Ateneo - UPO

Presentation of statistical methodology for the analysis of one-dimensional and two-dimensional data. Introduction to probability theory and to sample statistics with special attention to inference for large samples.

Lecture notes and exercises are available in the web page of the course at the URL: https://dir.uniupo.it

The goal of the course is to introduce some basic techniques of univariate and bivariate data analysis and some elements of inferential statistics. The learning process focuses on:
1. definition of concepts by using examples and applications;
2. mastery of technical and formal language;
3. development of data analysis skills and of the ability to comment on and communicate the results.

Basic elements of mathematics and calculus.

Lectures and exercises. Some extra-activities are planned.

Some on-line supports are available on the web page of the course.

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents-physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The evaluation is based on a compulsory written exam and an oral exam.
The written exam includes:
- theoretical questions whose scope is to verify the knowledge level,
- exercises to verify the abilities in applying the introduced numerical tools,
- structured problems to test abilities in providing coherent comments on the results and communicating them with a proper statistical language.
The oral exam measures the knowledge on the theoretical and formal aspects.
Partial exams will be planned during the course.
Please note that after the third attempt to sit the exam in the course of a calendar year, the registration block is automatically applied.

Part I – Statistics for Populations

The population and the variables. Frequency distributions and graphics. Analysis of quantitative variables: the cumulative distribution functions and the quantiles. Measures of the central tendency. Chisini’s average. Measures of absolute and relative variability. Measures of shape. Analysis of qualitative variables: the heterogeneity.
The joint distributions, the marginal and the conditional distributions. The study of the dependence and the Chi square index. Total mean and variance theorems. Correlation and eta square index. Linear correlation and covariance. The regression model. The ordinary least square (OLS) method for the linear model. Analysis of residuals and goodness of fit.

Part II – Elements of Probability and Inference

The random experiments and the probability space. Probability measure on finite sample spaces. Conditional probability and independence. Bayes rule. The random variables and probability distributions. Moments. Some useful probability distributions: Uniform, Bernoulli, Binomial, Geometric, Poisson; Rectangular, Exponential). Normal r.v.: standard normal, linear transformations, computation of moments. The inferential paradigm. Parameters, statistics and estimators. Asymptotic statistics: consistency, the Central Limit Theorem and the plug-in principle. The point estimation and the asymptotic confidence intervals for mean, proportion, variance and regression coefficient. Introducing hypothesis testing (for a mean, a proportion and a regression coefficient). P-value: calculation and interpretation.

Students will need to know and be able to use uni- and bi-variate statistical tools: descriptive statistics, measures of dependence (in mean), measure of linear correlation, regression model and linear regression model. Students will need to know and be able to use probability and inference tools: random experiments, notable distributions (bernoulli, binomial, uniform, negative exponential, Gaussian, etc.), point estimators (correct, efficient, consistent), confidence intervals, hypothesis tests. Students will be able to apply these tools to small examples of data and learn to interpret the results.