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Table 1 Type I error of competing tests of \(H_{0}: \sigma _{A}^{2} \geq \sigma _{0}^{2}\) with intended size 0.05

From: Exact distributions of statistics for making inferences on mixed models under the default covariance structure

ng

n

\(\sigma ^{2}_{0}\)

REML

PL

Proposed

3

10

.01

.254

.014

.043

3

10

.1

.082

.020

.046

3

10

1

.006

.010

.046

3

100

.01

.168

.012

.051

3

100

.1

.011

.008

.054

3

100

1

NA

.006

.051

5

10

.01

.281

.021

.042

5

10

.1

.076

.020

.043

5

10

1

.013

.016

.044

5

100

.01

.177

.019

.044

5

100

.1

.022

.017

.044

5

100

1

NA

.016

.048

10

10

.01

.300

.031

.047

10

10

.1

.095

.023

.050

10

10

1

.022

.022

.050

10

100

.01

.208

.026

.050

10

100

.1

.034

.028

.050

10

100

1

NA

.023

.048