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Table 12 Fit-values for equality test of \(\varvec{G}_{\varvec{gz}}\) across scaling models z given country g

From: Assuming measurement invariance of background indicators in international comparative educational achievement studies: a challenge for the interpretation of achievement differences

Country Fit-value
\(\chi ^2\) df p SRMR GFI RMSEA \(CI_l\) \(CI_u\)
Azerbaijan 323.41 9 <0.0001 0.11 0.98 0.08 0.08 0.09
Australia 42.21 9 <0.0001 0.03 1.00 0.02 0.02 0.03
Austria 426.86 9 <0.0001 0.13 0.98 0.10 0.09 0.11
Chinese Taipei 21.22 9 0.01 0.03 1.00 0.02 0.01 0.03
Croatia 177.11 9 <0.0001 0.08 0.99 0.06 0.06 0.07
Czech Republic 195.84 9 <0.0001 0.08 0.99 0.07 0.06 0.08
Finland 37.48 9 <0.0001 0.03 1.00 0.03 0.02 0.04
Georgia 64.84 9 <0.0001 0.05 1.00 0.04 0.03 0.04
Germany 355.66 9 <0.0001 0.13 0.98 0.10 0.10 0.11
Honduras 1561.82 9 <0.0001 0.32 0.90 0.21 0.20 0.22
Hungary 817.51 9 <0.0001 0.09 0.96 0.13 0.12 0.14
Iran, Islamic Rep. of 1157.06 9 <0.0001 0.21 0.95 0.15 0.14 0.16
Ireland 24.14 9 0.004 0.03 1.00 0.02 0.01 0.03
Italy 259.85 9 <0.0001 0.11 0.98 0.08 0.07 0.09
Lithuania 125.05 9 <0.0001 0.07 0.99 0.05 0.05 0.06
Malta 1701.07 9 <0.0001 0.49 0.87 0.23 0.22 0.24
Morocco 2346.54 9 <0.0001 0.27 0.92 0.18 0.18 0.19
Oman 324.51 9 <0.0001 0.06 0.99 0.06 0.05 0.06
Poland 31.48 9 0.0002 0.03 1.00 0.02 0.01 0.03
Qatar 153.41 9 <0.0001 0.08 0.99 0.06 0.05 0.07
Romania 237.43 9 <0.0001 0.09 0.99 0.07 0.06 0.08
Saudi Arabia 136.58 9 <0.0001 0.07 0.99 0.05 0.04 0.06
Singapore 357.01 9 <0.0001 0.11 0.99 0.08 0.07 0.09
Slovak Republic 128.30 9 <0.0001 0.06 0.99 0.05 0.04 0.06
Slovenia 354.37 9 <0.0001 0.09 0.98 0.09 0.08 0.10
Spain 70.70 9 <0.0001 0.05 1.00 0.04 0.03 0.05
Sweden 11.68 9 0.23 0.02 1.00 0.01 0.00 0.02
Abu Dhabi, UAE 192.68 9 <0.0001 0.09 0.99 0.07 0.06 0.08
  1. \(\chi ^2\), under the null hypothesis of equality of the covariance matrix \(\texttt {G}_{\texttt {gz}}\) across scaling models, this value should not be statistically different from zero; SRMR, standardized root mean square residual should be zero under the null hypothesis; GFI, goodness-of-fit index should be one under the null hypothesis; RMSEA, root mean square error of approximation should be zero under the null hypothesis; \(CI_l, CI_u\), lower and upper bound of RMSEA