BackgroundLearning outcomes are considered positive indicators towards future economic social and cultural opportunities of a number of countries (Woessmann 2004). Therefore, over the last decades, studies facing inequality issues in educational outcomes using cognitive achievement tests and variables from large-scale assessment data have increased. From a methodological point of view, the traditional approach used to explore the relationship between explicative variables and students' performance is based on average effects within a classical linear regression setup (OECD 2012). Undoubtedly, estimates on average will yield straightforward interpretations but will represent only a part of the information concerning the complex and nuanced nature of the relation between predictors and conditional performance distribution. Essentially, the main concern for policy purposes might be not only to assess if the relevant variables carry an impact or not, but AbstractThe number of studies addressing issues of inequality in educational outcomes using cognitive achievement tests and variables from large-scale assessment data has increased. Here the value of using a quantile regression approach is compared with a classical regression analysis approach to study the relationships between educational outcomes and likely predictor variables. Italian primary school data from INVALSI large-scale assessments were analyzed using both quantile and standard regression approaches. Mathematics and reading scores were regressed on students' characteristics and geographical variables selected for their theoretical and policy relevance. The results demonstrated that, in Italy, the role of gender and immigrant status varied across the entire conditional distribution of students' performance. Analogous results emerged pertaining to the difference in students' performance across Italian geographic areas. These findings suggest that quantile regression analysis is a useful tool to explore the determinants and mechanisms of inequality in educational outcomes. A proper interpretation of quantile estimates may enable teachers to identify effective learning activities and help policymakers to develop tailored programs that increase equity in education. Costanzo and Desimoni Large-scale Assess Educ (2017) -scale Assess Educ (2017) 5:14 also to investigate if and how they are associated with greater or lower variation in educational outcomes. METHODOLOGYPage 2 of 25 Costanzo and Desimoni LargeConsistently, some studies have been recently enhanced by using models which extend the viewpoint on the whole conditional distribution of performance representing the different levels of students' attainment (Fryer and Levitt 2010;Davino et al. 2013), i.e. the quantile regression model (Koenker and Basset 1978). In the present study, the differential impact of variables related to inequalities in educational outcomes will be assessed through the quantile regression (QR) approach using data from the Italian Annual Survey on Educational Achievement (SNV)...

The effectiveness of a training program on students' achievements has primarily relied on estimation approaches which capture the mean effect on students' performances. While estimating how "on average" variables affect educational outcomes yields straightforward interpretations, the standard methodology may miss what is crucial for policy purposes, namely how educational programs affect students achievements differently at different points of the conditional test score distribution. The aim of this study is to investigate the short term effects of M@tabel on Italian sixth grade students performance in mathematics at secondary schools through a multilevel quantile regression approach. The proposed model allows to fully characterize the entire conditional distribution of performances in mathematics, providing a more complete view of a possible relationship between M@tabel treatment and the observed math score gain. The main concern is not only "does the training program have an impact" but also the question "for whom does it matter, and how".

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