# STATISTICS

**Academic Year 2023/2024**- Teacher:

**Salvatore INGRASSIA**

## Expected Learning Outcomes

The course will introduce the main conceptual elements of the statistical analysis of data, statistical model building and the corresponding interpretation of the results. Application to real case studies will be carried out using the R software.

## Course Structure

## Required Prerequisites

Basics of algebra, geometry, calculus and probability.

## Attendance of Lessons

## Detailed Course Content

Simple Statistical Distribution. Data tables. Numerical and categorical data. Frequency distributions. Frequency density. Statistical ratios and index numbers. Arithmetic mean, geometric mean, harmonic mean. Median and percentiles. Variation. Variance, standard deviation, Relative variation: variation coefficient. Box-plot. Asymmetry.

Multiple Statistical Distributions. Contingency Tables. Joint distributions, marginal and conditional distributions. Means and variance of marginal and conditional distributions. Association between statistical variables. Covariance and correlation.

Basics of Probability. Rules for probability. Conditional events. Conditional probability. Independent events. Random variables. Association between random variables. Probability models for count data: uniform, binomial, Poisson. Gaussian probability model. Skewness and Kurtosis.

Statistical inference. Sample distributions: Student-t, chi-square, F. Point estimation. Point estimate. Properties of estimators. Methods of estimation: method of least squares, maximum likelihood estimation.

Confidence estimation. Confidence level. Confidence bounds for means, variances, proportions.

Hypothesis testing. Null hypotheses and alternative hypotheses. Types of errors in testing hypothesis. Test rules. Significance level. Power of a test. Statistical tests for means, variances, proportions, comparison of means, comparison of proportions. Test for independence and homogeneity.

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

## Textbook Information

*Statistics. Principles and Metodhs*, Pearson, 2021

Author | Title | Publisher | Year | ISBN |
---|---|---|---|---|

G. Cicchitelli, P. D'Urso, M. Minozzo | Statistica. Principi e Metodi. | Pearson | 2017 | |

G. Cicchitelli, P. D'Urso, M. Minozzo | Statistics. Principles and Metodhs | Pearson | 2022 | 9788891911032 |

## Course Planning

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

1 | Basic concepts. Measurement scales and types of variables. | Suggested textbook, chap. 1. |

2 | Frequency distributions. Graphical representation of data. | Suggested textbook, chapp. 2,3. |

3 | Central tendency: arithmetic mean, geometric mean, harmonic mean. Median, quartiles and quantiles. Mode. Box-plot. | Suggested textbook, chap. 4. |

4 | Variability. Variance, standard deviation. Range. Relative measures of variability. Shape of frequency distribution. | Suggested textbook, chapp. 5,6. |

5 | Contingency tables. Marginal and conditional frequency distributions. Statistical association between pairs of variables. The chi-square index. | Suggested textbook, chap. 9. |

6 | Covariance and correlation. Mean and variance of a linear combination of statistical variables. | Suggested textbook, chap. 11 and appendix B. |

7 | Basics of probability. Conditional probability. Independent events. Bayes' rule. | Lecture notes. |

8 | Random variables. Density functions. Distribution functions. Mathematical expectation and variance. | Lecture notes. |

9 | Probabilistic models. Discrete uniform distribution, Bernoulli distribution, Binomial distribution, Poisson distribution, Hypergeometric distribution. Gaussian distribution and its properties. | Lecture notes. |

10 | Asymptotic results: De Moivre-Laplace theorem, Central limit theorem. | Lecture notes. |

11 | Sampling distributions of statistics. Sampling from Gaussian distributions. Chi-square distribution, t-distribution. | Lecture notes. |

12 | Point estimation and properties of estimators. Confidence intervals. Asymptotic results. | Lecture notes. Suggested textbook, chapp. 18-19. |

13 | Hypothesis testing. Comparing two populations. p-value | Lecture notes. Suggested textbook, chapp. 20-22. |

14 | Simple linear regression. Least square estimation. Goodness of fit of the regression line. Inference on the simple linear regression model. | Lecture notes. Suggested textbook, chapp. 10,23. |

## Learning Assessment

### Learning Assessment Procedures

To guarantee equal opportunities and in compliance with the laws in force, interested students can ask for a personal interview in order to plan any compensatory and / or compensatory measures, based on the didactic objectives and specific needs. It is also possible to contact the referent teacher CInAP (Center for Active and Participated Integration - Services for Disabilities and / or SLD) of the Department, prof. Filippo Stanco.