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

Wendt, Heike; Kasper, Daniel; Trendtel, Matthias

doi:10.1186/s40536-017-0043-9

Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 2 Descriptive statistics for mathematics achievement, early literacy/numeracy tasks, and home resources for learning index under different scaling models

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

Country	Variable
	N		MAT		ET		HRL
	N		MAT		ET		RP		M1		M2		M3		M4
	ST	SL	M	SE	M	SE	M	SE	M	SE	M	SE	M	SE	M	SE
Azerbaijan	4871	169	458.1	6.05	9.5	0.08	9.0	0.03	−0.7	0.02	−0.7	0.02	−0.6	0.02	−0.7	0.01
Australia	5943	280	514.2	2.94	9.4	0.03	11.2	0.03	0.6	0.02	0.6	0.02	0.6	0.02	0.5	0.02
Austria	4587	158	505.2	2.65	9.3	0.03	10.5	0.05	0.3	0.03	0.2	0.03	0.3	0.03	0.1	0.03
Chinese Taipei	4265	150	590.3	1.86	11.2	0.02	10.3	0.05	0.2	0.03	0.1	0.03	0.2	0.03	−0.0	0.03
Croatia	4545	152	486.1	1.89	10.5	0.03	10.0	0.04	−0.0	0.02	−0.2	0.02	−0.0	0.02	−0.2	0.03
Czech Republic	4433	177	508.3	2.48	9.9	0.03	10.6	0.04	0.3	0.02	0.2	0.02	0.3	0.02	0.1	0.03
Finland	4541	145	543.5	2.33	10.4	0.04	11.2	0.03	0.7	0.02	0.6	0.02	0.6	0.02	0.5	0.02
Georgia	4774	173	444.2	3.54	9.8	0.05	10.1	0.05	−0.0	0.03	−0.1	0.03	0.0	0.03	−0.2	0.03
Germany	3928	197	524.8	2.21	9.5	0.03	10.5	0.05	0.3	0.03	0.2	0.03	0.3	0.03	−0.0	0.03
Honduras	3830	147	388.7	5.71	10.7	0.05	8.1	0.07	−1.1	0.04	−0.7	0.02	−1.1	0.04	−0.7	0.02
Hungary	5149	149	512.4	3.40	9.3	0.03	10.1	0.07	0.1	0.04	−0.0	0.04	0.0	0.04	−0.2	0.04
Iran, Islamic Rep. of	5734	244	423.5	3.53	9.6	0.06	8.7	0.07	−0.7	0.04	−0.6	0.03	−0.7	0.04	−0.6	0.03
Ireland	4383	150	525.8	2.82	9.4	0.03	10.8	0.05	0.4	0.03	0.3	0.03	0.4	0.03	0.3	0.03
Italy	4125	202	503.8	2.71	9.2	0.02	9.9	0.04	−0.1	0.02	−0.2	0.02	−0.1	0.02	−0.3	0.02
Lithuania	4584	154	531.5	2.63	10.1	0.04	10.1	0.04	0.0	0.02	−0.1	0.02	0.0	0.02	−0.1	0.02
Malta	3492	96	491.8	1.27	10.2	0.03	10.3	0.02	0.2	0.01	0.1	0.01	0.1	0.01	−0.4	0.01
Morocco	7614	284	321.9	4.02	9.7	0.08	8.2	0.04	−1.0	0.02	−0.8	0.02	−1.0	0.02	−0.8	0.02
Oman	10,237	327	376.5	2.94	10.6	0.03	9.2	0.03	−0.5	0.02	−0.6	0.01	−0.5	0.02	−0.6	0.01
Poland	4962	150	477.0	2.26	9.9	0.04	10.1	0.05	0.1	0.03	−0.1	0.03	0.0	0.03	−0.2	0.03
Qatar	4104	166	406.4	3.46	10.8	0.03	10.4	0.04	0.2	0.02	0.1	0.02	0.2	0.02	0.3	0.02
Romania	4643	148	476.4	6.01	9.6	0.10	9.2	0.06	−0.5	0.03	−0.5	0.03	−0.5	0.03	−0.5	0.03
Saudi Arabia	4470	171	403.0	5.31	10.6	0.08	9.5	0.06	−0.4	0.03	−0.4	0.03	−0.3	0.03	−0.4	0.03
Singapore	6208	176	606.4	3.35	11.3	0.04	10.8	0.03	0.4	0.02	0.3	0.02	0.4	0.02	0.3	0.02
Slovak Republic	5561	197	503.1	3.93	9.0	0.04	10.1	0.05	0.1	0.03	−0.1	0.03	0.1	0.03	−0.1	0.03
Slovenia	4433	195	509.8	1.99	9.3	0.03	10.5	0.03	0.3	0.02	0.2	0.02	0.3	0.02	0.1	0.02
Spain	4105	151	478.8	2.81	10.6	0.04	10.3	0.05	0.2	0.03	0.1	0.03	0.2	0.03	−0.1	0.03
Sweden	4482	152	502.0	2.20	10.3	0.04	11.2	0.04	0.7	0.02	0.6	0.02	0.7	0.02	0.5	0.02
Abu Dhabi, UAE	4100	164	409.7	4.91	10.5	0.04	10.1	0.06	−0.0	0.03	−0.1	0.03	0.0	0.03	0.1	0.03

ST, student sample size; SL, school sample size; MAT, mathematics achievement of fourth grade; ET, early literacy/numeracy tasks index; RP, HRL index replicating the scaling model from Martin et al. (2013); M1, HRL index using scaling model 1; M2, HRL index using scaling model 2; M3, HRL index using scaling model 3; M4, HRL index using scaling model 4

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