Data Analysis and Applications 2

11 How Variation of Scores of the Programme for International Student Assessment can be Explained through Analysis of Information

The Programme for International Student Assessment (PISA) is a triennial international survey that aims at evaluating education systems worldwide by testing the skills of 15-year-old students in three competence fields. The present contribution analyzes variations of PISA scores from 2003 to 2012 in France and Germany for mathematics literacy through a multiplicative model whose choice of parameters was introduced by Zighera in 1985. Thanks to construction through repeated analysis of Kullback–Leibler divergence, the parameters are meaningful in terms of information for testing simultaneously both direct and crossed effects of all explanatory variables on the evolution of scores. In particular, Zighera’s method is shown to highlight evolution in the sociodemographic composition of the sampled population that may affect the observed evolution of performance of students.

11.1. Introduction

PISA, coordinated by the OECD, compares outcomes of learning in mathematics, reading and science literacy around the end of compulsory schooling in numerous countries. Surveys are conducted every 3 years with samples of 15-year-old pupils who answer to many demographic and personal questions before scored questions in three competence fields, with a major and two minors. An OECD service is devoted to the development of questionnaires, management of surveys, analysis ...