20.2 (0.08) | 20.2 (0.08) | 20.4 (0.08) | 20.4 (0.08) | 20.5 (0.09) |
Median (p1–p99) | 22 (14–30) | 21 (17–26) | 21 (16–25.5) | 20 (16–26) | 20 (15–25) | 20 (14–26) | 20 (15–26) | 20 (14–26) | 20.5 (14–26) | 20 (14–26) | 21 (14.5–27) | |
p = 0.7 | Mean (SE) | 21.1 (0.10) | 21.0 (0.06) | 20.5 (0.07) | 20.5 (0.07) | 20.3 (0.08) | 19.9 (0.07) | 20.2 (0.08) | 20.1 (0.08) | 20.5 (0.08) | 20.4 (0.08) | 20.5 (0.09) |
Median (p1–p99) | 21 (14–29) | 21 (17–26) | 20 (16–26) | 20 (16–26) | 20 (15–26) | 20 (14.5–25) | 20 (14.5–26) | 20 (14–26) | 20 (15–26.5) | 20 (14.5–26) | 21 (14.5–27) | |
p = 0.8 | Mean (SE) | 20.8 (0.09) | 20.7 (0.05) | 20.3 (0.06) | 20.4 (0.07) | 20.1 (0.08) | 20.1 (0.08) | 20.2 (0.08) | 20.2 (0.08) | 20.2 (0.08) | 20.5 (0.08) | 20.5 (0.09) |
Median (p1–p99) | 21 (14–28) | 21 (17–24) | 20 (16–25) | 20 (15–25) | 20 (15–25) | 20 (14.5–26) | 20 (14–26) | 20 (14–27) | 20 (15–27) | 20 (14.5–27) | 20 (14.5–27) | |
p = 0.85 | Mean (SE) | 20.4 (0.09) | 20.5 (0.05) | 20.3 (0.06) | 20.4 (0.07) | 20.3 (0.07) | 20.2 (0.08) | 20.0 (0.08) | 20.2 (0.08) | 20.3 (0.08) | 20.5 (0.08) | 20.4 (0.08) |
Median (p1–p99) | 20 (14–27) | 20 (17–24) | 20 (16–25) | 20 (16–26) | 20 (15–26) | 20 (15–26) | 20 (15–26) | 20 (14–26) | 20 (14–26) | 21 (14.5–26.5) | 21 (14–26) | |
p = 0.9 | Mean (SE) | 20.4 (0.09) | 20.2 (0.04) | 20.2 (0.06) | 20.2 (0.07) | 20.3 (0.07) | 20.0 (0.08) | 20.2 (0.08) | 20.2 (0.08) | 20.2 (0.08) | 20.5 (0.08) | 20.5 (0.09) |
Median (p1–p99) | 20 (14–27) | 20 (17–24) | 20 (16–25) | 20 (15–25) | 20 (15–26) | 20 (14–26.5) | 20 (15–26) | 20 (14.5–26) | 20 (15–27) | 20 (14.5–27) | 21 (14.5–27) | |
p = 0.95 | Mean (SE) | 20.2 (0.09) | 20.2 (0.04) | 20.1 (0.06) | 20.3 (0.07) | 20.2 (0.08) | 20.0 (0.08) | 20.1 (0.08) | 20.1 (0.08) | 20.6 (0.08) | 20.5 (0.08) | 20.5 (0.09) |
Median (p1–p99) | 20 (14–27) | 20 (17–23) | 20 (16–24) | 20 (15.5–25) | 20 (14.5–26) | 20 (14–27) | 20 (15–26) | 20 (14–26) | 21 (15–27) | 20 (14.5–27) | 21 (14.5–27) |