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Table 1 Type I error rates of the methods for different combination of sample sizes in homogenous studies

From: A comparative study of the impacts of unbalanced sample sizes on the four synthesized methods of meta-analytic structural equation modeling

\(\bar{n}\)

Types

k = 5

k = 10

k = 15

UNIr

UNIz

MGLS

TSSEM

UNIr

UNIz

MGLS

TSSEM

UNIr

UNIz

MGLS

TSSEM

50

E

4.4

3.8

4.8

6.7*

6.4*

5.4

6.8*

9.1*

6.7*

5.3

7.9*

10.7*

 

M

5.6

4.2

5.7

6.7*

7.0*

5.2

7.2*

11.4*

8.1*

4.8

8.8*

11.0*

 

H

6.7*

5.6

8.5*

10.0*

6.6*

4.6

8.6*

10.1*

8.5*

5.4

9.8*

13.3*

100

E

5.1

5.8

5.9

7.3*

5.2

5.3

5.2

6.7*

5.2

3.7

5.3

6.2

 

M

5.9

5.2

6.0

7.1*

6.6*

4.3

6.2

7.4*

4.7

4.2

6.5*

6.6*

 

H

5.9

4.3

6.0

5.7

6.2

4.7

6.7*

6.6*

6.8*

4.4

7.6*

8.3*

200

E

4.4

4.4

5.1

5.2

5.3

4.9

5.5

6.0

5.1

3.8

5.4

5.9

 

M

4.5

3.3*

4.4

4.5

4.7

4.5

6.2

7.2*

4.9

4.1

5.1

5.6

 

H

5.0

4.9

5.7

5.6

4.4

4.2

5.4

5.5

7.1*

6.0

6.5*

6.2

500

E

5.3

5.4

5.7

5.7

5.2

6.2

5.8

5.9

3.7

3.2*

5.3

5.5

 

M

4.7

4.8

5.6

5.3

5.3

5.2

5.0

5.0

3.9

3.8

5.7

5.3

 

H

5.4

4.7

4.9

5.2

5.1

4.3

5.0

5.3

5.2

4.5

6.4*

6.3

1000

E

4.8

5.0

5.0

5.4

4.9

5.3

4.2

4.2

4.2

4.2

5.3

5.3

 

M

4.2

3.9

5.5

5.6

4.5

4.2

4.5

4.8

5.2

5.0

5.2

5.4

 

H

4.7

5.0

5.7

5.6

4.3

4.6

5.2

5.6

4.1

3.9

4.5

5.2

  1. \(\bar{n}\) average sample sizes k number of studies, UNIr univariate-r, UNIz univariate-z, MGLS modified generalized least squared, TSSEM two-stage structural equation modeling, E equally sized studies M moderately unequal sized studies H highly unequal sized studies
  2. * Values falls outside the 95% acceptance regions