An IEA-ETS Research Institute Journal

# Table 4 Weighting approaches for the simulation study and their application and formulas for the different levels of the hierarchies

Weighting approaches School level Student level
No weights
Unscaled weights $${w}_{i}$$ $${w}_{ij}$$
Only student weights   $${w}_{ij}$$
Only school weights $${w}_{i}$$
Scaled weights: Cluster $${w}_{i}$$ $${w}_{ij }\frac{{n}_{i}}{\sum_{j=1}^{{n}_{i}}{w}_{ij}}$$
Scaled weights: ECluster $${w}_{i}$$ $${w}_{ij }\frac{{{n}^{*}}_{i }}{\sum_{j=1}^{{n}_{i }}{w}_{ij}}$$
Withincluster weights $${{w}_{i }}^{*}$$ $${{w}_{j }}^{*}$$
House weights   $${w}_{ij }\frac{n}{\sum_{j=1}^{n}{w}_{ij}}$$
Clustersum $$\sum_{j=1}^{{n}_{i}}{w}_{ij}$$ $${w}_{ij }\frac{{n}_{i}}{\sum_{j=1}^{{n}_{i}}{w}_{ij}}$$
1. Weighting parameters are $${w}_{i}$$ = final school weights, $${w}_{ij}$$ = final student weights, $${n}_{i}$$ = number of sampled students in a school,  $${{n}^{*}}_{i}$$ = number of assessed students in a school, $$n$$ = number of assessed students from all schools and $${w}_{j}$$= final within school weights