# 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

Lectures and practical applications in the R language.

## Required Prerequisites

Basics of algebra, geometry, calculus and probability.

## Attendance of Lessons

Face to face teaching.

## 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

G. Cicchitelli, P. D'Urso, M. Minozzo, Statistics. Principles and Metodhs, Pearson, 2021

AuthorTitlePublisherYearISBN
G. Cicchitelli, P. D'Urso, M. Minozzo Statistica. Principi e Metodi.Pearson2017
G. Cicchitelli, P. D'Urso, M. MinozzoStatistics. Principles and MetodhsPearson20229788891911032

## Course Planning

SubjectsText References
1Basic concepts. Measurement scales and types of variables.Suggested textbook, chap. 1.
2Frequency distributions. Graphical representation of data.Suggested textbook, chapp. 2,3.
3Central tendency: arithmetic mean, geometric  mean, harmonic mean. Median, quartiles and quantiles. Mode. Box-plot.Suggested textbook, chap. 4.
4Variability. Variance, standard deviation. Range. Relative measures of variability. Shape of frequency distribution.Suggested textbook, chapp. 5,6.
5Contingency tables. Marginal and conditional frequency distributions. Statistical association between pairs of variables. The chi-square index.Suggested textbook, chap. 9.
6Covariance and correlation. Mean and variance of a linear combination of statistical variables.Suggested textbook, chap. 11 and appendix B.
7Basics of probability. Conditional probability. Independent events. Bayes' rule.Lecture notes.
8Random variables. Density functions. Distribution functions. Mathematical expectation and variance.Lecture notes.
9Probabilistic models. Discrete uniform distribution, Bernoulli distribution, Binomial distribution, Poisson distribution, Hypergeometric distribution. Gaussian distribution and its properties.Lecture notes.
10Asymptotic results: De Moivre-Laplace theorem, Central limit theorem.Lecture notes.
11Sampling distributions of statistics. Sampling from Gaussian distributions. Chi-square distribution, t-distribution.Lecture notes.
12Point estimation and properties of estimators. Confidence intervals. Asymptotic results.Lecture notes. Suggested textbook, chapp. 18-19.
13Hypothesis testing. Comparing two populations. p-valueLecture notes. Suggested textbook, chapp. 20-22.
14Simple 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

Statistical analysis of data  (in R) and oral exam.

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.

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

The exams will focus on the program of the course and related exercises discussed in the room.