Surmise Relations Between Tests - Mathematical Considerations

Test Surmise Relations, Test Knowledge Structures, and Their Characterizations

This paper investigates natural, left-, right-, and total-covering test surmise relations on a set of tests partitioning the domain of a knowledge structure. The properties of reflexivity, transitivity, and antisymmetry are examined. In particular, it is shown that the property of antisymmetry is satisfied for the left-, right-, and total-covering test surmise relations when the underlying know...

The Correlational Agreement Coefficient CA(≤, D) - a mathematical analysis of a descriptive goodness-of-fit measure

The Correlational Agreement Coefficient, CA(V,D), was introduced by J.F.J. van Leeuwe in 1974 within Item Tree Analysis (ITA), a data-analytic method to derive quasi orders (surmise relations) on sets of bi-valued test items. Recently, it has become of interest in connection with Knowledge Space Theory (KST). The coefficient CA(V,D) is used as a descriptive goodness-offit measure to select out ...

Ordering Inductive Reasoning Tests for Adaptive Knowledge Assessments An Application of Surmise Relations between Tests

Knowledge Spaces for Inductive Reasoning Tests

Die Wissensraumtheorie (Doignon & Falmagne, 1985;1999), in der Testitems durch sog. Vermutungsrelationen geordnet werden, wurde verallgemeinert, um Vermutungsrelationen zwischen Tests zu definieren (Albert, 1995, Brandt, Albert & Hockemeyer, 1999;accepted). Als erste exemplarische Anwendung dieses Modells werden verschiedene Typen von induktiven Denkaufgaben nach dem Prinzip der komponentenweis...

Knowledge Space Theory

This document explains algorithms and basic operations of knowledge structures and knowledge spaces available in R through the kst package. Knowledge Space Theory (Doignon and Falmagne, 1999) is a set-theoretical framework, which proposes mathematical formalisms to operationalize knowledge structures in a particular domain. The most basic assumption of knowledge space theory is that every knowl...