30456 - STATISTICS - MODULE 1 (THEORY AND METHODS)

The aim of the course is to provide students with a first introduction to the main concepts of statistical thinking, both descriptive and inferential. The most relevant techniques for collecting and analyzing data are first explored. The course then introduces the fundamental principles of probability theory and random variables, as a basis for better understanding the point estimation theory. The focus is on analyzing real data, illustrating some of the methods and concepts with the help of the statistical software R.

The course focuses on the following main topics:

• Basic univariate exploratory data analysis: frequency distributions, graphical representations, summary statistics of centrality and variability. 
• Basic bivariate exploratory data analysis: contingency tables, summary statistics of association and linear association, simple linear regression model.
• Probability: elementary set theory, events, algebras, axiomatic definition, conditional probability and elementary rules of calculus, Bayes' rule. 
• Random variables:  discrete and continuous distribution, expectation and moments, common families of distributions (Bernoulli, binomial, geometric, Poisson, uniform, normal, negative exponential).
• Functions of random variables.
• Random vectors: joint, marginal and conditional distributions, covariance and correlation coefficient, stochastic independence.
• Sampling: population and sample, inferential process, sample variability and sampling error, statistics.
• Sample mean: expected value and variance, distribution for normal and Bernoulli population, central limit theorem and convergence in distribution.
• Sampling from the normal distribution: sample variance and the Chi-square distribution, t-distribution.
• Point estimation: method of moments, maximum likelihood. Properties of estimators: unbiasedness, consistency and mean squared error. 

• Understand the fundamentals of statistical thinking, both descriptive and inferential.
• Reproduce the basics of descriptive statistics to economic data analysis.
• Illustrate the main concepts of probability and point estimation theory.
• Analyze real dataset on different socio-economic phenomena, with the aid of an adequate computer software.

• Summarize and visualize information contained in real data sets.
• Study the relationship between relevant variables.
• Choose adequate probabilistic models to represent data and learn from it in a statistical setting.
• Estimate unknown population parameters based on sampling information.
• Interpret the obtained results.

• Face-to-face lectures
• Exercises (exercises, database, software etc.)

Teaching and learning activities for this course are divided into:

• Face-to-face lectures during which statistical methods are explained and discussed.
• Exercises on quantitative methods.
• Applications on real data using the statistical software R. 

Both for attending and for non-attending students, the exam can be taken in two alternative ways:

• Two partial written exams (one in the middle and one at the end of the course), with exercises and questions about theory.
•  A written general exam with exercises and questions about theory.

Moreover, students have the opportunity to prepare a PC home assignment with the task of analysing a dataset, by applying the techniques learnt along the course. The PC home assignment is evaluated with a score of up to 2 points, which are added to the final grade of the written exam.

For both attending and non-attending students:

• S. M. ROSS, Introductory Statistics, Academic Press, Third Edition.
•  Additional teaching materials are announced before the start of the course and indicated on the Bboard platform. The slides of the course and additional exercises are uploaded to the Bboard platform of the course.