ABSTRACT
This chapter introduces a completely different approach to assessing ability from test scores, one that does not require the use of norms and does not even require that respondents should all take the same items. It refers to ability scales, as the mathematics for these is somewhat easier given that each item is only scored 1 or 0. The chapter outlines the principles apply to Likert-scaled items too – these are known as 'ordered-response' scales in the item response literature. It points out that one of the problems with Louis Guttman scaling is that data simply do not fit that convenient model in real life unless the items differ so enormously in difficulty that administering them would make little sense. The chapter argues that that the item characteristic curve shows the chances of people with various levels of ability passing a particular test item. It explores several techniques that estimate people's abilities and item difficulties simultaneously.
