Programme for International Student Assessment data from 29 countries was used to measure immigrant school gaps (differences in scores between immigrants and natives) in relation to various potentially correlated factors. Results show that negative gaps are concentrated in the European Union; in the South, they are mainly correlated with school types--academic, intermediate or vocational--and country of origin; and in the North, they remain negative in all model specifications. This suggests a lack of assimilation, in some cases reinforced by educational institutions. Gaps are generally small in English-speaking countries; in the USA and GBR they are influenced by background.