## STATISTICS

No specific requirements. However, it is recommended a good knlowledge of the basic matematical concepts.

The exam aims to evaluate the achievement of the educational objectives related to the knowledge of basic statistical tools.

There are two forms of examination:

1) Full written examination focused on all course topics; 2) Two partial written examinations.

1) The Full 2-hour exam includes 6 exercises with the same overall score: 3 exercises focus on the topics of the first part of the course, 3 exercices on the second part of the course.

2) Two partial examinations lasting 1 hour and 30 minutes each.

The first partial exam, related to the topics of the first part of the course, includes 4 exercises with the same overall score. This exam can be taken only at the end of the first part of the course.

The following second partial exam, to whom are admitted the students who demonstrate an acceptable knowledge of the basic notions in the first, includes 4 exercises on the second part of the course, with the same overall score. The second partial exam can be taken during the session at the end of the lessons (three dates are available).

The final grade is given by an average of the two grades obtained in the partial examinations.

The minimum overall grade (both types of exams) requires the demonstration of an elementary knowledge of the basic notions relevant to the topic addressed while the maximum grade requires a full mastery of the analytical tools used during the lessons.

The aim of the course is to provide the student with the basic concepts and tools for conducting a statistical analysis.

At the end of the course, the student will have:

(1)Knowledge and understanding skills.

The student will have the knowledge and the ability to use the main methods of descriptive statistics, mastering, in particular, the main concepts and techniques for the collection, processing, summary description and study of data to conduct a statistical analysis. The student also obtains a basic knowledge of probability theory and methods of statistical inference.

(2)Ability to apply knowledge and understanding

The student will be able to: a) represent the phenomena studied, graphically and through appropriate synthesis indicators; b) perform probabilistic assessments in basic applications; c) perform interval estimates and perform simple hypothesis tests in the case of random sampling from normal statistical populations.

(3) Autonomy of judgment

Ability to interpret social economic phenomena, analyzed through the use of statistical indicators, framing them in the appropriate reference context and conducting correct comparisons over time and space.

(4)Communication skills

Although the course does not provide specific activities aimed at developing communication skills, the student will be able to operate within diverse working groups, using a quantitative analysis perspective and a statistical approach. The student will also be able to produce summary statistical reports on the main economic and social phenomena.

5) Learning skills

At the end of the course, the student will be able to use the pivotal concepts of the descriptive statistics and the basic elements of the inferential statistics to deepen the related themes in the context of advanced specialized courses.

Part 1 - DESCRIPTIVE STATISTICS

Introduction. Statistical surveys, phases of the survey. The data matrix.

Summary of the distribution of a character. Absolute and relative frequencies. Cumulative frequency distribution. Graphic representations.

Position and dispersion indices. Concentration.

Relationships between two characters. Double entry tables. Joint, marginal and conditional distributions. Independence in distribution and connection indexes. Linear dependence: covariance, correlation.

Part 2 - Linear Regression. Calculation of probabilities and Inference

The simple linear regression model.

Introduction to probability. Random phenomena and uncertainty. Events and sample space. Axioms of probability. Conditional probability.

Random variables: distribution and probability / density function. Expected value and variance. Normal distribution and standard normal distribution.

Population model and parameters. Random sampling: estimators and their sample distributions. Estimates and confidence intervals for the average of a normal distribution. Hypothesis testing: errors of I and II type, level of significance. Hypothesis testing in the case of random sampling from normal statistical populations.

S. Borra e A. Di Ciaccio (2014) Statistica. Metodologie per le Scienze Economiche e Sociali (III ed.), McGraw-Hill.

The course is held with lectures and tutorials, both based on the blackboard. The lessons are devoted to the exposition of the methodological concepts contained in the program, but also include examples and exercises. The tutorials include a synthetic presentation of the methodological concepts, but essentially have an applicative character (solution of exercises).

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