STATISTICS
Instructional goals
Basic understanding of data collection, presentation and analysis, including use of statistical software. The basic notions of statistical analysis include the formulation of statistical models, the point and interval estimation of parameters and the interpretation of significance tests. The essentials of elementary probability theory, including elementary probability calculus formulae, discrete and continuous distributions and their (first and second order) moments, the law of large numbers and the basic central limit theorem.
By the end of the course the student will be able to continue the studies with a more advanced course on statistical methods, as well as to manage a first elaboration of a data set.
Intended learning outcomes
Knowledge and understanding: The student - by participating in the lectures and exercise sessions - develops the ability to understand the fundamental notions of Statistics and data analysis. The student will also be introduced to the use of statistical software
Applying knowledge and understanding: The student will be able to apply the notions and techniques described during the course and to present the results in a suitable way.
Making autonomous judgements:
The student will have acquired the ability to identify suitable solution methods for various problems and developed critical thinking and problem solving skills
Communication skills: At the end of the course the student will be able to express judgments and present the results of a statistical analysis of problems and/or data, with the required terminological precision and the appropriate technical lexicon.
Learning skills: The knowledge acquired during the course will allow the student to autonomously understand and interpret more advanced notions and techniques of the subject and adapt them to a specific reference context. The knowledge of the fundamental aspects of the subject acquired during the course will allow the student to engage in further studies in the subject, even on his/her own, and to participate in future post-graduate training.
Course Contents
Basic ideas in statistics: data collection, presentation, summary statistics and plots. Basic probability. Statistical models, and probability based statistical inference: estimation and hypothesis testing. Introduction to the use of statistical software
Reference Books
Ross, S. M. (2017). Introductory statistics (4th ed.). Elsevier/Academic Press.
Teaching Methods
Frontal lectures, exercise sessions with teaching assistant, use of R for data analysis.
Assessment Method
Students will be evaluated through the final written exam, covering the whole course program.
The final written exam consists of theoretical questions and practical problems aimed at verifying the student’s mastering of the basic notions and their application. In general, the exam will be formed by 5-6 questions.
During the semester, there will be 3 intermediate tests on various parts of the program, which may give bonus points to add to the final exam result.
NOTE: bonus points will be effective only if the final exam is taken during the summer session.
Thesis assignment criteria
Not relevant
Week 1 Contenuto sessioni on line e on campus
Ch 1 Introduction, data collection. Statistical models and parameters. The population and the sample.
Ch 4 Basic probability, events, experiments, conditional probability, independence, uniform spaces and notions of combinatorics.
Week 2 Contenuto sessioni on line e on campus
Ch 2/3
Descriptive statistics: tables, line plots, histograms, etc. Data examples. Summary statistics, mean, median, variance, standard deviation, covariance and correlation coefficient and percentiles
Week 3 Contenuto sessioni on line e on campus
Ch 4 Bayes' formula.
Ch 5 Discrete random variables, Bernoulli sequences, Bernoulli and Binomial distributions.
Week 4 Contenuto sessioni on line e on campus
Ch 5 Expectation and variance for discrete random variables. Transformations of discrete random variables. Linear transformations.
Joint distributions and independence. Hypergeometric and Poisson random variables.
Week 5 Contenuto sessioni on line e on campus
Ch 5 Covariance and correlation.
Ch 6 Continuous random variables, Normal random variables
Week 6 Contenuto sessioni on line e on campus
Ch 7 Sampling distribution of the sample mean and the sample variance. Central Limit theorem and its use for normal approximations. Very short outline on the chi-square and T distributions.
Week 7 Contenuto sessioni on line e on campus
Ch 8 Short introduction to inference questions and answers. Estimation, basic notions. Point estimation of population mean, variance and proportions.
Confidence intervals for the mean. Approximate confidence intervals based on Central Limit Theorem.
Week 8 Contenuto sessioni on line e on campus
Ch 9 Hypothesis Testing: basic ideas, significance level and related concepts. Test for a population means and for a population proportion.
Week 9 Contenuto sessioni on line e on campus
Ch 10 Hypotheses tests concerning two populations
Week 10 Contenuto sessioni on line e on campus
Ch 13 Goodness of fit and independence chi-square tests
Ch 12 Linear regression, the basic model and examples. Data examples for regression.
Estimation of parameters in linear regression. The Least Squares method.
Week 11 Contenuto sessioni on line e on campus
Ch 12 Regression to the mean. Correlations, residual analysis.
Week 12 Contenuto sessioni on line e on campus
Review