Table 1
Estimated type I error rates for the bootstrap, direct, and multivariate tests at the nominal 
and 
levels based on 5000 datasets, by number of subjects (n) and observations per subject (m). The standard error was 0.003 and 0.004 for 
and 
, respectively. The multivariate test is applicable for only the dense 
setting
| Bootstrap | Direct | Multivariate | |||||
| n | m | α=0.05 | α=0.10 | α=0.05 | α=0.10 | α=0.05 | α=0.10 |
| 100 | 10 | 0.059 | 0.126 | 0.044 | 0.086 | n/a | n/a |
| 20 | 0.045 | 0.105 | 0.049 | 0.098 | n/a | n/a | |
| 40 | 0.042 | 0.093 | 0.049 | 0.102 | n/a | n/a | |
| 80 | 0.042 | 0.091 | 0.045 | 0.096 | 0.053 | 0.103 | |
| 500 | 10 | 0.047 | 0.105 | 0.049 | 0.096 | n/a | n/a |
| 20 | 0.050 | 0.103 | 0.049 | 0.096 | n/a | n/a | |
| 40 | 0.050 | 0.100 | 0.043 | 0.090 | n/a | n/a | |
| 80 | 0.044 | 0.093 | 0.046 | 0.096 | 0.053 | 0.105 | |
| Bootstrap | Direct | Multivariate | |||||
| n | m | α=0.05 | α=0.10 | α=0.05 | α=0.10 | α=0.05 | α=0.10 |
| 100 | 10 | 0.059 | 0.126 | 0.044 | 0.086 | n/a | n/a |
| 20 | 0.045 | 0.105 | 0.049 | 0.098 | n/a | n/a | |
| 40 | 0.042 | 0.093 | 0.049 | 0.102 | n/a | n/a | |
| 80 | 0.042 | 0.091 | 0.045 | 0.096 | 0.053 | 0.103 | |
| 500 | 10 | 0.047 | 0.105 | 0.049 | 0.096 | n/a | n/a |
| 20 | 0.050 | 0.103 | 0.049 | 0.096 | n/a | n/a | |
| 40 | 0.050 | 0.100 | 0.043 | 0.090 | n/a | n/a | |
| 80 | 0.044 | 0.093 | 0.046 | 0.096 | 0.053 | 0.105 | |
Table 1
Estimated type I error rates for the bootstrap, direct, and multivariate tests at the nominal and levels based on 5000 datasets, by number of subjects (n) and observations per subject (m). The standard error was 0.003 and 0.004 for and , respectively. The multivariate test is applicable for only the dense setting
| Bootstrap | Direct | Multivariate | |||||
| n | m | α=0.05 | α=0.10 | α=0.05 | α=0.10 | α=0.05 | α=0.10 |
| 100 | 10 | 0.059 | 0.126 | 0.044 | 0.086 | n/a | n/a |
| 20 | 0.045 | 0.105 | 0.049 | 0.098 | n/a | n/a | |
| 40 | 0.042 | 0.093 | 0.049 | 0.102 | n/a | n/a | |
| 80 | 0.042 | 0.091 | 0.045 | 0.096 | 0.053 | 0.103 | |
| 500 | 10 | 0.047 | 0.105 | 0.049 | 0.096 | n/a | n/a |
| 20 | 0.050 | 0.103 | 0.049 | 0.096 | n/a | n/a | |
| 40 | 0.050 | 0.100 | 0.043 | 0.090 | n/a | n/a | |
| 80 | 0.044 | 0.093 | 0.046 | 0.096 | 0.053 | 0.105 | |
| Bootstrap | Direct | Multivariate | |||||
| n | m | α=0.05 | α=0.10 | α=0.05 | α=0.10 | α=0.05 | α=0.10 |
| 100 | 10 | 0.059 | 0.126 | 0.044 | 0.086 | n/a | n/a |
| 20 | 0.045 | 0.105 | 0.049 | 0.098 | n/a | n/a | |
| 40 | 0.042 | 0.093 | 0.049 | 0.102 | n/a | n/a | |
| 80 | 0.042 | 0.091 | 0.045 | 0.096 | 0.053 | 0.103 | |
| 500 | 10 | 0.047 | 0.105 | 0.049 | 0.096 | n/a | n/a |
| 20 | 0.050 | 0.103 | 0.049 | 0.096 | n/a | n/a | |
| 40 | 0.050 | 0.100 | 0.043 | 0.090 | n/a | n/a | |
| 80 | 0.044 | 0.093 | 0.046 | 0.096 | 0.053 | 0.105 | |
