Aim of the project is to use modern psychometric methods to analyze group differences in educational measurement, caused by gender, region, type of school, ethnicity, first language etc. Project covers methodology of psychometric models, especially models for detection of differential item functioning, mixed regression and latent models. These methods are further applied to data coming from formative assessment, such as concept inventories, as well as to data coming from summative assessment and high-stakes testing, such as leaving examinations or admission tests. As part of the project, new psychometric models are proposed, properties of which are studied by means of simulation studies. New methods are provided to wide research community by means of freely available software. By analyzing real data of educational measurement, and by further discussion of the obtained results, project aims to contribute to effectiveness in education.