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ICCS 2009 Technical Report - IEA

ICCS 2009 Technical Report - IEA

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The team next selected a sample from the sorted school sampling frame by engaging in thefollowing tasks:• Calculating a sampling interval in each explicit stratum, a process that involved dividingthe total MOS in the stratum by the number of units to be sampled from that stratum;• Determining a random starting point in each explicit stratum, a step that decided the firstsampled school in the explicit stratum;• Selecting the units by adding the sampling interval to the point of the random start andthen subsequently to each new value every time a school was selected. Whenever thecumulated MOS equaled or exceeded the corresponding value, the team selected thecorresponding unit.Figure 6.1 visualizes the process of systematic PPS sampling within an explicit stratum. Inthis diagram, the schools in the sampling frame are sorted in descending order by MOS.The height of the cells reflects the number of target-grade students in each school. A randomstart determines the second school in the list for selection, and a constant sampling intervaldetermines the next two sampled schools. Sampled schools are displayed in blue.Figure 6.1: Systematic PPS sampling of schools150 studentsrandom start120 students100 studentssampling interval80 students75 students70 students65 students62 students60 students58 students55 students53 students52 students…The team occasionally deviated from this general procedure. If very small schools are selectedwith PPS, there is a risk of obtaining extremely large sampling weights for students from thoseschools. In order to prevent this, it is necessary to select small schools with equal selectionprobabilities. The <strong>ICCS</strong> team regarded a school as small if the number of students enrolled inthe target grade was lower than the number enrolled in a class of average size in the school’sexplicit stratum. Conversely, technical problems arise whenever the MOS of a school is largerthan the sampling interval. In this case, the sampling team set the MOS of the school to thesampling interval, thereby ensuring that the school would be selected with certainty but notmore than once.66 <strong>ICCS</strong> <strong>2009</strong> technical report

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