# STATISTICAL LABORATORY

**Academic Year 2020/2021**- 1° Year

**Teaching Staff:**

**Antonino Furnari**

**Credit Value:**3

**Laboratories:**36 hours

**Term / Semester:**1°

## Learning Objectives

**AIMS AND SCOPE**

The aim of the course is introduce the knowledge of the R language for statistical data analysis with special focus on descriptive statistics, probability distributions and statistical inference.

**LEARNING OBJECTIVES**

**Knowledge and understanding (Conoscenza e capacità di comprensione).**The students will learn the basic concepts behind the R language for statistical data analysis with special focus on descriptive statistics, probability distributions and statistical inference.**Applying knowledge and understanding (Capacità di applicare conoscenza e comprensione).**The students will be able to utilize the R language for:*i*) providing basic statistical analyses of data;*ii*) simulating data according to given probability distributions;*iii*) applying main methods of statistical inference.**Making judgements (Autonomia di giudizio).**The students will learn to indepedently analyse data to extract knowledge from it through statistical analyses in R.**Communication skills (Abilità comunicative).**The students will acquire the necessary communication skills and the appropriate use of technical language to present the results from the statistical analyses, based on the use of the statistical software R.**Learning skills (Capacità di apprendimento).**The students will learn to use the statistical software R for basic data analysis and modeling. They will also acquire the competences needed to learn new data analysis and presentation techniques through the statistical software R.

## Course Structure

Lectures and practical activities and data analysis in R. Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

## Required Prerequisites

Basics of linear algebra and statistics.

## Attendance of Lessons

Mandatory.

## Detailed Course Content

**Use of the statistical software in R regarding:**

**Descriptive Statistics**. Simple Statistical Distributions. Data tables. Frequency distributions. Main summary statistics: arithmetic mean, geometric mean, harmonic mean. Median and percentiles. Variance, standard deviation, relative variation. Graphical representations. Multiple Statistical Distributions. Contingency Tables. Joint distributions, marginal and conditional distributions. Covariance and correlation.

**Probability. **Random number generation and data modeling according to different probability distributions: uniform, binomial, Poisson, Gaussian.

**Statistical inference. **Sample distributions: Student-t, chi-square. Confidence estimation. Confidence level. Confidence bounds for means, variances, proportions. Hypothesis testing. Null hypotheses and alternative hypotheses. P-values. Statistical tests for means, variances, proportions, comparison of means, comparison of proportions.

**Statistical models. **The simple regression model. Goodness of fit. Residual analysis. Inference on the parameters of a linear regression model.

**R programming. **Basic commands. Data types. Vectors. Matrices. Lists. Dataframes. Loading and saving data. Charts. Conditional statements and loops. Writing R functions.

## Textbook Information

- James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning. New York: springer.
- Garrett Grolemund, Hadley Wickham. R for Data Science (2016). O'Reilly Media, Inc.
- Joseph Adler. R in a nutshell 2nd edition (2012).O'Reilly Media, Inc.
- Documents available on the web page of The R Project for Statistical Computing: https://www.r-project.org and other resources available on the web.

## Course Planning

Subjects | Text References | |
---|---|---|

1 | Introduction to R, Basic Commands in R, Indexing Data, Matrices and Lists, Loading Data; | Sections 2.3 and 2.4 of [1] |

2 | Charts and Data Visualization | Lecture notes |

3 | Mean, Median, Variance, standard deviation, quantiles, percentiles, interquartile distance, boxplot, outlier detection | Lecture notes |

4 | Bivariate analysis, statistical inference, contingency table, joint probability, marginal probability, chi-squared test, t-test, linear regression. | Section 3.6 of [1], lecture notes |

## Learning Assessment

### Learning Assessment Procedures

Practical activity and data analyis with R. Learning assessment may also be carried out on line, should the conditions require it.

### Examples of frequently asked questions and / or exercises

- Perform a statistical analysis of a dataset using the statistical software R;
- Fit a linear regression and evaluate the signficance of the regression coefficients;
- Compute descriptive statistics of a dataset and produce visualizations of the data.