Ability measures based on response probabilities representing knowledge.

Autor/in	Rohwer, Götz
Institution	Ruhr-Universität Bochum
Titel	Ability measures based on response probabilities representing knowledge.
Quelle	Bochum: Ruhr-Universität Bochum (2015), 33 S. PDF als Volltext kostenfreie Datei Link als defekt meldenVerfügbarkeit
Beigaben	Literaturangaben
Sprache	englisch
Dokumenttyp	online; Monographie; Graue Literatur
Schlagwörter	Rasch-Modell; Kompetenzmessung; Test; Wahrscheinlichkeitstheorie; Studie
Abstract	I refer to a competence test, T_m, consisting of m binary items. The items are represented by variables, X1, . . . , Xm, having values 1 (if there is a correct answer) or 0 (otherwise). Values of these variables for the members of a population (or sample) P are given by vectors x_i= (x_i1, . . . , x_im), the sum score is denoted s_i:= sum_j(x_ij); i identifies members of P. A standard approach to the estimation of individual abilities w.r.t. T_m uses the Rasch model. This model postulates item parameters delta=(delta_1, . . . , delta_m), and for each person i a parameter theta_i, which together determine probabilities pi^R_ij:= Pr(X_j= 1\|theta_i, delta_j) := L(theta_i-delta_j) where L(x) := exp(x)/(1 + exp(x)), for person i's correctly answering to item j. A problem with this approach concerns the interpretation of these probabilities. How to understand, for example, that a person can correctly solve a mathematical task with a probability 0.2, or 0.4, or 0.6? In this paper I consider an alternative approach which defines response probabilities pi_ij by a reference to a distinction between 'knowing' and 'not knowing' (and possibly guessing) the correct answer to an item. By introducing interval-valued response probabilities, this approach also allows one to express the idea that a person's ability to correctly solving items is, to some degree, a vague notion. In Section 2 I introduce the approach for tests containing items which cannot be solved by guessing. In Section 3 I discuss multiple-choice (MC) items, and in Section 4 I compare the approach with the Rasch model. (Orig.).
Erfasst von	DIPF \| Leibniz-Institut für Bildungsforschung und Bildungsinformation, Frankfurt am Main
Update	2018/3