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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
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
  1. 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