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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