STATISTICS AND THE THEORY OF MEASUREMENT

Just as there are different interpretations of probability, leading to different kinds of inferential statements and different conclusions a bout statistical models and questions, so there are different theories of measurement, which in turn may lead to different kinds of statisti cal model and possibly different conclusions. This has led to much con fusion and a long running debate about when different classes of stati stical methods may legitimately be applied. This paper outlines the ma jor theories of measurement and their relationships and describes the different kinds of models and hypotheses which may be formulated withi n each theory. One general conclusion is that the domains of applicabi lity of the two major theories are typically different, and it is this which helps apparent contradictions to be avoided in most practical a pplications.