30457  STATISTICS  MODULE 2 (APPLIED STATISTICS)
Course taught in English
Go to class group/s: 13
Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)
Students are strongly advised to have the knowledge of basic concepts and methods of probability theory, descriptive statistics and statistical inference introduced in the course Statistics  Module 1 (Theory and Methods)  cod. 30456. It is strongly recommended that students thoroughly review these concepts before the course begins.
The empirical study of economic and social phenomena relies on the collection of significant amounts of data to describe the relationships among customers and firms on the markets. Similarly, managerial decision making needs to explicitly take into account data to identify the most profitable action in a business problem. Appropriate summary and organization of the data collected are crucial steps in a proper description of the phenomenon of interest. Nonetheless, by its very nature, available data represents only incomplete information about the subject matter; consequently conclusions drawn from it are affected by uncertainty, and decisions based on these conclusions might be subject to errors. The course aims at providing the student with appropriate methods and procedures to assess the reliability of the conclusions drawn from data and to monitor and guide the decision making process, avoiding gross mistakes and unpleasant consequences. These methods and procedures are widely known as Statistical Inference.

Introduction to the course content and teaching materials. Point estimation: basic concepts and examples (Chapters 5.1 of the textbook A and notes).

Estimators: definition and properties. Estimation methods (Chapters 5.1 of the textbook A and notes).

Confidence intervals based on pivotal quantities (Notes).

Confidence intervals: mean (with known and unknown variance) and variance of the normal population (Chapters 5.3 of the textbook A and notes).

Confidence intervals based on large samples for the mean, proportion and other parameters (Chapters 5.2, 5.3 and 5.4 of the textbook A and notes).

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).

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).

Pvalue. 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).

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).

Confidence intervals and hypothesis testing: the pivotal quantity approach (Notes).

Likelihoodbased inference: basic concepts (Chapters 2.1, 2.2, 2.3 and 2.5 of the textbook B and notes).

Likelihoodbased inference: confidence intervals (Chapters 2.4, 2.6, 2.7, 4.1, 4.4 and 4.8 and notes).

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

Review of the likelihoodbased inference and exercises (Notes).

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

Linear regression: least squares and model assumptions (Chapters 9.2, 9.3 and 9.6 of the textbook A and Notes).

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

Linear regression model: prediction and goodness of fit (Notes).

Inference for linear regression model based on the likelihood method (Notes).

Analysis of variance. (Chapters 12.112.3 of the textbook A and notes).

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

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

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

Rebiew of Logistic regression (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.
 Facetoface lectures
 Exercises (exercises, database, software etc.)
 Group assignments
 Facetoface 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.
Continuous assessment  Partial exams  General exam  

x  x  
x  x 
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 problemsolving ability of students. They need to be able to correctly identify a proper statistical methodology to solve a realworld 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. The grade of the assignment is valid also for the following academic years; hence you do not need to repeat the assignment. To consider the final successfully passed students need to obtain a grade of 18 points out of 31. A successful assignment will be valid for the whole current academic year. If a student does not pass the written exam within current 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).