OVERVIEW

The course “Statistics 1” aims to provide the main tools for quantitative data analysis with special attention to the measurement of economic and social phenomena. The skills acquired with this course are essential for the continuation of studies in subsequent courses in the statistical and quantitative area; they also constitute a fundamental tool for understanding the statistical analyses introduced in other disciplines of the Degree Programme.

AIMS AND CONTENT

LEARNING OUTCOMES

The main aim of the course is to provide students with the fundamental tools of descriptive and inferential statistical analysis. The first part - Elements of descriptive statistics - relates to the fundamental concepts of univariate and bivariate descriptive statistics and is essential for any subsequent study. The second part - Introduction to probability theory - is designed to present the basic ideas needed for the study of statistical inference. The third part - Introduction to statistical inference - addresses the fundamental issues of sampling and inference, with particular regard to the theory of estimation and hypothesis testing.

AIMS AND LEARNING OUTCOMES

The learning objectives that will be evaluated for the purpose of passing the final exam are summarized in the following scheme:

Knowledge and understanding: Knowledge of the main tools for the synthesis and presentation of data, through the acquisition of the main techniques of descriptive statistics; knowledge of probabilistic techniques for the analysis of simple random phenomena; acquisition of basic statistical inference tools for estimation, hypothesis testing and regression analysis problems.

Ability to apply knowledge and understanding: Ability to use the appropriate techniques based on the type of data under analysis; be able to carry out basic descriptive analyzes for univariate and bivariate phenomena using the main summary indices; be able to carry out simple computations in situations of uncertainty; know how to apply the main statistical inference techniques; know how to carry out dependence/independence and regression analyses, also in the inferential context; know how to read statistical analyses carried out with the methodologies presented in the course.

Making judgements: Be able to understand and comment on the results obtained from statistical analyses in practical examples based on the context of the application, thus being able to use the results in decision-making processes.

Communication skills: Acquire the basics of technical statistical language to communicate clearly and without ambiguity with both statisticians and non-statisticians.

Learning skills: Be able to correctly read the results of statistical analyses, also in contexts of greater complexity than those presented in the course.

PREREQUISITES

The course requires knowledge of the basic skills of a course in General Mathematics for Business and/or Economics. 

TEACHING METHODS

Classroom lessons and exercises, both traditional and via the AulaWeb platform. Since the training objectives concern both theoretical and applicative skills, the lessons focused on methodological aspects of statistics will be alternated with exercises in which numerical problems and examples of simple analyses on real data are addressed.

SYLLABUS/CONTENT

Part I: Descriptive statistics

1. Introduction to statistics. Descriptive and inferential statistics. Populations and samples.
2. Distributions, frequencies, and cumulative frequencies. Graphs to describe categorical variables, time series, and quantitative variables. Graphs and tables to describe relationships between variables.
3. Location measures: mean, median, mode, percentiles.
4. Variability measures. Box-plot. Measures of  concentration.
5. Measures of relationships between variables.

Part II: Probability

1. Random experiments, outcomes, events.
2. The probability function and its axioms. Rules of probability.
3. Conditional probability and independence. Bivariate probabilities.
4. Bayes’ theorem.
5. Discrete random variables and their properties.
6. Bernoulli, Binomial, Poisson distributions.
7. Continuous random variables and their properties.
8. Uniform and normal distributions.
9. Joint distributions.

Part III: Inference

1. Sampling and sampling distributions. 
2. Distribution of the sample mean. The central limit theorem. Distribution of the sample proportion.
3. Point estimation. Estimators and their properties.
4. Confidence intervals. Confidence intervals for the mean and for the proportions.
5. Confidence interval for a proportion
6. Theory of statistical hypothesis testing. Test for a mean, test for a proportion.
7. Comparison of two means.

Part IV: Relationships between variables

1. Correlations and linear regression. The simple linear regression model. Least squares technique least squares coefficient estimators. The explanatory power of a linear regression equation. Inference on the coefficients.
2. Statistical independence and chi-square test.

RECOMMENDED READING/BIBLIOGRAPHY

Newbold, Carlson, Thorne, Statistica. Nona edizione. Pearson (2021). Foreign students can refer to the original version of this book. For a topic not covered by the textbook, documentation will be provided in Aulaweb by the teacher.

TEACHERS AND EXAM BOARD

Exam Board

MARTA NAI RUSCONE (President)

DANIELE DE MARTINI

FABIO RAPALLO

LESSONS

LESSONS START

Classes will start in the first week of the second semester according to the calendar of the Department of Economics. 

Class schedule

STATISTICS 1 C

EXAMS

EXAM DESCRIPTION

The examination consists of a written test which includes: 

1) multiple-choice questions of a theoretical nature. 

2) theoretical questions with open answers 

3) exercises  

The examination regulations are published on the course's Aulaweb page. 

As a result of the COVID 19 pandemic, the examination procedures may change in relation to the University regulations.  

ASSESSMENT METHODS

The questions and exercises in the written exam are chosen to cover, as far as possible, all the topics of the program. The theoretical questions are used to assess the student's level of understanding, while the exercises are used to measure the ability to apply the acquired knowledge. The details on the exam preparation and the required level of detail for all the topics will be illustrated during the lectures. 

Exam schedule

FURTHER INFORMATION

Additional information for non-attending students 

For non-attending students, no program changes or assessment procedures are applied.