League tables and school effectiveness: a mathematical model.

'School performance tables', an alphabetical list of secondary schools along with aggregates of their pupils' performances in national tests, have been published in the UK since 1992. Inevitably, the media have responded by publishing ranked 'league tables'. Despite concern over the potentially divisive effect of such tables, the current government has continued to publish this information in the same form. The effect of this information on standards and on the social make-up of the community has been keenly debated. Since there is no control group available that would allow us to investigate this issue directly, we present here a simple mathematical model. Our results indicate that, while random fluctuations from year to year can cause large distortions in the league-table positions, some schools still establish themselves as 'desirable'. To our surprise, we found that 'value-added' tables were no more accurate than tables based on raw exam scores, while a different method of drawing up the tables, in which exam results are averaged over a period of time, appears to give a much more reliable measure of school performance.