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

Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 7 Variance of the discrimination parameter \(c_{gi}\) across items (given country g), χ ²-value and asymmetric confidence interval (\(CI_l\) lower bound, \(CI_u\) upper bound; countries ordered in descending order of \(s^2_{gi|g}\))

Country	\(s^2_{gi\|g}\)	\(\chi ^2\)	\(CI_l\)	\(CI_u\)
Qatar	2.75	2748.28	0.99	22.69
Australia	2.42	2424.20	0.87	20.02
Iran, Islamic Rep. of	1.98	1975.20	0.71	16.31
Malta	1.97	1971.18	0.71	16.28
Abu Dhabi, UAE	1.62	1617.25	0.58	13.35
Spain	1.34	1337.09	0.48	11.04
Poland	1.21	1208.22	0.43	9.98
Morocco	1.13	1132.15	0.41	9.35
Saudi Arabia	0.88	878.82	0.32	7.26
Hungary	0.83	826.57	0.30	6.83
Oman	0.73	734.58	0.26	6.07
Ireland	0.69	690.84	0.25	5.70
Singapore	0.66	663.00	0.24	5.47
Chinese Taipei	0.66	660.04	0.24	5.45
Austria	0.48	476.37	0.17	3.93
Romania	0.42	415.65	0.15	3.43	\(\blacktriangle\)
Italy	0.41	409.38	0.15	3.38	\(\blacktriangle\)
Finland	0.33	330.66	0.12	2.73	\(\blacktriangle \triangle\)
Georgia	0.33	327.40	0.12	2.70	\(\blacktriangle \triangle\)
Slovenia	0.32	319.78	0.11	2.64	\(\blacktriangle \triangle\)
Lithuania	0.31	314.68	0.11	2.60	\(\blacktriangle \triangle\)
Honduras	0.28	278.98	0.10	2.30	\(\blacktriangle \triangle \bullet\)
Germany	0.24	238.93	0.09	1.98	\(\blacktriangle \triangle \bullet\)
Slovak Republic	0.22	223.86	0.08	1.85	\(\blacktriangle \triangle \bullet\)
Azerbaijan	0.21	218.44	0.08	1.80	\(\blacktriangle \triangle \bullet\)
Sweden	0.13	132.81	0.05	1.10	\(\blacktriangle \triangle \bullet \circ\)
Croatia	0.13	126.27	0.05	1.04	\(\blacktriangle \triangle \bullet \circ\)
Czech Republic	0.12	118.46	0.05	0.98	\(\blacktriangle \triangle \bullet \circ\)

\(\blacktriangle\), country variance is statistically different from Qatar; \(\triangle\), country variance is statistically different from Australia; \(\bullet\), country variance is statistically different from Iran, Islamic Rep. of, Malta and Abu Dhabi, UAE; \(\circ\), country variance is statistically different from Spain, Poland, Morocco, Saudi Arabia and Hungary