The main aim is to endow students with basic statistical tools for collecting and analysing univariate and bivariate data for political, economic, and social sciences applications. Descriptive statistics provide methods for data explorative analysis. Probability theory provides models for phenomena that are subject to uncertainty. Statistical inference provides methods for analyzing data obtained from random experiments. Practical lessons dealing with real-world examples are designed to allow students to improve their abilities in collecting, analyzing, interpreting, and presenting findings and data, also using statistical software and advanced spreadsheet (EXCEL). The EU digital competencies DIGCOMP 2.1 are developed (Competence area 1: information and data literacy; Competence area 2: communication and collaboration; Competence area 3: digital content creation).

Knowledge and understanding: knowledge of data types and related univariate analysis techniques (frequency distributions, graphical representations, central tendency, and dispersion measures), probability theory, statistical inference, association in two-way tables, and linear regression. Applying knowledge and understanding: ability to select appropriate data analysis methods to analyze the relationship between variables in economics, finance, and business Making judgments: ability to collect, use and critically interpret quantitative and qualitative data relating to economics and social sciences, achieved through the analysis of documents issued by official national and international statistics, scientific articles on statistical methods and applications, and case studies. Digital competencies are developed. Communication skills: effective skills in communicating data analysis output through written tests and the presentation of research results on empirical data. Learning skills: ability to learn autonomously data analysis techniques in professional activities or subsequent studies, achieved through the analysis of statistical methods applied in economics and social sciences

Theoretical lessons. Descriptive statistics: Basic concepts. Statistical variables. Frequency distributions. Data graphical representations. Measures of central tendency. Index numbers. Variability. Joint distributions: dependence, regression, correlation. Probability. Random experiments and events. Probability axioms and theorems. Discrete and continuous random variables. Probability distributions. Statistical inference: Sampling distributions. Point Estimation. Interval Estimation. Statistical hypothesis testing. Practical lessons dealing with real-world examples in political, economic, and social sciences.

Cicchitelli, P. D'Urso, M. Minozzo Title: "Statistics: principles and methods" con MyLab – Pearson Seeing Theory: https://seeing-theory.brown.edu

Lectures, exercises, applied exercises, interactive visualization, case studies in political, economic and social sciences based on real data, also using statistical and econometric packages and advanced spreadsheet

The final examination is in the form of a written test and a Project Work on real data. The written test can consist of three tests with an evaluation out of tenths (the last test is taken during the first session), and the final score is the sum of the scores in the three tests. During the first session, it is possible to keep the first two partial tests valid and to take only the third test (note that the student can take it just once; if she/he withdraws, the test is not counted). Alternatively, the student can opt for a single complete test with an evaluation out of thirty. Therefore, the student can take three written tests, each with an evaluation in tenths or a unique test with an evaluation out of thirty. In the case of three tests, the final score is the sum of the three scores. If the student is not satisfied with the grade obtained, she/he can refuse it and take the exam with a single complete test, in any case. Any written test consists of both theoretical and empirical questions, including multiple-choice questions. It verifies the acquisition of Knowledge and understanding, Applying knowledge and understanding, Making judgments. The project work on real data consists of a report on the statistical analysis of empirical data to be carried out in groups of a maximum of three students with the aid of the advanced spreadsheet (EXCEL). It verifies the acquisition of Making judgments, Communication Skills, Learning Skills, Digital skills (1, 2, 3), teamwork, time management, and development of new strategies and solutions to solve problems. The Project Work involves an additional score of up to 1 point on the grade obtained in the written test. The final grade of the exam is obtained by adding to the outcome of the written test the grade obtained in the Project Work (0 or 1 point), limited to the test taken - with any outcome – during the first exam session. WRITTEN EXAMINATION: this type of examination ("scritto verbalizzante") consists of a written test without a subsequent oral examination. The student must book for the written test. At the end of the final examination, the teacher corrects the homework and publishes the results on the dedicated VOL web page (within one week from the end of the written examination). The students enrolled in the final exam will receive a communication with the results of the final examination (the outcomes of the written examination will also be displayed on the web self-service). Since the publication of the results, the student has 3 days to reject the grade. Once the 3-day period is elapsed, the rule of "tacit consent" applies, and the examination result is verbalized by the teacher. The teacher has to close down the verbal through the digital signature. Once the verbal is closed down, the student receives an e-mail communication reporting the mark obtained. The text of the final proof and the corresponding solutions are made available on the class website before the publication of the results. Each candidate can access the solution of the written exam in a way that, independently from the final outcome of the exam, the student will be on time to be able to reject the proposed vote.

The final essay is a work in which statistical methods are applied in politics, economics, or society. The topic is agreed upon with the teacher.