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 8 Distribution of \(\hat{\beta }_3\) across scaling models and countries, \(\chi ^2\)-value and asymmetric confidence interval (\(CI_l\) lower bound, \(CI_u\) upper bound; countries ordered in descending order of the conditional variance of \(\hat{\beta }_3\) across scaling models 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	\(\hat{\beta }_3\)				\(s^2_{\hat{\beta }_{3gz.g}}\)	\(\chi ^2\)	\(CI_l\)	\(CI_u\)
Country	1	2	3	4	\(s^2_{\hat{\beta }_{3gz.g}}\)	\(\chi ^2\)	\(CI_l\)	\(CI_u\)
Iran, Islamic Rep. of	20.77	26.94	22.35	30.60	19.96	14,972.88	6.41	277.54
Malta	37.08	32.20	35.90	27.47	18.72	14,038.53	6.01	260.23
Slovenia	42.95	36.89	43.05	35.31	16.29	12,218.83	5.23	226.49
Czech Republic	38.89	33.79	38.75	31.75	12.90	9676.91	4.14	179.37
Abu Dhabi, UAE	18.66	16.57	21.90	24.43	12.07	9050.66	3.87	167.76
Qatar	29.36	25.81	30.85	33.90	11.29	8467.50	3.62	156.95
Romania	35.52	41.32	36.55	42.18	11.18	8383.35	3.59	155.39
Austria	39.15	34.52	39.11	33.51	8.89	6669.48	2.85	123.63
Germany	32.59	30.02	31.43	25.93	8.42	6313.93	2.70	117.03
Ireland	43.67	42.27	41.90	37.96	5.99	4492.46	1.92	83.27
Morocco	1.60	2.08	3.83	7.00	5.98	4482.99	1.92	83.10
Slovak Republic	40.91	37.52	41.50	36.85	5.52	4142.23	1.77	76.78
Oman	33.44	36.40	34.36	38.34	4.78	3583.85	1.53	66.43
Croatia	25.08	21.49	25.84	22.19	4.54	3406.78	1.46	63.15
Italy	27.06	23.71	27.00	23.40	4.04	3029.52	1.30	56.16
Georgia	25.31	23.78	26.93	22.26	4.03	3020.26	1.29	55.98
Lithuania	26.17	23.48	27.10	24.04	2.95	2210.88	0.95	40.98
Hungary	44.69	47.21	44.15	47.28	2.71	2033.31	0.87	37.69
Honduras	−2.39	−3.81	−0.59	−0.36	2.65	1984.88	0.85	36.79
Singapore	29.05	26.54	29.88	27.58	2.22	1664.81	0.71	30.86
Azerbaijan	22.50	24.54	22.70	25.43	2.04	1530.08	0.65	28.36	\(\blacktriangle\)
Poland	37.16	35.03	36.58	34.20	1.86	1397.34	0.60	25.90	\(\blacktriangle \triangle\)
Spain	26.46	24.59	26.00	23.60	1.71	1285.60	0.55	23.83	\(\blacktriangle \triangle \bullet\)
Australia	40.50	39.20	40.92	38.52	1.25	935.29	0.40	17.34	\(\blacktriangle \triangle \bullet \circ\)
Saudi Arabia	11.24	11.27	12.91	13.28	1.15	865.93	0.37	16.05	\(\blacktriangle \triangle \bullet \circ \blacktriangleleft\)
Chinese Taipei	28.56	27.29	29.20	28.07	0.65	487.64	0.21	9.04	\(\blacktriangle \triangle \bullet \circ \blacktriangleleft \triangleleft\)
Finland	25.44	24.89	25.37	23.78	0.59	440.63	0.19	8.17	\(\blacktriangle \triangle \bullet \circ \blacktriangleleft \triangleleft\)
Sweden	28.58	29.69	28.26	28.55	0.40	299.94	0.13	5.56	\(\blacktriangle \triangle \bullet \circ \blacktriangleleft \triangleleft\)
\(s^2_{\hat{\beta }_{3gz.z}}\)	135.82	129.56	119.69	102.71
\(CL_l\)	84.90	80.99	74.82	64.20
\(CL_u\)	251.64	240.04	221.75	190.28

1, scaling model 1; 2, scaling model 2; 3, scaling model 3; 4, scaling model 4; \(\blacktriangle\), country variance is statistically different from Iran, Islamic Rep. of; \(\triangle\), country variance is statistically different from Malta; \(\bullet\), country variance is statistically different from Slovenia; \(\circ\), country variance is statistically different from Czech Republic and Abu Dhabi, UAE; \(\blacktriangleleft\), country variance is statistically different from Qatar and Romania; \(\triangleleft\), country variance is statistically different from Austria, Germany, Ireland and Morocco

Back to article page