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.

The course is taught through lectures in which the following are presented and discussed: basic concepts, definitions, the steps leading to formalization, and initial application exercises. The lectures are supplemented by a series of in-class exercises aimed at applying the concepts introduced, selecting the most appropriate methods, and critically interpreting the results. Supplementary in-class activities (statistics labs) and individual online activities to be completed on the DIR platform are included. The lecture-based and interactive components are integrated into the course of study, accounting for approximately 3/4 and 1/4 of the total course load, respectively.

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/services-
students-physical-or-learning-disabilities

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.

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. 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 and proportion, variance. Introducing hypothesis testing (for a mean and a proportion). 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.
Fragmentary knowledge or knowledge containing substantial errors, an inability to correctly formulate and solve exercises or problems, and inadequate scientific language will result in a failing grade.
Essential and primarily descriptive knowledge, with the application of concepts demonstrated through the solution of basic exercises; the ability to solve simple problems—even with some uncertainties—but with a comprehensible presentation, ensures a passing grade.
Complete mastery of the content, combined with a high degree of independence in formulating and solving problems; effective analysis and synthesis with relevant connections and a rigorous presentation allow for excellent grades.