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<p>The diagnosis of learning disorders in children with German as a second language (L2) represents a challenge for psychological diagnostics. One goal of the DiLeDaZ project in the LONDI research network (Learning Disorders - Online Platform for Diagnostics and Intervention; coordination: M. Hasselhorn & G. Schulte-K├Ârne) is to review established reading, spelling and math tests with regard to their test fairness for L2 learners. One possible way to rule out discrimination against a subgroup (here: L2 learners) is to investigate measurement invariance (MI). In order to be able to compare latent mean values between different groups, here L1 vs. L2, the presence of MI is a prerequisite. So far, school achievement tests in Germany have not been tested sufficiently with regard to their invariance for children with German as their mother tongue (L1) and German second-language learners (L2). On the basis of available data sets, measurement invariance of some established reading, spelling and math tests was investigated by step-by-step procedures in two-group comparisons. The investigation revealed that all measurement models fit well with the data. A stepwise restriction of the models does not lead to a significant decrease in the model fit, so that the same assumptions hold for both groups regarding factor structure, loadings, item-specific difficulties and reliabilities. The assumption of a strict measurement invariance is justified for all tests examined here. Since the latent traits are thus measured identically in both groups, differences in test performance can be clearly attributed to existing differences in ability. Thus, the assessment of school achievement and a diagnosis of learning disorders based on these achievement tests are fair for L2 learners. However, the question now arises as to whether the same structural relationships between school achievement and known predictors can be demonstrated for children with L2 vs. L1, and whether weak reading, spelling or math performance in L2 learners can be attributed to the same underlying deficits as in children with German as their mother tongue.</p>
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