ABSTRACT
It would be a substantial achievement if in designing a way to make schools more effective we were able to overcome Matthew Effects and could make a significant difference to the disparities in achievement. But what would the evidence for this be? What would the evidence be that we have enabled schools to make a difference to those children not well served by schooling? What differences are educationally significant? The answers to these questions introduce several important concepts, which are partly statistical, and partly to do with defining educational significance. The concepts are acceleration, matched distributions of achievement, and shifting distributions.
