About 2 per cent of schools are being classified as "failing" by inspectors from the Office for Standards in Education. There are good reasons to believe that they are mistaken in the majority of cases because, among other things, they are "neglecting the base rate". Even a very accurate test is likely to make many errors when detecting something with a very low probability.
Given a base rate of 2 per cent, the probability of error could be calculated if we also knew the reliability of the inspectors' judgments and used that to estimate their accuracy. No proper tests of reliability have ever been made but if we assume, generously and unrealistically, an accuracy of 95 per cent, the likelihood of false classification is 72 per cent. The method for calculating this was published by the Reverend Thomas Bayes in 1763, and there is nothing new or controversial in it.
The real base rate is probably less than the 2 per cent currently found, and the accuracy of OFSTED's procedures lower than I have assumed. So an even greater proportion of its classifications are likely to be wrong.
These calculations must be taken seriously. It is unfortunate that OFSTED does not appear to consider them, or the measures which might give its judgments greater credibility. Among other things, it should estimate the reliability of its methods and use independent assessments to improve the accuracy of its classifications. A second visit is sometimes made, but this can hardly be described as independent. OFSTED's work is amateurish and our education system deserves better.
IAN HOWARTH Emeritus professor Department of psychology Nottingham University