NEPS technical report for mathematics: Scaling results of starting cohort 3 for grade 12

The National Educational Panel Study (NEPS) aims at investigating the development of competencies across the whole life span and designs tests for assessing these different competence domains. In order to evaluate the quality of the competence tests, a wide range of analyses based on item response theory (IRT) have been performed. This paper describes the data for the mathematical competence test in grade 12 for starting cohort 3 (starting fifth grade). The descriptive statistics for the data, the scaling model applied to estimate competence scores, and analyses performed to investigate the quality of the scale as well as the results of these analyses are explained. The mathematics test for grade 12 consists of 30 items (distributed among an easy and a difficult booklet) which represent different content areas as well as different cognitive components and use different response formats. The test was administered to 3,786 participants in grade twelve. A partial-credit model was used to scale the data. Item fit statistics, differential item functioning, Rasch-homogeneity, and the test ́s dimensionality were evaluated to ensure the quality of the test. The results show that the items exhibited good item fit and measurement invariance across various subgroups. Moreover, the test showed a good reliability and a sufficiently broad range of item difficulties. As the correlations between the four content areas were very high in a multidimensional model and the model fit criteria favored the unidimensional model, unidimensionality of the test was assumed. Analyses of the missing responses showed that the test had too many items for the allocated test time. Overall, the results revealed good psychometric properties of the mathematics test, thus supporting the estimation of a reliable mathematics competence score. This paper describes the data available in the Scientific Use File and provides the R- Syntax for scaling the data.