# STATISTICS

## Learning outcomes of the course unit

To have a general view of the main concepts of descriptive and inferential statistics

## Prerequisites

Basic knowledge of mathematics

## Course contents summary

The course is divided into two parts. In the first part the tools of descriptive exploratory statistics are described. The second part of the course deals with inferential statistics and basic concepts linked to probability calculus. The final aim is to enable the student to become familiar with quantitative analysis of business and economic data, enabling him to perform basic statistical data analysis, and to correctly interpret the results of the different statistical indexes. In the second part we present the basic tools for understanding the procedures of sampling and inference. During the course, the focus will be on a reduced set of techniques, but widely used in practice. Of each technique the focus will be given to the rationale of its introduction.

## Course contents

The course is divided into two parts. In the first part the tools of descriptive exploratory statistics are described. The second part of the course deals with inferential statistics and the basic concepts linked to probability calculus. The final aim is to enable the student to become familiar with quantitative analysis of business and economic data, enabling him to perform basic statistic data analysis and to correctly interpret the results of the different statistical indexes. In the second part we present the basic tools for understanding the procedures of sampling and inference. During the course, the focus will be on a reduced set of techniques, widely used in practice. Of each technique the focus will be given to the rationale of its introduction.

Contents

Part I

Introductory Elements

• the collection of data and statistical sources

• the data matrix, graphical representations.

Synthesis of a phenomenon

• frequency distribution and cross tabulations

• the mean, median, mode (location indexes)

• the absolute and relative indices of variability, the concentration

• the form of distribution (asymmetry indexes)

Time series

• the index numbers

• the concatenation of series with different base, the average annual rate of change

• composite index numbers of prices

Relations between two characters

• the covariance and correlation coefficient

• the covariance matrix and the correlation matrix

• the regression line: the method of least squares, parameter interpretation, the evaluation of the goodness of fit;

• linear and non linear interpolation of a time series

Part II

Introduction to probability and sampling

- The concepts of probability

- Random variables: general aspects and applications

- Theorems of probability theory

- Sampling distributions of statistical indices

Estimation problems

- Point estimation of the mean and relative frequency

- Interval estimation of the mean in the case of large and small samples

- Interval estimation of the relative frequency in the case of large samples

Problems of hypothesis testing

- Introduction to statistical tests, significance level (P-value)

- Hypothesis testing on the mean in the case of large and small sample. Hypothesis testing on the relative frequency in the case of large samples

- Hypothesis testing on the equality of means for two universes in the case of large samples

The simple linear regression model

-Meaning of the model and relations with the regression line

- Problems of estimation and hypothesis testing for the parameters of the model

- Test of the goodness of fit of the model, the analysis of variance table.

## Recommended readings

M.A. Milioli, M. Riani S. Zani, Introduzione all’analisi dei dati statistici, (seconda edizione ampliata) Pitagora, Bologna, 2011

http://www.riani.it/MRZ

Cerioli, M.A. Milioli, Introduzione all’inferenza statistica senza (troppo) sforzo, 2a edizione, Uni.nova, Parma, 2004.

A. Cerioli, M. A. Milioli, M. Riani, "Esercizi di statistica", uni.nova, Parma, 2012.

http://www.riani.it/CMR

## Teaching methods

Knowledge acquisition: frontal lessons

Acquisition of the ability of applying what has been studied: written tests

Acquisition of judgment: during the course students will be encouraged to detect strengths and weaknesses of the methods and of the basic statistic indices.

Acquisition of learning skills: for each topic we will start from the illustration of the problems which have to be solved and we will analyze critically the adopted solutions.

Acquisition of technical language. While teaching, the meaning of the terms commonly used in statistics will be described.

## Assessment methods and criteria

The Assessment is via a written test, using the same questions for all the students. The exam has a maximum duration of 90 minutes. The test generally consists of 4 exercises. To each is given a score. The different exercises are in turn divided into subgroups. The first two exercises generally concern the topic of descriptive statistics. The last two, on the other hand, refer to inferential statistics. The questions deal with some important points of the theory and practice of statistics and are intended to assess the ability of understanding, independence of judgment and the ability to communicate with appropriate statistical language.

The broad articulation of the questions in the different topics should enable to assess both the learning capacity and the ability to apply the knowledge which has been studied.

## Other informations

Further information on the exam together with additional material to download can be found at the web page http://www.riani.it/stat/stat.htm