On designing data-sampling for Rasch model calibrating an achievement test
Klaus D. Kubinger, Dieter Rasch, Takuya Yanagida · 2009
In correspondence with pertinent statistical tests, it is of practical importance to design data-sampling when the Rasch model is used for calibrating an achievement test. That is, determining the sample size according to a given type-I- and type-II-risk, and according to a certain effect of model misfit which is of practical relevance is of interest. However, pertinent Rasch model tests use chi-squared distributed test-statistics, whose degrees of freedom do not depend on the sample size or the number of testees, but only on the number of estimated parameters. We therefore suggest a new ap-proach using an F-distributed statistic as applied within analysis of variance, where the sample size directly affects the degrees of freedom. The Rasch model’s quality of specific objective measurement is in accordance with no interaction effect in a specific analysis of variance design. In analogy to Ander-sen’s approach in his Likelihood-Ratio test, the testees must be divided into at least two groups accord-ing to some criterion suspected of causing differential item functioning (DIF). Then a three-way analy-sis of variance design ()A B C×; with mixed classification is the result: There is a (fixed) group factor A, a (random) factor B of testees within A, and a (fixed) factor C of items cross-classified with A B; ; obviously the factor B is nested within A. Yet the data are dichotomous (a testee either solves