93064 - STATISTICS

Conoscenze e abilità da conseguire

The course aims at providing students with the main concepts of Statistical Theory and tools of Data Analysis. These include - exploratory techniques for describing and summarizing data by graphical devices and summary measures, in both univariate and bivariate problem; - inferential methods of point and interval estimation and hypothesis testing in the context of random sampling from Gaussian and Binomial populations. To be able to understand the probabilistic aspects involved in statistical inference, students will also acquire knowledge of basic results of Probability Theory. In addition, during lab sessions students will be introduced to the use of the statistical software R for the application of some of the methods covered in the conventional lectures.

Contenuti

The course program is organized in four parts as described below.

1. Exploratory data analyis
Graphical tools for data analysis and presentation. Frequency tables. Frequency distributions. Summary measures of position and dispersion. Two-way contingency tables. Joint, marginal and conditional distributions. Independence and Association. Covariance and correlation.  

2. Probability Theory
Approaches to Probability Theory. Axiomatic approach to probability. Sets and Events. Conditional probability. Independent events. Total probability theorem. Random variables. Mean, quantiles and variance. Discrete and Continuous Uniform distribution. Binomial distribution. Gaussian distribution. Independent variables. Sums of random variables. Central limit theorem and related corollaries. The Student's t distribution.

3. Inferential Statistics
Random sampling. Parametric statistical models. Sampling distributions. Point estimation. Bias, mean squared error and consistency. Confidence intervals for the mean of a Gaussian population. Approximate confidence interval for a probability. Approximate confidence interval for the mean of non-Gaussian population. Confidence interval for the difference between the means of two Gaussian populations. Hypothesis testing on the mean of a Gaussian population. The p-value. Large-sample test on a probability. Large-sample test on the mean of non-Gaussian population Test on the difference between the means of two Gaussian populations. 

 

4. Laboratory of Computer Programming

Some lectures will aim at providing a basic knowledge of Programming. No computer pre-requisites are required. A description of the R language is provided, including variables, expressions and statements; flow controls; functions, with particular attention to functions for importing data files and performing basic data analyses.

Testi/Bibliografia

For topics 1-3 of the "Course contents" section the recommended readings are:

• Cicchitelli, G., D'Urso, P., Minozzo, M. (2021). Statistics: Principles and Methods, Pearson.
  

• Lecture notes that will be made available online at the beginning of the course on the platform Virtuale

• For further reading: Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm. J.D., Cochran, J.J., Freeman, J., Shoesmith, E. (2020), Statistics for Business and Economics, Cengage Learning EMEA, Andover, UK. 5th Edition.

For topic 4 of the "Course contents" section the recommended readings are:

• E-Book: "R Programming", tutorialspoint. Website: https://www.tutorialspoint.com/r/index.htm

• E-Book: "Get started in R: a complete beginners workbook", R Statistics.Net. Website: http://rstatistics.net/r-tutorial-exercise-for-beginners/

Metodi didattici

For topics 1-3 of the "Course contents" section: Traditional classroom lectures

For topic 4 of the "Course contents" section: Classroom lessons and practice using the student's notebook. It is therefore important that the students bring their personal notebooks during the lab lessons. In the absence of a personal notebook, the student can work with a partner.

Modalità di verifica e valutazione dell'apprendimento

Format

For both Module 1+3 and Module 2 the assessment is via a written examination.The Module 1+3 full exam will comprise exercises and theoretical questions on all the topics covered in class. Examples of past exam papers will be made available at the beginning of the Module. The Module 2 exam is a pass/fail written test. The Module 2 test can be taken on any of the available dates regardless on when the Module 1+3 exam is taken. The Module 1+3 mark will be registered only after passing the Module 2 test. 

Students taking the Module 1+3 first midterm exam can sit the Module 1+3  second midterm exam only if they obtained a sufficient mark. The Module 1+3 second midterm exam can be taken only once either right at the end of the Module or on the following call. If the student fails the Module 1+3 second midterm exam, he/she will have to resit the Module 1+3 full exam and will lose the mark obtained in the Module 1+3 first midterm exam. 

In some cases, after the Module 1+3 full or second midterm exam, the lecturer may require an oral test as a further tool of assessment of the student's preparation.

 

 

Grade rejection

Students can reject the grade obtained at the Module 1+3 exam once. To this end, he/she must email a request to the instructor within the date that will be specified after the notification of the exam results.

Rejection is intended with respect to the whole Module 1+3  exam.  If the grade is rejected, the student must retake the full Module 1+3 exam, even if the second midterm exam was taken. The only grade that can be rejected without any communication from the student is the one of the Module 1+3 first midterm exam: in this case the student can either take the Module 1+3 second midterm exam  or sit the Module 1+3 full exam (thus losing the grade obtained in the first midterm exam).

Strumenti a supporto della didattica

For topics 1-3 of the "Course contents" section: Teaching material (lecture notes, exercises, past exam papers, etc) and further information about the course will be available at the beginning of the course on the platform Virtuale.

For topic 4 of the "Course contents" section:

• under the "Teaching" section of Filippo Piccinini's personal website all the slides used during the lessons are available for download as well as software tools for practice.

• The statistical software R can be freely downloaded from the web page https://www.r-project.org/

• The software RStudio can be used as an interface for R and can be freely downloaded from the site https://rstudio.com/products/rstudio/

Link ad altre eventuali informazioni

https://virtuale.unibo.it/

Orario di ricevimento

Consulta il sito web di Paola Bortot

Consulta il sito web di Filippo Piccinini