Course 2024-2025 a.y.

1. Introduction to the course content and teaching materials. Introduction to statistical inference: basic notions and notation (notes).

2. Point estimation: basic concepts and examples. Estimators: definition and examples. Estimation methods: basic techniques and examples (Chapters 5.1 of the textbook A and notes).

3. Estimators: properties and examples (Chapters 5.1 of the textbook A and notes).

4. Confidence intervals: basic concepts, intervals for the mean with known and unknown variance of the population (Chapters 5.3 of the textbook A and notes).

5. Confidence intervals based on large samples for the mean, proportion and other parameters. Relationship between sample size and length of the confidence interval (Chapters 5.2, 5.3 and 5.4 of the textbook A and notes).

6. Confidence interval for the difference between the means of two normal populations: case of dependent samples and independent samples with known variances and with unknown but equal variances (Chapters 7.1, 7.2, 7.3 and 7.4 of the textbook A and notes).

7. Confidence interval for the variance of the population (Notes).

8. Hypothesis testing: basic concepts (null and alternative hypothesis, type I and type II errors, rejection region, level of significance). Test for the mean of a normal population (known variance) (Chapters 6.1 and 6.2 of the textbook A and notes).

9. Hypothesis testing: rejection and non-rejection scheme, P-value, test for the mean of a normal population (unknown variance), test for the proportion of a population (large samples) (Chapters 6.1, 6.3 of the textbook A and notes).

10. Calculation of the Type II error probability and of the power of a test. Test for the difference between the means of two normal populations: dependent samples, independent samples (with known variances and with unknown but equal variances) (Chapters 6.4 and 6.6 of the textbook A and notes).

11. Test for the unknown variance of the population (Notes).

12. Correlation and simple linear regression (basic notions and model assumptions) (Chapters 9.1 and 9.4 of the textbook A and notes).

13. Linear regression: least squares criterion and goodness of fit (Chapters 9.2, 9.3 and 9.6 of the textbook A and Notes).

14. Inference for linear regression model: confidence intervals and hypothesis testing (Chapter 9.5 of the textbook A and notes).

15. Linear regression model: prediction and Analysis of Variance (Notes).

16. Likelihood-based inference: definition, basic concepts and scopes (Chapters 2.1, 2.2, 2.3 and 2.5 of the textbook B and notes).

17. Likelihood-based inference: observed information, expected information and confidence intervals based on large sample theory (Chapters 2.4, 2.6, 2.7, 4.1, 4.4 and 4.8 of the textbook B and notes).

18. Likelihood-based inference: large sample testing (Chapters 9.1, 9.2, 9.3, 9.4 and 9.5 of the textbook B and notes).

19. Likelihood-based inference: linear regression parameters and further examples and exercises. (Notes).

20. Categorical data analysis: expected frequencies and Chi-squared test (Chapters 8.1 and 8.2 of the textbook A and notes).

21. Categorical data analysis: odds and odds ratio (Chapter 8.4 of the textbook A and notes).

22. Logistic regression I (Chapters 15.1, 15.3 of the textbook A and notes).

23. Logistic regression II (Chapters 15.4, 15.5 of the textbook A and notes).

24. Concluding remarks and exercises (Notes).

• Recognize different types of inferential problems.
• Identify the appropriate inferential tool to solve the problem.
• Recognize different types of statistical models underlying the problems.

• Build simple statistical models.
• Provide interval estimates and test hypotheses on the unknown parameters of a population on the basis of sample data.
• Use the R software to perform real data statistical analysis.

• Lectures
• Practical Exercises
• Collaborative Works / Assignments

• Face-to-face lectures and Exercises (exercises, database, software etc.)
• Exercises (Exercises, database, software etc.): the learning phase includes workshops where students practice with statistical analysis of real data sets in order to learn how to perform and interpret real research management reports. Students have the opportunity to learn how to use the software R for data analysis on real databases provided by the instructor. Finally theoretical exercises are solved together with the instructor during exercise and tutorial lessons.

The assessment methods have been designed to stimulate your active involvement in the course. The grade breakdown is as follows:

• Group assignment: 30%
• First and second partial or final written exam: 70%
• At the end of the course there is an exam to test the knowledge acquired. There is a written exam with questions and exercises on the topics taught in class (see the detailed description). The open answer questions ascertain the problem-solving ability of students. They need to be able to correctly identify a proper statistical methodology to solve a real-world problem, provide the correct solution of the problem and formulate the correct interpretation of the obtained results. The maximum grade for the final exam is 22 points. To consider the final written exam successfully passed students need to obtain a grade of 12 points. Alternatively, students can complete two partial exams during the course. The maximum grade for the partial exams is still 22 points for both. Students can attend the second partial exam if they have obtained a minimum grade of 11 points in the first partial exam. If the second partial exam is not handed in, the student must take the final exam. To consider the the two written partial exams successfully passed students need to obtain an average grade of 12 points between the two exams.
• During the course there is also an assignment (empirical analysis) that students should perform on their own or in groups and hand in before the end of the course. The assignment ascertains the ability of student to formulate a correct statistical methodology to analyse a real dataset, perform an appropriately statistical analysis of the available data and correctly interpret the outcome. The assignment is worth a maximum of 9 points. To consider the final successfully passed students need to obtain a grade of 18 points out of 31. A successful assignment is considered valid for the current academic year and the following one. If a student does not pass the written exam within the following academic year, the assignment must be retaken. The examination procedures are the same for students who attend and do not attend the classes.

• A. AGRESTI, B. FINLAY, Statistical Methods for the Social Sciences, Prentice Hall, 2017, 5th edition.
• Y. PAWITAN, In All Likelihood: Statistical Modelling and Inference Using Likelihood, Oxford University Press, 2001.
• A selection of notes and other materials, available in the course reserve (Bboard).