30401 - MATHEMATICS AND STATISTICS - MODULE 2 (STATISTICS)

To feel comfortable with some topics in this course, students should be familiar with differential and integral calculus.

The course explores techniques for collecting and analyzing data. Concepts of statistical thinking, both descriptive and inferential, are covered. The course introduces the fundamental principles of probability theory and random variables, as a basis for the better understanding of inferential techniques. 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 points:

• Introduction to probability: basic definitions and properties.
• Random variables: discrete and continuous models and their properties.
• Data collection and description through frequency distributions, graphical representation methods, and measures of location and spread.
• Inferential statistics, population, sampling, sampling variability and sample statistics.
• Point and interval estimation.
• Parametric hypothesis testing for the population mean and the proportion of successes.
• Nonparametric hypothesis testing for two-way tables.
• Introduction to ANOVA (Analysis of Variance) methods.

• Understand basic concepts of probability required for the use and interpretation of statistical methods.

• Describe a dataset through adequate graphs, tables and statistics.

• Identify if the structure of the data allows the application of basic statistical inferential methods.

• Do inference on the mean of a population (point estimation/ prediction, interval estimation, hypothesis testing).

• Understand the fundamental logic of estimation and hypothesis testing.

• Do inference regarding the difference (or not) between the means of more than one population.

• Do basic nonparametric tests for two-way tables.

• Understand the challenges derived from the presence of uncertainty in real-life situation.

• Choose and apply adequate (basic) statistical tools to aid in the decision-making process by learning from available data.

• Interpret charts, graphs and statistics and identify possible misrepresentations of data.

• Question statements based on data, by analysing the statistical elements and the validity of the assumptions made.

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

Exercises (Exercises, database, software etc.):

• Special sessions (delivered by a second lecturer) for the application of theoretical concepts to solving exercises. Emphasis is given to the use of statistical software R for application to real-life and simulated datasets. 

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. Access to the second partial exam is limited to students who have passed the first (obtaining at least 18 points on each). For students taking both partial exams, the final grade is the average of the two partial marks.
• A written general exam with exercises and questions about theory.  

Both formats may require the use of the computer (R statistical software) for the exercise questions.  Exam rules and program are the same for attending and non-attending students. Further information and detailed syllabus for the course are published on the Bocconi University website.

• M. W. TROSSET, An Introduction to Statistical Inference and Its Applications with R, Chapman and Hall/CRC, 2009.
• Additional resources (lecture notes, exercises with solutions, past exams with solutions) may be available at the discretion of the lecturers.