Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

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
Country	\(\chi ^2\)	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

\(\chi ^2\), 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

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