| △ Average score is higher than U.S. average score. |
|---|
| ▽ Average score is lower than U.S. average score. |
| 1 National Defined Population covers 90 to 95 percent of National Target Population (see appendix A). |
| 2 Met guidelines for sample participation rates only after replacement schools were included. |
| 3 National Target Population does not include all of the International Target Population (see appendix A). |
| 4 Nearly satisfied guidelines for sample participation rates after replacement schools were included. |
| 5 Exclusion rates for Azerbaijan and Georgia are slightly underestimated as some conflict zones were not covered and no official statistics were available. |
| 6 The TIMSS International Study Center has reservations about the reliability of the average achievement score because the percentage of students with achievement too low for estimation exceeds 15 percent, though it is less than 25 percent. |
| 7 The TIMSS International Study Center has reservations about the reliability of the average achievement score because the percentage of students with achievement too low for estimation exceeds 25 percent. |
| 8 National Defined Population covers less than 90 percent, but at least 77 percent of National Target Population (see appendix A). |
| NOTE: Education systems are ordered by 2011 average score. Italics indicate participants identified and counted in this report as an education system and not as a separate country. Participants that did not administer TIMSS at the target grade are not shown; see the international report for their results. All U.S. state data are based on public school students only. All average scores reported as higher or lower than the U.S. average score are different at the05 level of statistical significance. The tests for significance take into account the standard error for the reported difference. Thus, a small difference between the United States and one education system may be significant while a large difference between the United States and another education system may not be significant. The standard errors of the estimates are shown in table E-22 available athttp://nces.ed.gov/pubsearch/pubsinfor.asp?pubid=2013009. |
| SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2011. |