Schools' socioeconomic status (SES) has been claimed as an important influence on student performance and there are calls for a policy response. However, there is an extensive literature which for various reasons casts doubt on the veracity of school-SES effects. This paper investigates school-SES effects with population data from a longitudinal cohort of school students which includes achievement measures in Years 3, 5 and 7. Estimates for school-SES are unstable under differing model and measurement specifications. School-SES effects are trivial controlling for student-and school-level prior ability. Inconsistent with theoretical explanations, school-SES effects were stronger with weaker SES measures. Furthermore, school-SES effects differ somewhat by achievement domain. Also contrary to expectations, there were school-SES effects on Year 7 achievement in secondary school for the primary schools students attended in Year 5. In each of five domains of achievement, fixed effect models show a small negative effect for school-SES and a small positive effect for school-level prior ability. The large school-SES effects prominent in some research and policy literatures are statistical artefacts.