The interpretation of the results from different assessments of an educational system comes with the problem of the comparability of scores. This is why the information provided by autonomic, national or international assessment programs can, in some cases, show important discrepancies. Under these circumstances, the questions are: Are the results of these assessments comparable? Is it possible to improve their interpretation? How can we benefit from the information of these assessments? The usual answer implies an equating design involving anchor items. But when one of the assessments affects the whole population of students, it’s extremely hard to warrant the due security of the items used as anchor. So, is it possible to relate the scale of such an assessment program to the scale of a well known program as PISA, which is tested on a sample of the population?
In order to answer these questions this paper introduces a procedure for comparing results from different evaluations. More specifically, it has been proposed a model to compare the results of the Diagnostic Evaluation of Educational System, carried out in the Region of Madrid (Spain), with the information provided by the OECD Program for International Student Assessment (PISA).
According to the Organic Law of Education (2/2006, 3rd of may), the General Subdirection of Assessment  and analysis of the Community of Madrid (Spain) (BOCM 31st of august) is responsible of the diffusion, the application and the correction of the tools in the Diagnostic Evaluation of this region and, for this purpose, it has been methodologically advised by the Education System Measurement and Assessment Group (Grupo MESE) of the Complutense University of Madrid. This assessment is intended to students of 4th year of Primary Education (EP) and 2nd year of Compulsory Secondary Education (ESO) of public, semi-private and private schools.
During the academic year of  2009/10, tests used in the program International Schools´ Assessment – ISA, designed and launched by the  Australian Council for Educational Research (ACER) in 2001 - were adapted to the Spanish educational system (ESP-ISA tests). ISA is an international assessment program for students in schools over the world in Grades 3 to 10 (9 to 16 years old). It shares the theoretical framework of the PISA program. ESP-ISA tests were constructed from a pool of ISA items, linked to PISA tests. Additionally,  ESP-ISA tests included released PISA  items. This way, two sets of item parameters were involved, those from English version of ISA items, and those from the Spanish version of released PISA items. Ideally, fixing these parameters would allow to estimate the score for each individual based on their answers to the whole test. But to refine the process, a procedure was implemented to select, as fixing items only those showing invariance when a free calibration took place.

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