Page 1 of 6

Web-based Supplementary Materials for “Multiple

Imputation Methods for Multivariate One-sided Tests

with Missing Data”

by Tao Wang and Lang Wu

Page 2 of 6

Web Table 1

Table 1: Simulation results for p=2 under MAR (n=200, equal missing rate=20%)

Bound method Substitution method

μ Σ TW TCW CC TW TCW CC

Type I Error Rates (in %)

(0,0) Σ1(ρ = 0) 3.7 3.7 3.5 5.4 5.5 5.5

Σ2(ρ = 0.6) 1.9 1.9 2.4 4.6 4.6 5.7

(-2,0) Σ1(ρ = 0) 1.3 1.5 1.2 2.7 2.8 2.1

Σ2(ρ = 0.6) 1.2 1.2 1.5 2.8 2.8 2.9

Power Comparisons (in %)

(-1,0.2) Σ1(ρ = 0) 60 60 53 69 69 61

Σ2(ρ = 0.6) 60 60 51 73 73 65

(0.2,0.2) Σ1(ρ = 0) 92 92 87 95 95 91

Σ2(ρ = 0.6) 78 78 68 88 88 79

1

Page 3 of 6

Web Table 2

Table 2: Simulation results for p=5 based on the bound method (n=50, equal missing rate =

20%)

μ Σ1(ρ = 0) Σ2(ρ = 0.2) Σ3(ρ = 0.6)

TW TCW CC TW TCW CC TW TCW CC

Type I Error Rates (in %)

(05

) 2.7 3.2 5.7 1.5 1.9 3.2 0.5 0.7 1.2

(−1, 0

4

) 1.7 1.9 3.3 0.9 1.6 2.9 0.3 0.4 1.0

(−1

2

, 0

3

) 0.7 1.1 1.7 0.6 0.8 1.8 0.1 0.1 1.1

(−1

3

, 0

2

) 0.4 0.5 0.5 0.4 0.4 0.7 0.1 0.1 0.8

(−1

4

, 0) 0.2 0.2 0.3 0.1 0.1 0.4 0.0 0.0 0.3

Power Comparisons (in %)

(0.1

5

) 24 27 19 11 12 11 4 4 6

(−1, .3

4

) 89 90 60 70 72 38 28 30 18

(−1

2

, .3

3

) 72 74 38 52 54 27 22 24 13

(−1

3

, .3

2

) 41 45 18 33 35 17 15 17 11

(−1

4

, .3) 12 14 5 13 14 6 12 13 6

Note: (−1

2

, .3

3

) denotes (−1, −1, 0.3, 0.3, 0.3), etc.

2