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# Regional Economic Disparities as Determinants of Students’ Achievement in Italy: Data and methodology

The statistical methodology: a description of the multilevel strategy
The strategy is based upon a two-stage approach: in the first, we estimated an “empty” model, to decompose the variance between student-level and school-level, while in the second we added explanatory variables both at student and school levels.
Phase 1. The “empty” model
The coefficient represents the part of the total variance that could be imputed to the “among schools ” variance. If P^0,a multilevel model will be adopted to account for the hierarchical nature of the data. Mobile phones

Phase 2. The multilevel model with random intercept
In this second step, we added to the empty model some independent variables, which aim is to explain the within-school and among-schools variance.
In the analysis, we employed two levels of variables (to account for the hierarchical structure of data): student-level (level 1) and school-level (level 2).
All the data at the individual level come from the Invalsi dataset, which refer to the final examination at the end of the lower-secondary education (reference year: 2008/09). We used two alternative output indicators: the test scores in reading (Reading_Score) and Math (Math_Score). In the remainder of the paper, all results concern Math Scores, as no interesting alternative patterns emerged for Reading. The scores have been standardized into a range, that represents the percentage of right answers to the questions of the test. We chose to use data about 2008/09, even though also those for 2007/08 were available, after a previous wave of research on the latter. We found that they were unreliable. Indeed, we found no differences among macro-areas (Northern, Central and Southern Italy), and this fact was very unrealistic given that previous literature unanimously acknowledged the existence of strong differences. This problem has been widely discussed in the descriptive report provided by Invalsi (2008a), that suggests three potential hypotheses:
•    Higher motivation for students in the South at the moment of a national (standardized) test, that also is important for their academic career (indeed, it is the final exam at the end of lower secondary education, and not an experimental test – as typically are the international ones);
•    The items proposed in the test are more focused on the specific competences provided by Italian schools than others proposed elsewhere (e.g. OECD-PISA, TIMSS, PIRLS), so differences are lower here than in other cases because the specific questions included in the national test are more specifically taught homogenously in the different geographical areas (while competencies as measured by OECD-PISA etc. are more related to socio-economic conditions);
•    There was an opportunistic behaviour by teachers in the schools of the South (e.g. cheating).