In protracted longitudinal studies of cognitive changes in old age volunteers must be repeatedly tested. Even with intervals of several years between assessment, this raises the possibility that improvements due to practice mask other changes. This problem is much more acute in brief studies of cognitive changes associated with progressive pathologies such as Alzheimer's disease or the effects of clinical interventions. Both types of study also encounter problems of selective dropout of frail and less able individuals leaving relatively 'elite' survivors. An analysis of data from repeated testing at 2-3 years intervals on the AH4 (1) intelligence test is presented to illustrate how a random effects model can be used to identify and disassociate age-related changes and practice effects at the population level, after effects of selective dropout and of background demographical variables have been taken into consideration. This analysis also provides some new, substantive empirical findings. Age-related changes are relatively slight between 49 and 70 years but much more marked between 70 and 80 years. Even with assessment points, several years apart the population average effect of practice is large relative to that of age-related change. Variation between individuals increases as samples age, providing the first clear evidence from a longitudinal study for marked individual differences in trajectories of cognitive ageing.