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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 \(s^2_{gi|g}\))

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

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 \(\blacktriangle \triangle \bullet \circ\)
  1. \(\blacktriangle\), 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