Instructional goals
The Statistics course aims to introduce students to the main topics of probability and statistics, with particular emphasis on descriptive statistics, inferential statistics, the basic principles of econometrics, and causal analysis.
The course is designed to provide students with both theoretical and applied tools to understand, analyze, and interpret data in a rigorous, competent, and informed manner. Special attention will be devoted to the use of statistics as a support for economic analysis and evidence-based decision-making.
By combining methodological foundations with practical applications, students will develop the skills required to conduct data analysis in economic, business, and social contexts.
Prerequisites
Although there are no formal prerequisites, a basic knowledge of mathematics and programming is highly useful for a quicker understanding and application of the course contents.
Intended learning outcomes
By the end of the course, students will be able to understand and use the main tools of probability, descriptive statistics, and inferential statistics. In particular, they will be able to organize, represent, and summarize quantitative data, interpret key statistical measures, and assess the uncertainty associated with observed phenomena.
Students will also acquire the ability to apply basic statistical and econometric methods to the analysis of economic, business, and social data, developing the skills needed to formulate hypotheses, test them empirically, and interpret the results in a rigorous manner. They will be introduced to the principles of causal analysis and to the use of data as a support for economic and managerial decision-making.
Finally, the course aims to develop a critical and informed approach to empirical analysis, enabling students to distinguish between simple statistical associations and possible causal relationships, assess the quality of available evidence, and clearly communicate the results of their analyses.
Course Contents
The course is organized into four main modules, designed to guide students progressively from the understanding of data to their statistical and econometric analysis.
The first module is devoted to descriptive statistics. In this part of the course, students will be introduced to the fundamental tools used to collect, organize, represent, and summarize data. The module will cover the main measures of location, dispersion, and distribution shape, together with graphical and tabular methods for representing quantitative phenomena.
The second module focuses on probability theory. Students will study the basic concepts of uncertainty, random events, random variables, and probability distributions. Particular attention will be paid to the role of probability as the theoretical foundation of statistical inference and of the analysis of economic and social phenomena characterized by uncertainty.
The third module is dedicated to inferential statistics. Students will learn how to use information obtained from a sample to draw conclusions about a reference population. Topics will include sampling distributions, point and interval estimation, hypothesis testing, and the interpretation of statistical results.
The fourth module provides an introduction to the basic principles of econometrics. This part of the course will present the fundamentals of regression analysis, with particular reference to simple and multiple linear regression models. Students will be guided in understanding the connection between economic theory, empirical data, and statistical models, with an introduction to issues of causal interpretation and the use of data for economic and decision-making analysis.
Overall, the course combines theoretical foundations, practical applications, and examples drawn from economic, business, and social contexts, with the aim of providing students with a solid preparation for quantitative data analysis.
Reference Books
The reference textbook for the course is Prem S. Mann, Introductory Statistics, 7th edition. The textbook will serve as the main support for the study of the theoretical and applied topics covered during the course, with particular reference to descriptive statistics, probability, inferential statistics, and the introduction to statistical data analysis.
Additional materials, exercises, datasets, and supplementary readings may be provided by the instructor during the course.
Teaching Methods
The course combines theoretical lectures, applied exercises, and practical data analysis activities. Theoretical lectures will introduce the main concepts of probability, descriptive statistics, inferential statistics, and introductory econometrics, with particular attention to their interpretation and application in economic, business, and social contexts.
In addition to the theoretical component, the course includes statistics practice sessions aimed at consolidating the topics covered during the lectures. Students will be guided through problem sets and practical exercises, including dedicated in-class sessions with the Teaching Assistant, in order to develop an operational understanding of statistical methods.
Part of the course will also be devoted to the use of Python for statistics and data analysis. Through in-class practical sessions, students will have the opportunity to apply theoretical tools to real or simulated datasets, learning how to organize, analyze, interpret, and present the results of an empirical analysis.
Assessment Method
Students’ learning will be assessed through two main components: a mid-term quiz and a final written exam.
The mid-term quiz, scheduled halfway through the course, will consist of multiple-choice questions aimed at assessing students’ understanding of the main concepts covered in the first part of the course. The quiz will account for 20% of the final grade.
The final written exam will account for 80% of the final grade and will include open-ended theoretical questions and applied exercises. The exam is designed to assess both students’ knowledge of the theoretical concepts and their ability to apply statistical and econometric tools to concrete problems.
The overall assessment will therefore take into account students’ theoretical understanding of the topics, their ability to solve quantitative exercises, and their capacity to correctly interpret the results of statistical analysis.
Thesis assignment criteria
No specific criteria are provided for the assignment of the final paper.
Week 1
Introduction to the role of statistics in economic, business, and social analysis. Definition of population, sample, qualitative and quantitative variables. Data collection, classification, and organization. Frequency tables, frequency distributions, and introductory graphical representations.
Week 2
Analysis of the main measures of location: mean, median, mode, quartiles, and percentiles. Introduction to measures of dispersion: range, variance, standard deviation, and coefficient of variation. Economic interpretation of statistical measures.
Week 3
Study of the shape of distributions, skewness, and kurtosis. Graphical analysis of data through histograms, boxplots, and scatterplots. Introduction to relationships between quantitative variables: covariance and correlation. Applications to economic and business data.
Week 4
Introduction to uncertainty and random events. Sample space, simple and compound events, classical, frequentist, and subjective probability. Basic probability rules, complementary events, union and intersection of events.
Week 5
Conditional probability, independent and dependent events. Multiplication rule, law of total probability, and introduction to Bayes’ theorem. Applications of conditional probability to economic, managerial, and decision-making problems.
Week 6
Definition of discrete and continuous random variables. Expected value, variance, and standard deviation of a random variable. Introduction to the main probability distributions, with particular attention to the binomial distribution and the normal distribution.
Week 7
Introduction to sampling and the role of samples in statistical inference. Concept of sampling distribution. Sample mean, sample proportion, standard error, and the central limit theorem. Connection between probability and statistical inference.
Week 8
Estimation of population parameters using sample data. Properties of estimators. Construction and interpretation of confidence intervals for means and proportions. Confidence level, margin of error, and sample size.
Week 9
Introduction to the logic of statistical tests. Null and alternative hypotheses, Type I and Type II errors, significance level, and p-value. Tests for means and proportions. Interpretation of results and connection with economic and empirical applications.
Week 10
Introduction to the simple linear regression model. Relationship between dependent and independent variables. Ordinary least squares method. Interpretation of coefficients, residuals, and goodness of fit.
Week 11
Extension to the multiple linear regression model. Interpretation of coefficients holding other variables constant. Control variables, statistical significance, R-squared, and limitations in the interpretation of results. Applications to economic and business data.
Week 12
Distinction between correlation and causality. Introduction to endogeneity, omitted variables, and causal interpretation of coefficients. Examples of empirical analysis in economic and managerial contexts. Review of the main course topics and connection between descriptive statistics, probability, inference, and econometrics.