The influence of Bhaskar's critical realism has become increasingly evident in the debate on the nature of educational research. This philosophy, dedicated to the overthrow of positivist doctrines, in particular those of empiricism, nominalism, and causation as constant conjunction, is the foundation of contemporary proposals for new perspectives and possibilities in educational research. There are, however, aspects of critical realism, as it is presented, that may repay further reflection. This article suggests that the rejection of statistical modelling by critical realism is not supported by scientific realism. The argument is illustrated by substantive analyses of the relationship between poverty and educational attainment (reading) using the PISA (Programme for International Student Assessment) 2000 UK data set. It is concluded that an approach to the construction of explanatory narratives based on scientific realism is more likely to effect a principled integration of the theory and practice of qualitative and quantitative research.