Ateneo - UPO

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

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

The course aims to introduce some basic techniques of univariate and bivariate data analysis and some elements of probability and inferential statistics. The learning process is structured on three levels:
1. Definition of concepts, using examples and applications;
2. Proficiency in technical and formal language;
3. Development of the ability to process the data autonomously, to comment on the results obtained and to communicate them.

Basic elements of mathematics and calculus.

Teaching is delivered through lectures that present and discuss basic concepts, definitions, the steps leading to formalization, and initial application exercises. Lectures are complemented by series of in-class exercises aimed at applying the concepts introduced, selecting the most appropriate methods, and critically analyzing the results. Supplementary classroom activities (statistics labs) and individual online activities are planned on the DIR platform. The teaching and interactive components are integrated into the curriculum, accounting for approximately three-quarters and one-quarter of the total, respectively.

The course page on DIR offers online tests and interactive exercises that allow students to self-assess their level of preparation.

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 assessment is based on a written exam and an oral exam.
The written exam includes:
- theoretical questions to test knowledge of concepts and mastery of formal language;
- numerical exercises to test the student's skills in using computational algorithms;
- structured problems based on data comprehension and commentary on results, designed to assess autonomy in statistical analysis.

The written exam alone can yield a maximum score of 26/30.

The oral exam can be purely confirmatory (in which case it verifies the level achieved in the written exam) or supplementary/improving (in which case it verifies the student's command of language and the level of depth achieved in theoretical and formal aspects).
Registration for the exam is mandatory, as required, and within the prescribed deadlines.

Part I – Population Statistics

General concepts: collective, characteristics and modalities, measurement scales. Statistical variable (s.v.). Quantitative variances: real data and data in classes. Distribution function (cdf) and its characterization. Density function. Stick plots and histograms. Cauchy mean values. Central value and mode. Definition and calculation of quantiles. Box plots. Transferability and the arithmetic mean. Linearity properties, zero deviations, and least squares. Variability and its measurement. Ranges of variation and mean deviations. Variance, properties, and relativization. Shape indices. Qualitative variances: distributions, graphical representations, heterogeneity, Gini index. Double variance: joint, marginal, and conditional distributions. Definition of independence. Chi-square index and Cramer's V. Means and conditional variances. Mean and total variance theorems. Regression function and its graph. Correlation and Eta squared. Regression model and error properties. Covariance and its properties, linear correlation and rho squared index. Linear regression function and parameter calculation. Use of linear interpolants and the OLS method. Residual analysis and goodness of fit: determination ratio. Use of dummies.

Part II – Probability and Inference

Random experiment, events, incompatibilities, sigma algebra. Kolmogorov's definition of probability. Calculating a probability: classical and frequentist approaches. Conditional probabilities, stochastic independence, Bayes' formula, and composite and total probability theorems. Random variables (ARs). CDF, density function, quantiles. Calculating moments for discrete and continuous ARs. Some models: Uniform, Bernoulli, Binomial, Poisson, Rectangular, Exponential. ARs Normal: Standard normal, linear transformations and standardization, calculus of moments. Inference: parameters, i.i.d. samples, statistics, and estimators. Consistency, Chebichev's inequality, central limit theorem. Plug-in-based point estimates. Empirical mean: correctness, consistency, and limit law. Empirical variance: mean and corrected version, limit law. Confidence intervals using a.v. pivot. Introduction to hypothesis testing (mean, proportion). Null and alternative hypotheses. P-value.

Students must know and be able to use basic univariate and bivariate statistical tools: descriptive statistics, dependence measures (on average), linear correlation measures, regression models, and linear regression models. Students must know and be able to use probability and inference tools: random experiments, special distributions (Bernoulli, binomial, uniform, negative exponential, Gaussian, etc.), point estimators (unbiased, efficient, consistent), confidence intervals, and hypothesis testing. Students must be able to apply these tools to small data examples and interpret the results.

A fragmented or substantively flawed knowledge, the inability to correctly set up and solve exercises/problems, and inadequate scientific language will result in a failing grade.

Essential and predominantly descriptive knowledge, with application of concepts demonstrated through the solution of basic exercises; the solution of simple problems, albeit with some uncertainty, but with comprehensible presentation, will guarantee a passing grade.

A thorough mastery of the content combined with a high level of autonomy in problem solving and problem-solving; effective analysis and synthesis with pertinent connections and rigorous presentation allow for excellent grades.