Cognitive acceleration programmes, started in the early 1980s, have now been run in many hundreds of schools in many parts of the world. One important feature of these programmes is that their effects have been evaluated by following up participant students for some years after the intervention. This has provided extensive experience in the process of collecting and assessing the value of the evidence collected. In this paper, I will abstract this experience from the particularities of cognitive acceleration, in an attempt to draw general conclusions about what can, and what cannot, legitimately be claimed from long-term evidence obtained in various ways. In the process, some implicit guidelines for the design of educational experiments and of associated testing programmes will be developed.