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

S C A L I N G C H A P T E R 5
At this point L uniformly distributed random numbers, hi i
random draw the vector, j , that satisfies the condition
ni0
is selected as a plausible vector.
5.8 Scaling Steps
i0
-1
åqsn i0
< h i £ åqsn
s=
1
s=
1
L
{ } , are generated, and for each
=1
The item response model described above was fit to the data in two steps. In the first step a
calibration of the items was undertaken using a subsample of students drawn from the
samples of the participating countries. These samples were called the international calibration
samples. In a second step the model was fitted separately to the data for each country within
the item parameters fixed at values estimated in the first step.
There were three principal reasons for using an international calibration sample for estimating
international item parameters. First, it seemed unnecessary to estimate parameters using the
complete data set; second, drawing equal sized subsamples from each country for inclusion in
the international calibration sample ensured that each country was given equal weight in the
estimation of the international parameters; and third, the drawing of appropriately weighted
samples meant that weighting would not be necessary in the international scaling runs.
5.8.1 Drawing The International Calibration Sample
For each target population, samples of 600 tested students were selected from the database for
each participating country. This generally led to roughly equal samples from each target
grade. For Israel, where only the upper grade was tested, the sample size was reduced to 300
tested students. The sampled students were selected using a probability-proportionality-to size
systematic selection method. The overall sampling weights were used as measures of size for
this purpose. This resulted in equal selection probabilities, within national samples, for the
students in the calibration samples. The Populations 1 and 2 international calibration samples
contained 14,700 and 23,100 students respectively.
5.8.2 Standardizing the International Scale Scores
The plausible values produced by the scaling procedure were in the form of logit scores that
were on a scale that ranged generally between -3 and +3. For reporting purposes these scores
were mapped by a linear transformation onto an international scale with a mean of 500 and a
standard deviation of 100. Each country was weighted to contribute the same when the
international mean and standard deviation were set, with the exception of the countries that
tested only one grade. Countries that tested only one grade had only half the contribution of
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