The aim of this study is to construct an index to measure the socioeconomic status of students who took the standardized tests Saber 11◦ on 2012. In this study, the Colombian Institute for the Evaluation of Education (Icfes) is used corresponding to 424.916 students who participated in the tests and also responded to the sociodemographic questionnaire, consisting of 58 questions seeking some aspects related to their family, social, economic and cultural context. In the first part of the study a review of the literature is made, in order to define the variables and dimensions to be used in the construction of the socioeconomic status, once the possible variables are selected for inclusion in the index, it is passed to the second part in which a Principal Component Analysis (PCA) to summarize information as possible into a single component called socioeconomic index, using the methodology made in Flores et al. (2008). Since most categorical variables are plans to use the method of optimal allocation in order to attribute weights to analyze quantitatively those categories (De Leeuw & Mair 2009). Finally an analysis of the academic achievement given the socioeconomic status of students is made, a high correlation between the score and the socioeconomic status was obtained.

The methodology proposed by Tellez & L´opez-R´ıos (2013) for increasing the number of support points in a design is implemented in a D-optimal Bayesian design by two-compartment models. Data presented on Fresen(1986) are considered, referenced on Atkinson et al. (2007), where they modeled the ratio between Theophylline inoculated into the blood of a pony and the reaction time of the drug from a two-compartment model. The analytical results obtained in the paper previously validated and good behavior of the method is shown in terms of power and efficiency when compared to other designs available in the literature.

The Ministerio de Educaci´on Nacional de Colombia (MEN), is increasingly concerned about the continuous improvement on teaching processes of the foreign languages teachers and has commissioned the assessment of this process to the Instituto Colombiano para la Evaluaci´on de la Educaci´on (Icfes), in order to assess the knowledge of those teachers and ensure that they conforms to the quality standards of the Common European Framework of Reference for Languages (CEFR). The reduction of the estimation errors results as a key objective in the rating process of the tests That are Implemented by the Icfes, in order to improve increase accuracy for Evaluating parameters: such as the difficulty of the test and the performance of Those Who present the test. In a brief comparison este documento Between classical and Bayesian methodology for Rasch model is provided, esta comparison contains the behavior and upkeep of the classic assumptions for the second methodology. Furthermore the reduction of the errors for the Ability and difficulty parameters in the Bayesian framework is presented.