Students should have completed the intro course ¿Mathematics for Social Sciences and Basic Statistics¿ or its equivalent. Students should have a working knowledge of arithmetic, algebra, and elementary calculus. The course is suitable for students with a large range of prior exposure to statistics and mathematics.

Knowledge or Content: K-7. Advanced knowledge and understanding of statistics applied to Social Sciences. K-8. Specialized and applied learning of quantitative research methods in the study of political and social phenomena. K-9. Advanced learning about the role of causality in Social Sciences. Skills: S-5. Ability to organize and express ideas clearly and unambiguously, and to support theoretical arguments on a topic through a critical analysis of the literature. S-7. Understanding the fundamental concepts of descriptive statistics, probability theory, and the foundations of inferential statistics. S-8. Knowing the properties of different types of quantitative data associated with the study of Social Sciences and mastering data analysis techniques. S-9. Understanding the techniques of causal inference in social research. Competences: C-7. Ability to select appropriate statistical models for data analysis within the framework of conducting research in Social Sciences. C-8. Handling quantitative research data: mastering analysis tools and data management software in the empirical development of a research paper. C-9. Being able to generate new data and apply causal inference techniques in the empirical development of a research question.

TOPIC 1. PROBABILITY 1.1 Random variables. Definition. Discrete and continuous variables. Cumulative distribution, probability density and probability mass functions. 1.2 Univariate and multivariate variables: marginal and conditional distributions. 1.3 Summarizing information of univariate variables: mean, variance, asymmetry and kurtosis. 1.4 Summarizing information of multivariate variables: Covariances and independence. 1.5 Some common univariate distributions: Bernoulli, Binomial, Poisson, Uniform, Normal 1.6 The multivariate normal distribution TOPIC 2. INFERENCE AND ESTIMATION METHODS 2.1 Population and sample: Parameters and statistics 2.2 Point estimation: means and proportions 2.3 Interval estimation 2.4 Hypothesis testing 2.5 Large samples: consistency and asymptotic distribution 2.6 Method of Moments estimator 2.7 Maximum Likelihood estimator TOPIC 3. REGRESSION MODEL 3.1 Simple Regression model: Conditional means 3.2 Estimating the parameters: Least Squares estimator 3.3 Properties of LS estimator: Consistency, normality and efficiency 3.4 Residual diagnostic 3.5 Hypothesis testing 3.6 Heteroscedasticity 3.7 Using the regression model to predict

Training Activities: AF3 - Theoretical-practical class: learning theoretical content on mathematics, statistics, and causal inference. AF4 - Laboratory practices: using software programs on computers to develop statistical models learned in theoretical classes. AF5 - Tutorials: the possibility of weekly meetings with the course instructor. AF6 - Individual student work. Teaching Methodologies: MD1 - Classroom presentations by the professor with the support of computer and audiovisual media, in which the main concepts of the subject are developed. MD3 - Resolution of practical cases, problems, etc., proposed by the professor individually or in groups. MD5 - Preparation of individual or group assignments and reports.