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

S A M P L I N G V A R I A N C E C H A P T E R 8
pair of schools or “quasi” schools. When computing replicate weights for the estimation of
JRR sampling error, one member of each pair of schools is randomly selected to have its
weights doubled, while the weights of the other member are set to zero.
This variable JKZONE indicates the sampling zone to which the student’s school is assigned.
The sampling zones can have values from 1 to 75 in the Student Background and Written
Assessment data files. In the Performance Assessment data files there is a maximum of 42
sampling zones in Population 2 and 39 in Population 1. This variable is included in the
Student Background, the student Written Assessment, the Student-Teacher Linkage, and the
student Performance Assessment data files. For each individual student, this variable is
identical in the first three files, but differs in the Performance Assessment data files because
the performance assessment sample is a sub-sample of the written assessment sample.
The variable JKINDIC indicates how the student is to be used in the computation of the
replicate weights. This variable can have values of either 1 or 0. Those student records with a
value of 0 should be excluded from the corresponding replicate weight, and those with a
value of 1 should have their weights doubled. This variable is included in the student
background, the student written assessment, the student teacher linkage, and the student
performance assessment data files. For each individual student, this variable is identical in the
first three files, but differs in the performance assessment data files because the performance
assessment sample is a sub-sample of the written assessment sample.
8.3 Computing the JRR Replicate Weights
Having assigned the schools to zones, if it is desired to use standard statistical software such as
SAS or SPSS for sampling variance estimation, a convenient way to proceed is to construct a
set of replicate weights for each pseudo-replicate sample. In TIMSS, the schools in the sample
were assigned in pairs to one of the 75 zones indicated by the variable JKZONE, and within
each zone the pair members were randomly assigned an indicator (ui) represented by the
variable JKINDIC, coded randomly to 1 or 0 so that one of the members of each pair had
values of 1 on the variable ui, and the remaining one a value of 0. This indicator determined
whether the weights for the elements in the school in this zone was to be doubled or zeroed.
gi ,, j
The replicate weight (Wh ) for the elements in a school assigned to zone h is computed as
the product of kh times their overall sampling weight, where kh could take values of zero, one,
or two depending on if the case was not to contribute, be left unchanged, or have it count
double for the computation of the statistic of interest. In TIMSS, the replicate weights are not
permanent variables, but are created temporarily by the sampling variance estimation
program as a useful computing device. An example program which makes use of replicate
weights in computing JRR estimates is provided in the next chapter.
When creating the replicate weights the following procedure is followed:
gij ,,
1. Each sampled student is assigned a vector of 75 weights or Wh , where h takes values
from 1 to 75.
2. The value of W gij
0
,, is the overall sampling weight which is simply the product of the final
school weight, the appropriate final classroom weight, and the appropriate final student
weight as defined in the chapter on sampling and sampling weights.
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