Ordering Individuals with Sum Scores: The Introduction of the Nonparametric Rasch Model.
When a simple sum or number-correct score is used to evaluate the ability of individual testees, then, from an accountability perspective, the inferences based on the sum score should be the same as the inferences based on the complete response pattern. This requirement is fulfilled if the sum score is a sufficient statistic for the parameter of a unidimensional model. However, the models for which this holds true are known to be restrictive. It is shown that the less restrictive nonparametric models could result in an ordering of persons that is different from an ordering based on the sum score. To arrive at a fair evaluation of ability with a simple number-correct score, ordinal sufficiency is defined as a minimum condition for scoring. The monotone homogeneity model, together with the property of ordinal sufficiency of the sum score, is introduced as the nonparametric Rasch model. A basic outline for testable hypotheses about ordinal sufficiency, as well as illustrations with real data, is provided.
University of Amsterdam, Amsterdam, The Netherlands. zwitser@uva.nl.
Robert J
RJ
Zwitser
University of Amsterdam, Amsterdam, The Netherlands.|Cito Institute for Educational Measurement, Arnhem, The Netherlands.
Gunter
G
Maris
D015233:Models, Statistical; D011594:Psychometrics; D012107:Research Design; D018709:Statistics, Nonparametric
monotone latent variable model; nonparametric IRT; nonparametric Rasch model; ordinal inferences; sufficiency; sum score