User Guide for the TIMSS International Database.pdf - TIMSS and ...

C H A P T E R 3 S A M P L I N G
WGTADJ3 Student Weighting Adjustment
This is an adjustment applied to the variable WGTFAC3 to account for non-participating
students in the selected school and/or classroom. If we were to multiply the variables
WGTFAC2, WGTFAC3, and WGTADJ3 and add them up within each school, we would
obtain an estimate of the number of students within the sampled school.
The five variables listed above are all used to compute a student’s overall sampling weight. A twostage
sampling design was used in TIMSS: schools were first selected from a national list of
schools; in the second stage classrooms were selected within these schools. Some countries used a
third stage in which students were selected within classrooms. We compute the probability for
selecting an individual student as the product of three independent events: selecting the school, the
classroom, and the student. To obtain the probability of selection for an individual student we need
to multiply three selection probabilities – school, classroom, and student – and their respective
adjustment factors. The resulting product of these three probabilities gives us the individual
probability of selection for the student. Inverting this probability give us the sampling weight for
the student. The same result is achieved by multiplying the different weights of the different
selection stages (school, classroom, student).
Three versions of the students’ sampling weight are provided in the user database. All three give
the same figures for statistics such as means and proportions, but vary for statistics such as totals
and population sizes. Each one has particular advantages in certain circumstances.
TOTWGT Total Student Weight
This is obtained by simply multiplying the variables WGTFAC1,WGTADJ1, WGTFAC2,
WGTFAC3, and WGTADJ3 for the student. The sum of these weights within a sample
provides an estimate of the size of the population. Although this is a commonly used sampling
weight, it sometimes adds to a very large number, and to a different number within each
country. This is not always desirable. For example, if we want to compute a weighted estimate
of the mean achievement in the population across all countries, using the variable TOTWGT as
our weight variable will lead each country to contribute proportionally to its population size,
with the large countries counting more than small countries. Although this might be desirable
in some circumstances (e.g., when computing the 75th percentile for mathematics achievement
for students around the world), this is not usually the case.
A key property of the sampling weights is that the same population estimates for means and
proportions will be obtained as long as we use a weight variable proportional to the original
weights (TOTWGT). For example, we could take the sampling weights for a large country and
divide them by a constant to make them smaller. We could also take the weights of a smaller
country and multiply them by a constant to make them bigger. Regardless of which constant is
used within a country, the weighted estimates obtained from each of these proportional
transformations of the weights will be exactly the same. To this effect, two other weight variables
are computed and included in the student data files. Each of these is computed for a specific
purpose and will yield exactly the same results within each country, but will have some desirable
properties when estimates across countries are computed or significance tests performed.
3 – 1 6 T I M S S D A T A B A S E U S E R G U I D E