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 conducted through lectures and exercises in the classroom. Supplementary classroom activities are planned.

On the web page of the course are available online tests and interactive exercises that allow the student to autonomously evaluate the level of preparation achieved.

The evaluation is based on a compulsory written exam and an oral exam.
The written exam includes:
- theoretical questions to verify the knowledge level and the proficiency in the formal language;
- numerical exercises to verify the abilities in using the numerical tools,
- structured problems to verify the ability in providing coherent comments on the results and communicating them with a proper statistical language.
The oral exam is aimed at verifying the proficiency of the formal language and the knowledge of the theoretical and formal aspects.
Further details about the exam are available on the course web page.
Please note that after the third attempt to take the exam in a calendar year, enrollment is automatically blocked until the following calendar year.

Part I – Descriptive Statistics
The population and the statistical variables. Frequency distributions and graphical representations. Analysis of quantitative variables: the cumulative distribution functions and the quantiles. Measures of central tendency. Chisini’s average. Measures of absolute and relative variability. Measures of shape. Analysis of qualitative variables: the heterogeneity.
Bivariate data: joint, marginal, and conditional distributions. Statistical dependence and the Chi square index. Correlation and variance decomposition. The 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
Random experiments and the probability spaces. Definition of a probability measure on finite sample spaces. Conditional probability and independence. Bayes rule. Random variables and probability distributions. Moments of a random variable. Some useful probability distributions (discrete: Uniform, Bernoulli, Binomial, Geometric, Poisson; continuous: Rectangular, Exponential, Normal). The inferential paradigm: parameters, statistics, and estimators. Asymptotic statistics: consistency, the Central Limit Theorem, and the plug-in principle. Point estimates and asymptotic confidence intervals for the mean, proportion, variance, and regression coefficient. Introduction to hypothesis testing for the mean, proportion, and regression coefficient. P-value: calculation and interpretation.

Students should know and be able to use basic univariate and bivariate statistical tools: descriptive statistics, measures of dependence, regression, and linear regression models. Students should know and be able to use probability and inference tools: random experiments, notable distributions (bernoulli, binomial, uniform, negative exponential, Gaussian, etc.), point estimators, confidence intervals, hypothesis tests. Students should be able to apply these tools to small data examples and know how to interpret the results.