The analyses, publications and reports of quantitative data in education and the social sciences usually omit basic information on the construct measured. Probabilistic models for test data make it possible to delineate coherent and richly described measurement continua that facilitate interpretation of student achievement. The potential of conjoint measurement to bring about fundamental advances in educational testing practice lies in part in the opportunities it provides to build useful maps of learning domains and to use those maps in communicating student achievements. This chapter presents two applications of conjoint measurement aimed at constructing and describing achievement variables, developing insights into the structure of learning domains, and providing descriptive interpretations of students' levels of achievement within those domains. Both applications are taken from work of the Australian Council for Educational Research in Melbourne.