Surmise relations between tests

Abstract

Abstract Our work is based upon the theory of knowledge spaces, which was introduced by Doignon an Falmagne in 1985. They used prerequisite relationships between items within a body of information for the assessment and training of knowledge. Often it is useful to partition such a body of information into special fields - subjects, tests , courses or whatever. As we are mostly interested in psychological applications, we will refer to these special fields as tests, but, generalized, it is of course also possible to regard subjects, courses or grades instead of tests. Regarding a given set of such tests, we now want to investigate the relations and dependencies, parallelity and unifiability of these tests. Therefore, we extend the concept of prerequisite relationships items within tests to prerequisite relationships between tests . Such a prerequisite relationship is the surmise relation between tests . After its definition we discuss its properties and special cases. Then we introduce the test knowledge space, which plays a central role in our concept. Under certain circumstances it is possible to find a base for a test knowledge space. The base is a very effcient way of storing information about the test knowledge space. Moreover, we show that by means of the base not only the test knowledge space, but also the surmise relation between tests and its properties can be inferred. As this is a report on research in progress, we finally want to give a short overview about the further research regarding this mathematical model. This model will be a basis for a software system that will analyze tests as well as partition sets of items into tests.