Table 4.
Results and model uncertainty of 11 different scaling models for country 10th and 90th percentiles in PISA 2009 reading.
| Country 10th Percentile | Country 90th Percentile | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CNT | N | M | rg | SE | ME | ER | TE | M | rg | SE | ME | ER | TE | ||
| AUS | 14,247 | 379.5 | 5.5 | 2.98 | 1.52 | 1.49 | 0.50 | 3.33 | 646.8 | 11.2 | 3.33 | 3.10 | 3.04 | 0.91 | 4.51 |
| AUT | 6585 | 332.9 | 20.5 | 4.82 | 5.37 | 5.32 | 1.10 | 7.18 | 602.8 | 4.8 | 3.64 | 1.26 | 1.07 | 0.30 | 3.79 |
| BEL | 8500 | 369.0 | 7.7 | 4.09 | 2.15 | 2.08 | 0.51 | 4.59 | 644.7 | 16.8 | 2.78 | 4.24 | 4.24 | 1.52 | 5.07 |
| CAN | 23,200 | 400.8 | 4.9 | 2.40 | 1.42 | 1.41 | 0.59 | 2.78 | 646.7 | 11.9 | 1.92 | 3.00 | 3.00 | 1.56 | 3.56 |
| CHE | 11,801 | 370.5 | 7.5 | 3.68 | 1.83 | 1.77 | 0.48 | 4.09 | 627.7 | 10.9 | 3.36 | 3.11 | 3.09 | 0.92 | 4.56 |
| CZE | 6059 | 357.5 | 8.4 | 4.67 | 2.19 | 2.13 | 0.46 | 5.14 | 603.3 | 6.2 | 3.18 | 1.58 | 1.53 | 0.48 | 3.53 |
| DEU | 4975 | 366.0 | 7.5 | 4.79 | 1.95 | 1.81 | 0.38 | 5.12 | 624.4 | 9.2 | 2.73 | 2.64 | 2.58 | 0.95 | 3.76 |
| DNK | 5920 | 378.2 | 4.1 | 2.82 | 0.96 | 0.91 | 0.32 | 2.96 | 604.0 | 4.7 | 2.57 | 1.45 | 1.43 | 0.56 | 2.94 |
| ESP | 25,828 | 359.0 | 8.7 | 3.24 | 2.18 | 2.12 | 0.66 | 3.87 | 595.1 | 3.0 | 1.86 | 0.78 | 0.74 | 0.40 | 2.00 |
| EST | 4726 | 390.9 | 7.3 | 3.83 | 1.81 | 1.76 | 0.46 | 4.21 | 610.7 | 6.2 | 3.17 | 1.50 | 1.46 | 0.46 | 3.49 |
| FIN | 5807 | 419.2 | 10.0 | 2.90 | 2.45 | 2.45 | 0.85 | 3.80 | 653.3 | 21.6 | 2.66 | 5.75 | 5.75 | 2.16 | 6.34 |
| FRA | 4280 | 350.5 | 13.8 | 5.93 | 3.68 | 3.59 | 0.60 | 6.93 | 638.6 | 16.3 | 4.92 | 3.88 | 3.82 | 0.78 | 6.23 |
| GBR | 12,172 | 365.9 | 9.9 | 3.00 | 2.57 | 2.57 | 0.86 | 3.95 | 621.7 | 5.0 | 3.01 | 1.45 | 1.39 | 0.46 | 3.31 |
| GRC | 4966 | 350.5 | 16.2 | 6.24 | 3.51 | 3.29 | 0.53 | 7.05 | 607.5 | 3.6 | 3.06 | 1.03 | 0.97 | 0.32 | 3.21 |
| HUN | 4604 | 368.6 | 7.0 | 6.08 | 1.56 | 1.40 | 0.23 | 6.24 | 613.4 | 4.5 | 4.08 | 1.21 | 1.12 | 0.28 | 4.23 |
| IRL | 3931 | 370.0 | 9.6 | 5.61 | 2.45 | 2.38 | 0.43 | 6.09 | 619.7 | 5.7 | 2.84 | 1.31 | 1.24 | 0.44 | 3.10 |
| ISL | 3628 | 366.3 | 6.0 | 2.67 | 1.40 | 1.28 | 0.48 | 2.96 | 628.2 | 11.2 | 2.33 | 2.84 | 2.76 | 1.18 | 3.62 |
| ITA | 30,905 | 352.4 | 12.2 | 2.65 | 2.67 | 2.65 | 1.00 | 3.75 | 613.7 | 7.7 | 1.86 | 2.01 | 2.00 | 1.07 | 2.73 |
| JPN | 6082 | 381.0 | 4.8 | 7.46 | 1.17 | 1.01 | 0.14 | 7.52 | 652.9 | 25.9 | 3.39 | 5.73 | 5.67 | 1.68 | 6.60 |
| KOR | 4989 | 430.5 | 13.8 | 4.18 | 3.53 | 3.31 | 0.79 | 5.33 | 644.5 | 14.7 | 3.51 | 3.68 | 3.60 | 1.02 | 5.03 |
| LUX | 4622 | 328.3 | 24.5 | 2.42 | 6.36 | 6.31 | 2.61 | 6.76 | 609.8 | 5.9 | 1.83 | 1.63 | 1.55 | 0.85 | 2.40 |
| NLD | 4760 | 386.8 | 3.5 | 5.84 | 0.91 | 0.73 | 0.13 | 5.89 | 632.7 | 12.9 | 5.35 | 3.47 | 3.36 | 0.63 | 6.31 |
| NOR | 4660 | 377.1 | 3.5 | 3.47 | 0.85 | 0.77 | 0.22 | 3.55 | 625.7 | 13.7 | 3.28 | 3.45 | 3.45 | 1.05 | 4.76 |
| POL | 4917 | 381.9 | 5.0 | 3.25 | 1.25 | 1.24 | 0.38 | 3.48 | 620.5 | 12.8 | 3.18 | 3.46 | 3.43 | 1.08 | 4.68 |
| PRT | 6298 | 369.9 | 6.6 | 4.51 | 1.43 | 1.34 | 0.30 | 4.70 | 606.8 | 3.5 | 3.20 | 0.83 | 0.74 | 0.23 | 3.29 |
| SWE | 4565 | 363.1 | 8.8 | 3.97 | 2.19 | 2.13 | 0.54 | 4.51 | 627.6 | 7.9 | 3.60 | 2.13 | 2.06 | 0.57 | 4.15 |
Note. CNT = country label (see Appendix B); N = sample size; M = weighted mean across different scaling models; rg = range of estimates across models; SE = standard error (computed with balanced half sampling); ME = estimated model error (see Equation (20)); MEbc = bias-corrected estimate of model error based on balanced half sampling (see Equation (23)); ER = error ratio defined as MEbc/SE; TE = total error computed by (see Equation (24)).