# STATISTICAL LABORATORY

**Academic Year 2019/2020**- 1° Year

## 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 objectives aim at introducing the knowledge of 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).**On completion. 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).**On completion, students will able to extract knowledge from data through statistical analyses in R.**Communication skills (Abilità comunicative).**On completion, students will be able how to present the results from the statistical analyses, based on the use of the statistical software R.**Learning skills (Capacità di apprendimento).**On completion, students will able how to utilize the statistical software R for basic data analysis and modeling.

## Course Structure

Lectures and practical activities and data analysis in R.

## 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.

## Textbook Information

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 | Lecture Notes |

2 | Graphs, Data Types and Structures, Conditional Statements and Loops, Graphs and Data Visualization | Lecture Notes |

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

4 | Functions in R, data filtering | Lecture Notes |

5 | Bivariate analysis, statistical inference, contingency table, joint probability, marginal probability, chi-squared test, t-test, linear regression. | Lecture Notes |

## Learning Assessment

### Learning Assessment Procedures

Practical activity and data analyis with R