We discuss fixed and random effects models in the context of educational research and set out the assumptions behind the two approaches. To illustrate the issues, we analyse the determinants of pupil achievement in primary school, using data from the Avon Longitudinal Study of Parents and Children. We conclude that a fixed effects approach will be preferable in scenarios where the primary interest is in policy-relevant inference of the effects of individual characteristics, but the process through which pupils are selected into schools is poorly understood or the data are too limited to adjust for the effects of selection. In this context, the robustness of the fixed effects approach to the random effects assumption is attractive, and educational researchers should consider using it, even if only to assess the robustness of estimates obtained from random effects models. When the selection mechanism is fairly well understood and the researcher has access to rich data, the random effects model should be preferred because it can produce policy-relevant estimates while allowing a wider range of research questions to be addressed. Moreover, random effects estimators of regression coefficients and shrinkage estimators of school effects are more statistically efficient than those for fixed effects.