some of these indicators mainly hisei index parental education levels and family structure have a small number of missing observations to ensure that the sample size and performance distribution are untouched by the matching exercise missing values for matching covariates were imputed through multiple imputation models royston the pisa survey has a complex structure similar to methods commonly used in other educational surveys such as the international association for the evaluation of educational achievement s iea trends in international mathematics and science study timss and progress in international reading literacy study pirls or the united states national assessment of educational progress naep with sampling conducted with different probabilities in two stages within separate strata this complexity should be taken into account by using probability weights when calculating point estimates and by adjusting for clustering and strata design when estimating standard errors