Table 2 Proportions of superiority decisions and standard errors by data-generating mechanism, estimation method, and decision rule

Average treatment effect: \(\varvec{\delta } = (0.000, 0.000)\), \(\varvec{\delta } (\varvec{w}) = 0.000\)

J = 10, \(n_{j}\) = 10

     BMMLR

0.032

(0.006)

0.000

(0.000)

0.042

(0.006)

     BMLR

0.055

(0.007)

0.001

(0.001)

0.059

(0.007)

     BMB

0.050

(0.007)

0.001

(0.001)

0.046

(0.007)

J = 100, \(n_{j}\) = 10

     BMMLR

0.053

(0.007)

0.002

(0.001)

0.048

(0.007)

     BMLR

0.077

(0.008)

0.003

(0.002)

0.066

(0.008)

     BMB

0.069

(0.008)

0.002

(0.001)

0.056

(0.007)

J = 10, \(n_{j}\) = 100

     BMMLR

0.044

(0.006)

0.000

(0.000)

0.060

(0.008)

     BMLR

0.200

(0.013)

0.004

(0.002)

0.125

(0.010)

     BMB

0.188

(0.012)

0.003

(0.002)

0.113

(0.010)

J = 100, \(n_{j}\) = 100

     BMMLR

0.057

(0.007)

0.000

(0.000)

0.054

(0.007)

     BMLR

0.252

(0.014)

0.005

(0.002)

0.169

(0.012)

     BMB

0.245

(0.014)

0.005

(0.002)

0.159

(0.012)

Conditional treatment effect: \(\varvec{\delta } = (0.116, 0.069)\), \(\varvec{\delta } (\varvec{w}) = 0.092\)

J = 10, \(n_{j}\) = 10

     BMMLR

0.731

(0.014)

0.245

(0.014)

0.920

(0.009)

     BMLR

0.397

(0.015)

0.065

(0.008)

0.587

(0.016)

     BMB

0.183

(0.012)

0.025

(0.005)

0.294

(0.014)

J = 100, \(n_{j}\) = 10

     BMMLR

1.000

(0.000)

0.995

(0.002)

1.000

(0.000)

     BMLR

1.000

(0.000)

0.868

(0.011)

1.000

(0.000)

     BMB

0.933

(0.008)

0.520

(0.016)

0.980

(0.004)

J = 10, \(n_{j}\) = 100

     BMMLR

1.000

(0.000)

0.949

(0.007)

1.000

(0.000)

     BMLR

0.997

(0.002)

0.771

(0.013)

1.000

(0.000)

     BMB

0.917

(0.009)

0.445

(0.016)

0.969

(0.005)

J = 100, \(n_{j}\) = 100

     BMMLR

1.000

(0.000)

1.000

(0.000)

1.000

(0.000)

     BMLR

1.000

(0.000)

1.000

(0.000)

1.000

(0.000)

     BMB

1.000

(0.000)

1.000

(0.000)

1.000

(0.000)