This study examines the effect of school socioeconomic composition on student achievement growth in Australian schooling, and its relationship with academic composition utilising the National Assessment Program--Literacy and Numeracy (NAPLAN) dataset. Previous research has found that school composition predicts a range of schooling outcomes. A critique of school compositional research has been that measurement error may have biased findings of compositional effects. Prior studies have found that socioeconomic compositional effect sizes are small when models include academic composition. The relationship between socioeconomic and academic compositions has yet to be fully determined. Multi-level regressions and structural equation models were compared to estimate the degree of bias in socioeconomic compositional effects due to measurement error. Multi-level path models were used to test if academic composition mediated the relationship between socioeconomic composition and achievement growth. The results showed that measurement error did not bias compositional effects in the dataset, and academic composition mediates the relationship between socioeconomic composition and achievement growth. We argue that school value-add research should include academic composition to account for contextual effects. The socioeconomic compositional effect is of practical significance to policy makers and educational researchers due to its relative size compared to average student achievement growth. Potential reforms include ensuring public subsidies to private schools in Australia do not increase school segregation and the amelioration of the effects of residential segregation through school funding reforms.