Trends in International Mathematics and Science Study 2007

The TIMSS target populations are all fourth and eighth graders in each participating country. To obtain accurate and representative samples, TIMSS used a two-stage sampling procedure whereby a random sample of schools is selected at the first stage and one or two intact fourth or eighth grade classes are sampled at the second stage. This is a very effective and efficient sampling approach, but the resulting student sample has a complex structure that must be taken into consideration when analyzing the data. In particular, sampling weights need to be applied and a re-sampling technique such as the jackknife employed to estimate sampling variances correctly.

In addition, TIMSS 2007 uses Item Response Theory (IRT) scaling to summarize student achievement on the assessment and to provide accurate measures of trends from previous assessments. The TIMSS IRT scaling approach used multiple imputation-or "plausible values"-methodology to obtain proficiency scores in mathematics and science for all students. Each student record in the TIMSS 2007 international database contains imputed scores in mathematics and science overall, as well as for each of the content domain subscales and cognitive domain subscales. Because each imputed score is a prediction based on limited information, it almost certainly includes some small amount of error. To allow analysts to incorporate this error into analyses of the TIMSS achievement data, the TIMSS database provides five separate imputed scores for each scale. Each analysis should be replicated five times, using a different plausible value each time, and the results combined into a single result that includes information on standard errors that incorporate both sampling and imputation error.