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

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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. T I M S S D A T A B A S E U S E R G U I D E 8 - 3
C H A P T E R 8 S A M P L I N G V A R I A N C E 3. The replicate weights for a single case are then computed as: gi ,, j gi ,, j W = W0 * k , h where the variable k h for an individual i takes the value k hi=2*u i if the record belongs to zone h, and k hi=1 otherwise. In TIMSS, a total of 75 replicate weights were computed regardless of the number of actual zones within each country. If a country had fewer than 75 zones, then the replicate weights W h, where h was greater than the number of zones within the country, were each the same as the overall sampling weight. Although this involves some redundant computation, having 75 replicate weights for each country has no effect on the size of the error variance computed using the jackknife formula, but facilitates the computation of standard errors for a number of countries at one time. 8 - 4 T I M S S D A T A B A S E U S E R G U I D E hi
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International Association for the E
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Contents Chapter 1: Overview of TIM
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C O N T E N T S 7.3 Codebook Files
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C O N T E N T S Table 7.7 Classific
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Chapter 1 Overview of TIMSS and the
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I N T R O D U C T I O N C H A P T E
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Chapter 2 TIMSS Instruments and Boo
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Chapter 3 Sampling and Sampling Wei
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